Thermo-fluid Lab Jimma University Jit

JIMMA UNIVERSITYJimma Institute of Technology JITMechanical Engineering Department Thermo Fluid Lab Manual

Course Outline: Laboratory I (MEng 3107)Course offered to: year III, Sem-II, 2010-2011Course offered by:

TABLE OF CONTENTS

No. Contents PageI Preface| To the student iII Instruction for confection of report 1

I Laboratory I

1. Reynolds’s experiment 5

2. Evaluation of heat exchanger performance under parallel and counter flow

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3. Measurement of velocity profile and boundary layer growth over a flat plate

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4. Measurement of dispersion around turbulent jet 31

5. Flow Round a bend Duct (Characterization of energy losses in a bend)

41

6. Measurement of drag and lift of an aerofoil at different angles of attack

51

7. Comparison of losses in nozzle and diffuser type duct flows 58

8. Finding pressure distribution over an aerofoil at different velocity and angles

65

9. Assessments of the variance of lift and Drag on an aerofoil via flaps and slats

69

10. Verification of Bernoulli’s equation 75

11. Impact of a Jet 83

12 Measurements on Free and forced vortex flow 87

13 Validation of SFEE involving heat, mass and work transfer and work transfers

88

14 Bibliography 89

Manual for “Thermo-fluid Laboratory- MEng 3107”

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TO THE STUDENTS, With your laboratory data you will find the parameters or wanted functions. You will take care in the report of your results the analysis of the uncertainties. This will allow you to delimit the validity of your summations and suggestions. The final report is the entire product of your work in each practice. You will take care that it reflects the quality and the quantity of the realized work and that it shows the variety and wealth of your experiences associated to the development of the practice. When writing the final report you will put emphasis in the clarity, for which you should have in mind, which are the objectives of the practice and the achievements of the same one are. You will also stand out those aspects that you consider that could make original or different the realization of your practice with regard to what could be the usual thing. for example if you used a substance that you proposed, if you used some alternative method to measure some variable or if you developed some interesting explanation for some observed behavior that been able to governess to check that it was important to obtain improvements in your results, etc... This gives an idea of the creativity with which you have approached the task. You will have present to the potential readers of the report, so that when reading it they receive the wanted impression, this is that can appreciate the value of your work. For the time being this is important so that your evaluation is in agreement with the quality of the acquired experience and in the future this ability will mean a lot for your professional development. Another important facet is the realization of the teamwork. This is an important aspect in your vocational training. A very integrated team discusses each one of the activities, takes agreements on the way of carrying out them and it carries out them communicating and discussing the diverse experiences, so that the report is an integrated writing and not merely a bale of small sections without a conductive thread neither internal coherence. The teamwork is a professional activity that can be stimulant when there is a good relationship among the members of the team.

SECURITY There are safe-deposit norms that should be completed strictly to avoid accidents in the laboratory. This regulation is available for its consultation in the same laboratory and it is necessary that you are to the current of its content, reason why, if you have not read it or you don't remember it, it is convenient that you request it and understand before beginning your experimental work. By way of a reminder, it has been mentioned some of the most important points next. 1. The robe use in the laboratory is obligatory when are carried out experiments. To carry out some manipulations of chemical substances gloves, protective eyeglasses and masks they should also be used. For the laboratory sessions, it is advisable to dress simple clothes that protect most of the body and preferably of cotton, closed shoes, with thick soles and without heels or platforms. 2. Not introduce neither to consume or drinks in the laboratory. Not smoke. 3. Only operate an instrument or apparatus when you know how to make it, otherwise to request the instructor's help, of the assistant or of the technician of the laboratory, to acquire the necessary dexterity. 4. Once concluded the use of an apparatus or instrument, to follow the appropriate procedure to turn off it, to disconnect it, to keep it and to give it to the responsible for their custody. 5. When concluding a practice, to lift all the instruments, teams and used accessories, to verify that all the takings of water, gas, air or others in the working place are very closed and to leave clean and you dry the working tables and the floor of the laboratory.


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"It is never possible to introduce only quantities observables in a theory. It is the theory who decides what it should be observed." Albert Einstein, 1926.


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INSTRUCTIVE FOR THE ELABORATION OF REPORT

God willing and we could, when concluding a practice, to share these words of Rostand, however there are many aspects that sometimes prevent us to demonstrate with clarity the correspondence between the theory and the practice. When we notice remarkable likeness between the observed behavior and our theories, we acquire bigger certainty to manipulate the materials and to use our predictions like working tools, based on the knowledge acquired in the career. We are also able to determine which they are the factors that influence - and in what measure - in the differences and/or discrepancies among our theories, our laboratory operations and our observations. A bankrupt practice can be an excellent practice, if the students are able to identify and to evaluate the sources of the discrepancies. If it is feasible, a bankrupt practice will be repeated with the pertinent improvements.

Objective The final report of a practice has the objective of showing that students of the team has developed a coordinated group of activities starting from its theoretical knowledge of the topic of the practice that it has allowed them to design the experiment and to carry out the appropriate mensurations. That then has carried out the treatment and the analysis of their data to obtain results whose validity is able to define. Starting from this experience the students are able to discuss and to elaborate their summations and suggestions to improve the realization of the practice or they will be able to, alternating, to elaborate a critic based to demonstrate the disability of the theories or of the procedures continued in the realization of the practice, of being the case.

About of make of ReportThe report will contain the sections that are detailed below, all written in correct language and printed in typeface and uniform style that indicate an integrated work of team among the students that present it as product of its work. The report is an end product of the work carried out in the practice, for what includes most of the sections considered in the report that should incorporate the improvements suggested by the professor for the presentation of this report, more the relative sections to the realization of the experiment and the later treatment of the obtained information. The pages of the report will be numbered and they will follow the sequence of the following one:

Content 1. coverIt is the first page of the report. It will contain the complete identification: The University, the Career, and the Subject, the word "It Reports", the title of the practice, Experiment number, the names of the members of the team, the Professor's name and the contract date of the report.

The University, the Career, and the Subject, the word "It Reports” and Title should be written a top centerExperiment number: On left side page next to the date the serial number of experiment to be written

2. Summarize executive It is the second page of the report. In concise form it will be informed on the objective of the practice, the team and the main considerations of the model, those will be emphasized obtained results, this way how the limitations to their validity. The sections and sub-sections will be enumerated with the respective pages of their beginnings.


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3. Objectives It will be enunciated in brief, complete and numbered form the objectives of the realization of the practice, which clearly indicates the mean of the experiment. 4. Apparatus The main equipment will be described where it carried out the processes. This will include a drawing with the approximate dimensions and a description of processes apparatus that will be carried out in the system. And a list of apparatus used for the experiment should be written.5. Theoretical foundations and their application The purpose of this section is to develop the relationships that allow describing the processes that are carried out in the system. Starting from these relationships they will be considered the quantities or parameters of interest, requested in the results. This section consists of the following sub-sections:

Hypothesis The pertinent hypotheses that correspond to the simplified physical pattern will settle down. The hypothesis will be numbered and each a followed one for a specific justification enough. Mathematical Model It will be defined the systems where the principles and concepts will settle down. The variables and their meaning will be identified in a diagram of each system. It will be indicated that the complete development that takes from the principles to the working equations, where the models will be elaborated to detail, when it is pertinent.

In the body of the work the main components of the mathematical model will be included that are:

The equations that correspond to the thermodynamic numbered relationships. The solution corresponding to the group of relationships in game. The final expressions (working equations) to determine the estates or variables of

interest, objective of the practice. If it is required of a calibration of the equipment, the development that allows to

know the calibrated parameter starting from the expressions for an elected system with this end.

6. Procedure The purpose of this section is to determine the elements and necessary procedures for the development of the practice and it consists of the following sub-sections:

6.1 Variables and parameters Starting from the final expressions to determine the variables of interest, the quantities will be identified to be measured and the parameters that it is necessary to know and will intend the way to acquire the necessary information for each one of the previous elements, indicating the sources (you index) of the correlations or securities to use, as well as the necessary precision (for example, a longitude is required in cm, mm, 0.1 mm, µm, or another level of precision).

6.3 Sheet of data In a complete sheet a format will be elaborated to put all the necessary data for the realization of the practice. This leaf will contain in its header

The name of the practice The identification of the team that carries out it and the realization date It will also contain the following fields, indicating in each case the required units: The estimate parameters The measured parameters


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The variables measures, with their tabulation with regard to other variables (for example with regard to the temperature, for isothermic processes) of being necessary, as well as the repetitions of the readings

If a calibration is required, to elaborate the necessary previous points to carry out it and to repeat the pertinent ones for the unknown system (the problem)

To make a copy of this leaf of data, to be given the professor the day that is carried out the practice, with the experimental information and of the dear, complete parameters.

6.4 Equipment and materials It will be presented the outline of the installation, a list of the equipment and necessary instruments for the mensurations and another for the materials, indicating the sufficient quantities. 6.5 Development of the practice The practice will be descried in sequential and numbered form of the activities to develop. The aspects that are considered scoring important for the correct realization of the activities (for example, to take care that the level of a liquid doesn't surpass certain height that an instrument is dry or that a liquid is introduced sliding maintaining the inclined recipient, etc...).

7. Realization of the practice 7.1 mensurations It will incorporate the original sheet of data, with the complete information of the original

mensurations and of the parameters and/or securities of the literature. When the original sheet of data has suffered bigger modifications, when being carrying out the practice, an as amended leaf of data will be elaborated, with the all necessary information in it, making a self-critical comment about the changes required by the original sheet.7.2 observations A list of the observations of interest will be made, in the members' of the team opinion, carried out during the realization of the experiment, indicating in what its interest resides for the study matter.

8. Analysis of data and results In this section the treatment of the laboratory mensurations will be made to obtain the parameters or functions proposed as specific objectives of the practice as a result.

8.1 calculations The information of the sheet of data will spill in a sheet of Excel, and they will be carried out the pertinent operations, according to the developed expressions starting from the model, to find the results. 8.2 Statistical analysis and results In accordance with the scales of the instruments, only the significant figures will be included in the results. A statistical analysis will be made, taking into account, to report the final results with its uncertainties.8.3 Graphs If it is the case, they will be elaborated graphic for computer, to represent the behavior of the variables measures. They will be graphing the experimental securities with their uncertainties and the theoretical estimate of the model will be included. It will also incorporate other required graphs, in the students' opinion or requested specifically in the instructive of the corresponding practice. The graphs will be able to incorporate to the analysis sub-section and results, if is consider it convenient.8.4 Discussion and summations


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The obtained results will be compared with other acquaintances, either of the literature or of realized experiments previously for students of previous groups. With this information the members of the team will elaborate their conclusions, with a critical attitude and self-criticism.8.5 Suggestions and recommendations As a result of their experience, the members of the team will propose what you consider here that it can improve the realization of the experiment.

9. Reference bibliography The way to mention them will be for example: "... this model is solved in Felder and Rousseau (1991). " Corresponding to this mention, in the section of references will be included:

Felder, R.M. & Rousseau, R.W. Elementary Principles of the Chemical Processes Addison Wesley Iberoamericana (Second edition), 1991

That is to say that a referred book includes the following data in form ordinate: I nickname and the authors' initials (or of the editors) Title of the book (in italic letter) Editorial Edition. Year of publication of the consulted edition

If it is a collective book, where the chapters are written by diverse authors and the reference is in particular of a chapter, the following order will be continued:

I nickname and the authors' of the chapter initials Title of the chapter (in Roman letter) The word "In" Title of the book or manual (in italic letter) I nickname and initials of the editors of the book, followed by the abbreviation "(eds.) " Editorial Edition. Year of publication of the consulted edition

10. Appendixes Each Appendix will have a serial number and a name him to indicate its content and it will be mentioned in the text. The equations will take serial numeration, preceded by the letter A, for example, "(A.12) it is the equation #12 in the Appendixes.

In the Appendixes will be included, besides the aforementioned ones on the development of the pattern and the estates of the materials, those that are necessary for the complete documentation of the realized work, but whose inclusion in the main text would make it heavy or it would distract the attention of the sequence of ideas toward complementary discussions.


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Practical Lab # 1 Raynold’s experiment

INTRODUCTIONIn the practical engineering is very important to know the flow state, this is possible to determine the values of Reynolds’s number through such as we could by assigned to the transition from laminar or turbulent flow. The H65D has designed to study the march of the vertical flows, transitory and turbulent laminar and the visible phenomena of superior and inferior critical speed through a calibrated transparent tube, using an injection technique of the similar color to that of the group experimental original used by the Reynolds. It is demonstrated analytically that the physical meaning of the number of Reynolds is represented by the measure of the relationship of the inertia of the viscous forces that act on a fluid. It is extremely important to allow to those students of the first courses of mechanics of the fluids to visualize the difference among the flow to laminar and turbulent and to verify that this difference is reflected empirically in the terms of the number of measured Reynolds.

OBJECTIVE: To observe the laminar, transitional turbulent and velocity profile

APPARATUS:Equipment set up: the equipment to determine the flow regime in the stream of fluid is easy construction as showed in the figures.

Composition The main components of the group are: • Cylindrical Tank of feeding. • Needle of injection color. • Tank of feeding color. • Regulation Valve tints. • Flow indicator. • Spheres of calm.

Description The flow operation can be derived from any source (net hydria, bank H89.8D, etc.) by means of an appropriate one tube with device for the regulation of the flow, given with the apparatus, and it is introduced by means of a diffuser of ring in the cylindrical recipient of feeding. By means of a channel peculiar of constant jamb the variations of the speed of the flow are eliminated and they are determined condition uniforms of low speed in the load before the entrance of the vertical supporting tube. Then the fluid is introduced in the supporting tube, with screen background target to evidence the appearance of the color through a mouth with particular profile studied to accelerate it evenly without some spurious inertial effect. The used colored solution is a correspondent to the supporting section through a tube of very small diameter and the value of the color flow it is controlled by a valve in exit of the tank. By means of a special valve, placed to the base of the apparatus, the flow of the fluid is regulated in exit of the supporting section and their value is measured volumetric by means of a flow indicator.


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The group H65D is compatible with any elected means to vary the cinematic viscosity of the fluid, using different fluids, to exception of solvent and alcohols, or altering the temperature of the given fluid (the external circuit for this purpose is not understood in the supply).

Technical characteristics • Longitude of the supporting tube: 900 mm.; • internal Diameter of the supporting tube: 12 mm.; • Maximum flow of the supporting flow: 150 l/h (H2O at 15°C); • maximum Temperature recommended for the supporting fluid: 52°C.

The equipment is built totally in plastic and mounted material rigidly on a support of wide base endowed with leveling devices to assure the maximum stability and uprightness of the supporting tube. Experiences The group H65D has been designed to allow the reproduction of some experiments on the nature of the movement to laminate and turbulent.

In particular: • Experimental determination of the speed; • Study of flows laminar, turbulent and their transitory phenomena; • Search of the number of Reynolds.

6. Required services • Feeding of water from the net of low flow. 7. Pesos and Dimensions • Dimensions: 600 x 600 x h1950 mm. • Weight: 30 kg.

Fig. 1 - Synoptic General

A. Supports bell B. cylindrical Tank of feeding C. feeding Diffuser D. Flared E. Needle of injection color F. Tank of feeding color G. Covers

H. regulation Valve tints I. Screw of regulation needle J. Flow indicator K. Valve of regulation flow L. round Level M. Spheres of calm N. leveling Feet of support


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O. Bands of Hoffman

THEORYReynolds’s number (Re) is internationally recognized criterion denoting fluid flow , it is defined as:

Re = (v. d . )/

Where:Re: Reynolds’s numberv: velocity of fluid, m/s: Dynamic viscosity of the fluid, Pa . s: Density of the fluid, kg/m3

= /: Kinematics Viscosity, m2/s

Osborne Reynold’s determined that values of Re could be assigned to define from laminar, transitional or turbulent flow.

He was obtained that for Re values the flow is:Re <= 2100 the flow is laminar2100 < Re <4000 the flow is transitionalRe >=2100 the flow is turbulent

PROCEDUREFill the reservoir (2) with the dye connect the feed valve (9) to obtained maximum level, open the flow control valve (5) and open the valve inject or dye (7) , after observed the profile of the flow fluid in pipe glass (4) conduit, controlling the flow to obtain the parabolic profile of the flow of fluid observed and in this moment take the value the flow of fluid employed the reservoir (6) and the chronometer (12) taken the time necessary for completed the volume; after that repeat the procedure to obtain the variation in the profile an take the measuring and after continue increase de flow velocity and obtain the starting that transversal mixing will be completed and taken again the measurement of the flow. Known, the temperature of fluid, diameter of pipe line glass and the liquid water, to determine the density and viscosity.

To conclude, close the inlet of the dye (7) and close the feet valve of water to reservoir (9) and to finish close the valve (5) to control de flow.

OBSERVATIONTable 1. Data

NoObservation V, (m3) t, (s) d, (m) T, (0C)Visualization condition of profile Volume of water in

reservoir Time filled reservoir (6)

1 Parabolic profile2 Starting transversal mixing

color with water3 Mixing complete


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Taken technical data Internal diameter of pipe (d) , m Temperature of water (T) , 0C Viscosity of water (), Pa. s

CALCULATIONAccording to the experiment 1, 2 , and 3 will be calculating the flow (Q), as:

Q = V/t , m3//s ………………………………………….1.2

Therefore:v= Q/A , m/s ………………………………………………1.3A= (3.1416 . d2)/ 4 ………………………………………..1.4

Where; V: volume of water in reservoir (6), m3

t: filled time of reservoir, sA: cross sectional flow area of pipe line glass, m2

With temperature and fluid (water) , we can get the viscosity () in the literature.Therefore, with the equation 1.1, substituting the values, we obtain:

RESULTS AND DISCUSSION Table 1.2 Results

NoResult V, (m3) t, (s) d, (m) T, (0C) Q,(m3)A.(m2) v,(m/s)Re Observ.Visualization condition of profile

1 Parabolic profile2 Starting transversal mixing

color with water3 Mixing complete

QUESTION Do the results obtained agree with the statements under analysis? If not account for any

discrepancy. At what values of Reynold’s number have you observed the critical changes for each

state? What unique features differentiate the flow state you encountered?

CONCLUSION Taken in consideration the experiment carry out, results, analyze and question express yours conclusion about the practice.

REFERENCE That was explain in the topic of content of the report, the same way you should have the reference to the bibliography useful for this practice.


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Practical Lab # 2 Evaluation of heat exchanger performance under parallel and counter flow

Content:1. Calculated overall heat transfer coefficients2. Determination of temperature distributions along the length of the heat exchanger3. Calculate of mean value of the heat transfer rates in both the cases

INTRODUCTIONThe application of the principles of heat transfer to the design of equipment to accomplish a certain engineering objective is of extreme importance for in applying the principles to design.Eventually, economics plays a key role in the design and solutions of hest-exchanger design problem.A particular application will dictate the rules, which one must follow to obtain the best design commensurate with economic considerations, size, weight, etcFrom the standpoint of heat –exchanger design the plane wall is of infrequent application, a more important case for consideration would be that of double – pipe heat exchanger. In this application one fluid flow on the inside of the smaller tube whiles the other fluid flow in annular space between the two tubes.For all analyzed of design and evaluation of heat – exchanger is very important known of the overall heat-transfer coefficient and temperature profile in uniflow and counter flow equipment for that in this practical will be try about of this questions. As well as the log mean temperature difference (LMTD)

OBJECTIVE: 1. Calculated overall heat transfer coefficients2. Determination of temperature distributions along the length of the heat exchanger3. Calculate of mean value of the heat transfer rates in both the cases

Learning Objectives / Experiments- Determination of the temperature profile for parallel and counter flow operation- Determination of mean heat flow for parallel and counter flow operation- Determination of mean heat transfer coefficient

APPARATUS:Technical Description: Using the study unit, the characteristic properties of a heat exchanger can be demonstrated. The heat transfer takes place in a coaxial tubular heat exchanger. The hot water is fed through the inner tube. Using the system both parallel flow and counterflow operation with their different temperature profiles can be demonstrated. The non-linear temperature profile along a heat exchanger can be demonstrated by measuring temperatures at the inlet, outlet and halfway along the pipe. After the experiment the key parameters such as heat transfer rate, heat transfer coefficient and heat loss are determined. The closed hot water circuit includes a tank with electrical heater and a circulating pump. The hot water temperature is kept constant using a thermostat. The cold water is drawn from the water mains and is fed to a drain after use.

Precautions1. Before you start the experiment check that the water level in the heating tank is up the middle of

the sight glass provided for the purpose.2. If water level is no visible, fill the tank with water up to the middle of the sight glass.3. Then set the thermostat on the heater to the required temperature level.4. Change the valve settings as per your requirement of the flow, with the counter flow or parallel

flow.5. Give cold water supply connection after carefully identifying the could water inlet part


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6. Connect cold water inlet to the drain.7. Swich on the heater and start the experiment after about 20 minutes since heating may take this

time.8. Hondle the setup carefully.9. In case of doudt clarify your self with the instructor rather than speculating somethimg

Specification:

[1] Experimental mobile unit to investigate characteristic properties of heat transfer in a coaxial tubular heat exchanger

[2] Hot water to be fed through inner tube[3] Parallel and counterflow operation, Ball valves mounted in the cold water circuit to be used to choose the operating mode[4] Heat exchanger areas:

cold side 40212mm²hot side 30159mm²mean log. 34945mm²length: 1600mm

[5] Flow rate measurement with rotameters:cold water measuring range 0…96ltr/hhot water measuring range 0…96ltr/h

[6] 6 thermometers 0...100°C- hot water inlet - hot water outlet - cold water inlet - cold water outlet half way along the pipe:- at the inner pipe- at the outer pipe

[7] Sealed hot water circuit, insulated[9] Centrifugal submersible pump

3 stagesrating 70Wspeed 2400rpmmax. flow rate 3800ltr/h max. head 4m

[10] Tankcapacity 20ltrmade of stainless steelHeater 2kW

[-] Thermostat 0...85°C [-] Copper piping

Conductivity of Cu: 384W/mK[-] Cooling water to be supplied: min. 150ltr/h [-] To be supplied with emergency stop[-] 230VAC, 50Hz, 1 phase [-] l x w x h: 1385x550x1850mm, approx.110kg

THEORY

Following equation Q=Km . Am . Tln , Known Q= Q·

2 - Q·1

(1)

After that we can find the heat transfer coefficient, as:

Laboratory 1……..

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Heat exchangers are devices used for heat transfer between two media without direct contact or mixing of the two media. Heat passes from one medium to the other by convection of each medium and conduction through the partition that is separating the two media. There are different types of heat exchangers. The simplest type of heat exchanger consists of two concentric pipes of different diameters called the double pipe heat exchangers. The other type of heat exchanger, which is specifically designed to realize large heat transfer area per unit volume, is the compact heat exchanger. Some examples of heat exchanger are car radiator, oil coolers and cooling coils in refrigerator. In steady state the heat flux that is passing from the hot medium to the partition, through the partition and from partition to the cold medium is the same .In the analysis of heat exchanger, it is convenient to express the heat flux with the overall heat transfer coefficient Km ,logarithmic mean temperature difference LMTD, and mean area .

Qm = Um*Am*∆Tln (2)

Heat flux can also be calculated from the difference between the inlet and outlet heat flux. Q =m*Cp(T2-T1) (3)

m = ( . F * 10-3) / 3600 , kg/s (4)

where, - density of fluid, kg/m3

F- flow rate, L/ h

(-Qh ) = mhCph(T2h-T1h) , if no loss exist Qc & Qh are equal.

If the two fluxes found are not equal we use the mean heat flux i.e Q =((- Qh )+ Qc )/2 (5)

∆ Tm = (∆ Tmax –∆ Tmin)/ (Ln (Tmax / Tmin )) (6)

Km = Qm. Am. ∆ Tm (7)

PROCEDURE Check water level in the tank check and top up if necessary Switch on master switch Set desired hot water temperature thermostat (water tank) Switch on heater. Heating from an ambient temperature of 20C to 60C requires

approximately on 20 minutes. For uniflow: close ball clocks 2&4 and open 1&3 For counter flow: close ball clocks 1&3 and open 2&4

Switch on the pump (for hot water circulation) Set desired flow rates at control valves


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Take temperature reading at inlet, mid-section After regulation flow rate, wait until thermal equilibrium is attained. This is the case

when the temperatures fluctuate by less than 1 0C per minute. For this purpose, it is sufficient to observe the two outlet temperatures at thermometers T3 and T6 for uniflow current or T3 and T4 for counter-current. If thermal equilibrium is not achieved, the heat flux through the heat exchanger will no be correctly determined.

Once thermal stability has been attained, take temperature readings and enter them in the worksheet together with the set flow rates.

Attention mush be paid to the thermometer assignment indicated on the worksheet, as it is not the same for both uniflow and counter –current.

Note- the flow of hot water (F1) maintains its direction in both modes

OBSERVATIONTable 1 Data

Hot WaterCold Water Hot Water Cold Water

Tinlet Tmiddle Toutlet Tinlet Tmiddle Toutlet

F1, l/h F2, l/h t1, 0C t2, 0C t3, 0C t4, 0C t5, 0C t6, 0C Uniflow

100 25100 50100 75100 100

F1, l/h F2, l/h t1, 0C t2, 0C t3, 0C t6, 0C t5, 0C t4, 0CCounter-current

100 25100 50100 75100 100

F1, l/h F2, l/h t1, 0C t2, 0C t3, 0C T6, 0C t5, 0C T4, 0CCounter-current

50 2550 5050 7550 100

F1, l/h F2, l/h t1, 0C t2, 0C t3, 0C t4, 0C t5, 0C t6, 0C Uniflow50 2550 5050 7550 100

Taken technical data:Am = 0.0349 m2

CALCULATIONFor counter flow: Hot water fluid

Average temperature Tm = (Thi + Tho)/2


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With Tm for F1(n) (l/h) fine the specific Cph, (J/kg K) in the table of book or manual of equipment.

The heat loss flow rate of hot water in kg/s can be calculated for following relation:

mh = (F1(n) *10-3 * 1000 ) / 3600

Thus, with balance equation can be obtained the heat flow rate:

Qh = mh*Cph* ( Thi – Tho)

Where, mh – flow rate of water , kg/sF1(n) - Flow rate of hot water, L/hCph – heat specific of water at average of temperature, J/kg. KThi – Temperature of hot water inlet, K Tho – Temperature of hot water outlet, K

Cold water fluid Average temperature Tm = (Tci + Tco)/2 With Tm for F2(n) (L/h) fine the specific Cpc, (J/kg K) in the table of book or manual

of equipment. The flow rate of hot water in kg/s can be calculated for following relation:

mc = (F2(n).10-3 . 1000 ) / 3600

Thus, with balance equation can be obtained the cold flow rate:

Qc = mc.Cpc.( Tci – Tco)

Where, mc – flow rate of water, kg/sF1(n)- Flow rate of hot water, L/hCpc – heat specific of cold water at average of temperature, J/kg. KTci – Temperature of cold water inlet, K Tco – Temperature of cold water outlet, K

Mean heat flux:Qmean = (Qh + Qc) / 2The fluid temperature difference for counter flow at F2 (n) :

T1 = Thi – TcoT2 = Tho – Tci

Tm = (T1 - T2) / Ln (T2 / T1)

Q = U .A. Tm


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Uh = Qh / Am. TmUc = Qc / Am. Tm

Um = (Uh + Uc) / 2

For parallel flow: Hot water fluid

Average temperature Tm = (Thi +Tho)/2 With Tm for F1(n) (l/h) fine the specific Cph, (J/kg K) in the table of book or manual

of equipment. The heat loss flow rate of hot water in kg/s can be calculated for following relation:

mh = (F1(n) *10-3 * 1000 ) / 3600

Thus, with balance equation can be obtained the heat flow rate:

Qh = mh*Cph* ( Thi – Tho)

Where, mh – flow rate of water, kg/sF1(n) - Flow rate of hot water, L/hCph – heat specific of water at average of temperature, J/kg. KThi – Temperature of hot water inlet, K Tho – Temperature of hot water outlet, K

Cold water fluid Average temperature Tm = (Tci = Tco)/2 With Tm for F2(n) (L/h) fine the specific Cpc, (J/kg K) in the table of book or manual

of equipment. The flow rate of hot water in kg/s can be calculated for following relation:

mc = (F2(n) *10-3 * 1000 ) / 3600

Thus, with balance equation can be obtained the cold flow rate:

Qc = mc*Cpc* ( Tco – Tci)

Where, mc – flow rate of water, kg/sF1(n)- Flow rate of hot water, L/hCpc – heat specific of cold water at average of temperature, J/kg. KTci – Temperature of cold water inlet, K Tco – Temperature of cold water outlet, K

Mean heat flux:


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Qmean = (Qh + Qc) / 2

The fluid temperature difference for parallel flow at F2 (n) :

T1 = Thi – TciT2 = Tho – Tco

Tm = (T1 - T2) / Ln (T1 / T2)

Q = U .A. Tm

Uh = Qh / Am. TmUc = Qc / Am. Tm

Um = (Uh + Uc) / 2

The step of calculation should will be repeat for each flow rate F1(n) for n=1 to n = 4, to obtained the following results.

Result and discussion The result of experiment must be analyzed using the result shown in the table 2 for uniflow and counter – current flow experiment.

Table 2 Calculated and result

F1, l/h F2, l/h Tmax Tmin Tm Tmh h Cph Tmc Cpc c Uniflow

100 25100

50100

75100

100

F1, l/h F2, l/h Tmax Tmin Tm Tmh h Cph Tmc Cpc c

Counter-current

10025

10050

10075

100100

F1, l/h F2, l/h Tmax Tmin Tm Tmh h Cph Tmc Cpc c

Counter-current

50 2550

5050

7550

100

F1, l/h F2, l/h Tmax Tmin Tm Tmh h Cph Tmc Cpc c Uniflow50

2550

5050

7550

100


21

Table 3 Calculated and result (continuation)F1, l/h F2, l/h Am Q1, kJ/s Q2, kJ/s Qm Km,kJ/m2sK

10025

10050

10075

100100

F1, l/h F2, l/h Am Q1, kJ/s Q2, kJ/s Km,kJ/m2sK100

25100

50100

75100

100


2550

5050

7550

100


2550

5050

7550

100

Drawing the temperature measurements at different flow rates could be obtaining the temperature profile for uniflow current, as showed in following figure:

The inlet and outlet temperatures Tinlet and Toutlet, as well as the temperature Tm after half the heat-exchange distance, were plotted on the chart.

In the following figures showed the typical graphic for counter current temperature profile.

Counter flow

0

10

20

30

40

50

60

1 2 3Distance

Te

mp

era

ture

24.1 48.6 74.2 96 24.1 48.6 74.2 96

Counter flow

0

10

20

30

40

50

60

1 2 3Distance

Te

mp

era

ture

25 49.4 74.6 97.2 25 49.4 74.6 97.2


22

And with different values of the Um to different cold – water flow rate obtained the following figure which showed the relation of flow and heat coefficient transmission, for both in uniflow and counter flow:

Question What is heat transfer? How is defined the coefficient of heat transmission? How is defined the heat flux? How is defined the logarithmic mean of temperature?

Conclusion Taken in consideration the experiment carry out, results, analyze and question express yours conclusion about the practice.


C o e f f ic ie n t o f h e a t t r a n s fe r

00 . 20 . 40 . 60 . 8

11 . 21 . 41 . 61 . 8

0 5 0 1 0 0 1 5 0

F , L / h

Um

, J/

kg.

K U n i fl o w

C o u n t e r -c u r re n t

C o u n t e r -c u r re n t

U n i fl o w


23

Practical Lab # 3 Measurement of velocity profile and boundary layer growth over a flat plate

INTRODUCTIONIt is a fact well established by experiment that when a fluid flows aver a solid surface there is no slip at the surface. The fluid in immediate contact with a surface moves with it, and the relative velocity increases from zero at the surface to the velocity in the free stream trough a layer of fluid, which is called the boundary layer.OBJECTIVES · To Investigation of the velocity distribution on a plane plate in a longitudinal flow· To Investigation of the thickness of the boundary layer for turbulent flowAPPARATUS:Airflow Bench DescriptionA compact and mobile airflow bench which supports interchangeable experiment modules and provides a controlled, variable flow of air. The bench, when used with the modules (AF11 to AF18), enable a complete first course in airflow. The equipment is easy to set up and install, and experiments are quickly attached or removed. The experiment modules enable a complete first course in airflow, and the high levels of built-in safety make the equipment ideal for student experiments, lecture theatre demonstrations and project work.

A fan delivers atmospheric air via a flow control valve to a plenum chamber. Various test facilities may be attached to a 350 mm x 300 mm opening in the plenum chamber. An aerodynamically shaped contraction it has been supplied with the bench to provide an entry to a number of experiments, having 100 mm x 50 mm working section. Extensive use is made of toggle fasteners so that no tools are required for fitting the various experiments to the bench. Discharge from the experiments is normally downwards, the exhaust air passing through a pipe let into the bench top and terminating at the rear. This arrangement allows flexible ducting to be fitted (when experiments using smoke are in progress) to lead waste smoke safely away (figure 1).

The following figure 2 shows the arrangement of the test section attached to the outlet of the contraction of the Airflow Bench. A

flat plate is placed at mid height in the section, with a sharpened edge facing the oncoming flow. One side of the plate is smooth and the other is rough so that by turning the plate over, results may be obtained on both types of surface.A fine Pitot tube may be traversed through the boundary layer at the section near the downstream edge of the plat. This tube is the delicate instrument, which must be handled with extreme care if damage is to be avoided.


24

The end of the tube is flattened so that it presents a narrow slit opening to the flow. Thetraversing mechanism is spring loaded to the prevent backlash and a micrometer reading is used to indicate the displacement of the Pitot tube.Liners may be placed on the walls of the working section so that either a generally accelerating free stream may be produced along the length of the plate, depending on which way round they are fitted. With the liners removed, uniform free-stream flow conditions obtain over the plate length.

Boundary Layer ApparatusA flat plate is placed in the l00mm x 50mm transparent working section so that a boundary layer forms along it. A sensitive, wedge shaped Pitot tube mounted in a micrometer traverse allows velocity measurements to be made in the boundary layer. Both laminar and turbulent layers may be formed.Experiments which may be carried out include the measurement of the velocity profile:1. In laminar and turbulent boundary layers.2. In the boundary layer on rough and smooth plates.3. In the boundary layer at various distances from the leading edge of the plate.4. In the boundary layer on plates subject to an increasing or decreasing

pressure gradient in the

Pressure Po in air box

Flow from air

Plate smooth in one side and rough on other side.

Liners may be fitted to produce pressure gradient

Exhaust to atmosphere Traversing crosshead

with micrometer

Pitot pressure P

Fine pitot tube

Figure 2. Test Section


25

direction of flow (using the removable duct liners supplied).

THEORY Consider steady flow over a flat smooth plate as show in the figure, where the streaming velocity U is constant over the length of the plate. It is found that the thickness of the boundary layer grows along the length of the plate as indicated on the figure 3.

The motion in the boundary layer is laminar at the start, but if the plate is sufficiently long, a transition to turbulence is observed. This transition is produced by small disturbances which, beyond a certain distance, grow rapidly and merge to produce the apparently random fluctuations of velocity which are characteristics of turbulent motions. The parameter which characterizes the position of the transition is the Reynolds number Rex based on distance x from the leading edge:

Rex = Ux

Figure 3. General characteristics of boundary layer over flat plate

Definition of thickness: A little consideration will show that the boundary layer thickness , shown in before figure as the thickness where the velocity reaches the free stream value, is not an entirely satisfactory concept. The velocity in the boundary layer increases towards U in an asymptotic manner , so the distance Y at which we might consider the velocity to have reached U will depend on the accuracy of measurement thickness .This is defined as the thickness by the existence fluid outside the layer is displaced away from the boundary by the existence of the layer, as indicates schematically in the following figure 4:

XLaminar Turbulent

Transition

U

U


26

Figure 4. Velocity distribution and displacement thickness of boundary layer.

By the streamline approaching B the distribution of velocity u within the layer is shown as a function of distance y from the boundary as curve OA . If there were no boundary layer, the free stream velocity U would persist right down to the boundary as shown by the line CA. The reduction in volume flow rate (per unit width normal to the diagram) due to the reduction of velocity in the layer is therefore:

h

dyuUQ0

)(

When h is any arbitrary value, which satisfies the condition, U=U, for h rearrangement and introducing some consideration, we can obtain that,

0)1( dy

U

uQ

Momentum thickness,

0

)1( dyU

u

U

u

The overall skin friction coefficient,

LC L

f

2

Where L is the momentum thickness at distance L from the leading edge. L: length of the plateShape factor (H):H =

For laminar boundary layers along a flat plate with uniform free stream velocity, the velocity profile has been calculated,

y

h

A

BB’ U

u

O C

U-u

A’


27

x Rexx Rexfrom which it may be noted that the thickness along the plate grows in proportion to x. The shape factor is,H= 2.59

For a turbulent boundary layer along a smooth flat plate there are no corresponding calculated results, frequently the velocity the distribution is expressed in the form,

nY

U

u 1

)(

Where n is an index, which varies from 5 to 8 as the value of Rex.The displacement and momentum thicknesses are frequently expressed as,x/ (Rex)0.2

x/ (Rex)0.2 With the shape factor is,H= 1.29

The effect of pressure gradient We have saw as boundary layer development along a smooth pate with uniform flow in the free stream. If the free stream is accelerating or decelerating, substantial changes take place in the boundary layer development. For an accelerating free stream, the pressure falls in the direction of flow, the pressure gradient being by differentiating Bernoulli’s equation in the free stream as,

)(dx

dUU

dx

dP

The boundary layer grows less rapidly than in zero pressure gradient and transition to turbulent is inhibited. For a decelerating free stream, the reverse effects are observed. The boundary layer grows more rapidly and the shape factor increases in the downstream direction.

PROCEDURE Boundary Layer Plate with ProbeThe experimental set-up is placed in the measuring section of the Air Flow Bench. The set-up consists of 2 plates of different surface roughness, a plate bracket, a Pitot probe for velocity measurements and the bracket for the probe. To be able to measure the flow field in a horizontal direction, the Pitot probe can be very precisely adjusted using a micrometer drive. To be able to measure the velocity at different flow lengths, the plate can be moved in the direction of the flow. If, to measure the static pressure, the measuring gland on the bracket is connected together with the probe connection to a slanted tube manometer, the velocity distribution in the air flow can be determined.


28

To obtain the boundary layer velocity profile, the pitot tube is set at about 10 mm distance from the surface and the desired wind speed is established by bringing the pressure Po in the air box to

the required value. Readings of total pressure P measured by the pitot tube are then recorded over the range

of settings should be substantially constant, indicating that the traverse has been started in the free stream; if this is not the case, go back and start with an initial setting further from the plate.

As the Pitot tube reading being to fall, the step length of the traverse should be reduced so that at least 10 readings are obtained over the range of reducing readings.

The reading does not fall to zero as the tube touches the wall because of its finite thickness , so the traverse is stopped as soon as contact is indicated either by the electrical circuit or by the readings becoming constant as the micrometer is advanced towards the surface.

Readings obtained in turbulent boundary layer are subject to unsteadiness, which leads to difficulty in obtained average readings on the manometer.Damping may be provided by squeezing the connecting plastic tube, but care should be taken that the restriction is not too severe, which can led to false readings.

OBSERVATIONa) Turbulent boundary layers on smooth and rough surfacesAir temperature = 190CBarometric pressure 1010 mb Pressure in air box: 640, 640, 640, 640 N/m2

Length of plate from leading edge to traverse section, L = 0.265 mBarometric pressure 1010 mbReadings of Pitot pressures P are tabulated in the following table, values of y shown in the table are obtained from the micrometer reading at which the tube just touched the surface.

Table 1. DataMicrometer reading (mm)

y, (mm) P, N/m2

21.0 6.06 55020.0 5.0 55519.018.017.016.516.015.815.615.415.215.14

Taken technical data


29

From the manual of equipment

CALCULATIONa) Turbulent boundary layers on smooth and rough surfaces

The plate was installed in the test section without the lines fitted, and measurements were made in the boundary layer formed on the smooth surface and then an the rough surface,

Air temperature = 190C = 292KBarometric pressure 1010 mb = 1.010 x10 5 N/m2

Air density x10 5 N/m2 / 287,2 x 292 = 1.204 kg/ m3

Coefficient of viscosity = 1.80 x10 5 kg/m .sThickness of the Pitot tube, 2t = 0.40Where, displacement of tube center from surface when in contact, t = 0.20 mm,

As shown in the table, making allowance for the initial displacement t due to the thickness of the Pitot tube.

0P

P

U

u

Where Po is the Pitot tube readings in the free stream.

The free stream velocity U is obtained from:

½ U2 = 550 N/m2

where,

204.1

5502xU

U= 30.2 m/s

49.1

10265.02.30Re

5xUL

Re = 5.37 x105


30

RESULTS AND DISCUSSION The results should be given as shown in following tables:

Table 2 Velocity distribution in boundary layer on smooth flat plate, Re = 5.37 x105

Micrometer reading (mm)

y, (mm) P, N/m2 u/U

21.0 6.06 550 1.0020.0 5.0 555 1.0019.0 4.06 550 1.0018.017.016.516.015.815.615.415.215.14

Micrometer reading (mm)

y, (mm)

P,N/m2 u/U

25.0 9.10 540 1.0024.0 8.10 540 1.0023.0 7.10 525 0.9922.021.020.019.018.517.517.016.516.316.10

With help the Microsoft Excel you can obtain the following graphic to allow compares the velocity profile in both smooth and rough case,

CONCLUSION To express how it carry out the experiment, to compare the velocity profile on smooth and rough plate.


Velocity distribution

0

1

2

3

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1

u/U

Y (

mm

)

smooth

Rogh

Table 3. Velocity distribution in boundary layer on rough flat plate, Re = 5.37 x105


31

Practical Lab # 4 . Measurement of dispersion around turbulent jetINTRODUCTIONThe behavior of a jet as it mixes into the fluid, which surrounds it, has importance in many engineering applications. The exhaust from a gas turbine is an obvious example. In this experiment we establish the shape of an air jet as it mixes in a turbulent manner with surrounding air. It is convenient to refer to such a jet as a "submerged" jet to distinguish it from the case of the "free" jet where no mixing with the surrounding medium takes place, as is the case when a smooth water jet passes through the atmosphere.

OBJECTIVE:

APPARATUS:Round Turbulent Jet Apparatus A cylindrical tube having an aerodynamically rounded entrance, is fitted to the plenum chamber. The total pressure in the emerging jet maybe measured by means of a pitot tube mounted in a traverse gear, which is arranged so that a diametrical traverse may be made at various sections along the jet axis. Several diameters may be traversed to check the symmetry of the jet. Experiments which may be carried out include the following1. To observe the decay of centre-line velocity.2. To obtain velocity profile at various distances along the jet and observe the development and spread of the jet.3. By analysis of the velocity profiles, to show how the mass flux in the jet increases, the kinetic energy flux decreases and the momentum flux remains constant along the length.

Round Turbulent Jet Apparatus AF13

THEORYIn this experiment we establish the shape of an air jet as it mixes in a turbulent manner with surrounding air. It is convenient to refer to such a jet as a "submerged" jet to distinguish it from the case of the "free" jet where no mixing with the surrounding medium takes place, as is the case when a smooth water jet passes through the atmosphere.


32

If the Reynolds number of a submerged jet (based on the initial velocity and diameter of the jet) is sufficiently small, the jet remains laminar for some length — perhaps 100 diameters or more. In

this case the mixing with the surrounding fluid is very slight, and the jet retains its identity. Laminar jets are important in certain fluidic applications, where a typical diameter may be 1 mm, but the vast majority of engineering applications occur in the range of Re where

turbulent jets are produced.The essential features of a round turbulent jet are illustrated on fig. 1. The jet starts where fluid emerges uniformly at speed U from the end of a thin-walled tube, of cross-sectional radius R, placed in the body of a large volume of surrounding fluid. The sharp velocity discontinuity at the edge of the tube gives rise to an annular shear layer which almost immediately becomes turbulent.

The width of the layer increases in the downstream direction as shown on the diagram. For a short distance from the end of the tube the layer does not extend right across the jet, so that at section 1 shown in the figure there is a core of fluid moving with the undisturbed velocity U, the velocity in the shear layer rising from zero at the outside to U at the inside. Further down-stream the shear layer extends right across the jet and the velocity uo on the jet axis starts to fall as the mixing continues until ultimately the motion is completely dissipated.There is entrainment from the fluid surrounding the jet by the turbulent mixing process so that the mass flux in the jet increases in the downstream direction. The static pressure is assumed to be constant throughout, so there is no force in the direction of the jet. The momentum of the jet is therefore conserved. The kinetic energy of the jet decreases in the downstream direction because of the turbulent dissipation. It should be emphasized that the velocity profiles indicated on fig. 1 are mean velocity distributions, and that the very severe turbulence in the jet will cause instantaneous velocity profiles to vary considerably from these mean ones.

Fig.1. Schematic Representation of a Round Turbulent Jet


33

Velocity Distribution and Momentum FluxConsider the jet of fig. 1. If we assume that the flow pattern is independent of Reynolds number, then we might expect the velocity on the jet axis to depend on position in the dimensionless form

(1)

In the core of the jet, we have already observed that

Far downstream, when the length of the core ceases to have influence, there is some theoretical justification (supported by experiment) for expecting centerline velocity to decay inversely as x, viz.

(2)where c is a constant.The velocity u.at any position (r,x) in the jet may also be written in the dimensionless form (3)

Consider now the velocity distribution over a section far downstream, i.e. where x/R is large. We might reasonably expect that the velocity distribution across the section would not depend appreciably on the precise detail of the flow near the tube exit, so we might ignore the dependence upon — and write simply (4)

far downstream. Velocity profiles of this type, in which the velocity ratio depends on a parameter, are frequently called "similar", in the sense that a single expression is used to characterise the velocity distribution at any number of chosen sections. Using certain assumptions about the nature of the turbulent processes, it is possible to show that equation (4) should take the form (5)

where X is a constant which is to be determined by experiment.

Values of u/uo computed from this expression are presented in table 1. The value r/x = 1.287 is included, as this makes u/uo = 0.5. When comparing with experimental results it is useful to have this value, since the radius at which u/u0 = 0.5 is easily identified on the velocity profile.

r/x, mm

u/u0

0 00.2 0.9800.4 0.9250.60.81.0

Table 1 Calculated Velocity Profile of Round Jet.


34

Coming now to mass, momentum and energy flux, we see in fig. 2 an annular element of the jet through which fluid of density is flowing with velocity u. The area of the element is

So the mass flux 6m through it is

The total mass flux through the section of the jet is

(6)

The momentum flux J through the section is similarly found to be (7)

and the kinetic energy flux E to be

(8)

It is convenient in many instances to relate these to the corresponding fluxes at the tube exit, viz.

1.281.41.61.82.02.252.53.0 0.0954.0 0.040

Fig. 2 Annular Element of Round Jet


35

with the results (9) (10)

(11)

PROCEDUREThe round jet is produced by discharging air from the air box through a short tube as indicated

in fig.3. The inlet of the tube is rounded to prevent separation so that a substantially uniform

velocity distribution is produced at the tube exit. A traversing mechanism is supported on

the tube so that a Pitot tube may be brought to any desired position in the jet. Measurements

are normally made in one plane, but if it is desired to check on the symmetry of the jet about

the axis, the traversing mechanism may be rotated as a whole to any desired position.

Fig. 3. Arrangement of Jet Apparatus

The Pitot tube is first brought into the exit plane of the jet and the scale readings are noted for which the axial position x and the radial position r are zero. The latter may be obtained by taking the mean of the readings when the tube is set in line with one side and then the other

side of the tube. The pressure Po in the air box is then brought to a convenient value and traverses are made at various axial stations along the length of the jet. The readings of total pressure P fluctuate violently because of the turbulence and some damping is required; excessive


36

damping should however not be used. It is recommended that graphs of total pressure P against radius r be plotted as the experiment proceeds to ensure that the profile is well-established by

a sufficient number of readings in the critical regions.

OBSERVATIONTable 2 Data


CALCULATIONDiameter D of jet tube 51.6 mmRadius R 25.8 mmPressure Po in air box 900 N/m2

Air temperature 22°C = 295 KBarometric pressure 1025 mb = 1.025 x io5 N/m2

Air density = = 1.210 kg/m3

Coefficient of viscosity = 1.82x10-5 kg/ms

Coefficient of kinematics viscosity = 1.50 x 10-5 m2/s

Velocity U at tube exit: = 870 N/m2

Reynolds number Re at tube exitRe =

x 10s

Re = 1.30x105

x, mm

P,N/m2

0 87050 86075 845100125150175200225250300350400450


37

The velocity along the axis of the jet was first found by traversing axially, the results being presented in table 2 and fig. 4.

For the initial portion the centre line velocity uo is seen to be almost constant, and further downstream it starts to fall more rapidly as the shear layer extends to the centre. Extrapolating the falling curve backwards to the line =1 shows the length of the

core to be

RESULTS AND DISCUSSION Results and Calculations

Table 2 Velocity Distribution along Jet Axis xc = 175 mm or = 6.8

Fig. 4. Centerline Velocity along Jet

x, mm

P,N/m2 u0/U

0 870 1.0050 860 0.9975 845 0.99100 835 0.98125 830 0.98150 810 0.96175 775 0.94200 730 0.92225 675 0.88250 620 0.84300 505 0.76350 430 0.70400 340 0.63450 280 0.57

Table 3 Velocity Distribution at Various Sections of the Jet


38

Fig. 5.(a) Fig. 5.(b)

Fig. 5 (c) Fig. 5.(d)

The results of radial traverses made at various values of x are shown in table 3 and on figs. 5(a) to 5(d). It may be noted that for x = 300 mm a check was made to find whether the velocity distribution was symmetrical about the axis, and this established that there was no appreciable departure from roundness. The profile at x = 75 mm shows a distinct region of constant velocity in the core, and at x = 150 mm there is still some evidence of a flat top to the profile. Further downstream, however, this has disappeared. On fig. 6 a dimensionless comparison of the profiles is made by dividing the radius by the radius at which the velocity ratio is 0.5. The curves for x = 300 mm and x = 450 mm are virtually indistinguishable, indicating similar profiles — similarity having the meaning of the previous discussion. The transition from the square-topped profile at the tube exit to the similarity profile is clearly demonstrated on this figure. The curve calculated from equation (5) (values being shown in table 1) is also plotted. There is good agreement with the similarity profile near the centre of the jet, but equation (5) over estimates u/u0 at the outer edge.


39

Fig. 6. Dimensionless Velocity Profiles in JetA check on momentum conservation may be made by application of equation

(10). On fig. 5.7 the curves of are drawn as functions of for each of the sets of radial traverses. The areas under these curves represent the integrals

and so are a measure of momentum flux. The areas, measured by planimeter, lead to the results of Table 4. The values do not remain constant at 1.0 as expected, but rise significantly as the jet develops. There can be no doubt that the momentum flux does not increase since there is no force acting in the direction of the jet, so the apparent rise must be due to experimental error. The most likely source is turbulence which could have the effect of giving a mean velocity pressure which is in excess of the pressure corresponding to the mean velocity.

Fig. 7. Momentum Flux in Jet

CONCLUSION The diffusion of a turbulent air jet into the surrounding atmosphere has been measured by velocity traverses along the centerline and along several radii. The first part of the jet is found to have a central core of almost constant velocity which extends for a length xc = 6.8R along the axis. Thereafter the centerline velocity reduces and the velocity profile rapidly tends to similarity, i.e. to a profile which may be characterized by the single parameter r/x. The momentum flux in the jet, which must be constant in a constant-pressure atmosphere, appears

Table 4 Momentum Flux in Jet


40

to rise by about 14% along its length. The discrepancy is attributed to measurement error due to turbulence.

Suggestions for Experiments1. Obtain the angle at which the jet spreads by establishing the trajectory along which u/uo

= 0.5.

2. Compare the variation of centerline velocity with equation (2).

3. Investigate the effect of initial turbulence in the jet by placing wire gauze over the

exit of the tube and comparing the results with these obtained with a plain exit.REFERENCE That was explain in the topic of content of the report, the same way you should have the reference to the bibliography useful for this practice.


41

Practical Lab # . 5 Flow Round A bend Duct (Characterization of energy losses in a bend)

INTRODUCTIONThe engineer is frequently presented with problems of flow contained within tubes and ducts. Such flows may be classified as internal flows to distinguish them from flows over bodies such as aerofoils, called external flows. It is sometimes required to shape a duct in such a way that particular requirements are met. For example, it may be necessary to change the shape of the cross-section from square to rectangular with a small loss of total head, or it may be required to form a bend in such a way that the distribution of velocity at the exit is as nearly uniform as it can be made.Due to the presence of boundary layers along the duct walls, the fluid mechanics o f such flows are sometimes extremely complicated. Separation may be produced where pressure rises in the direction of flow.In this experiment we investigate the flow round 90 deg bend in a duct of rectangular section, using pressure tapings along the walls to establish pressure distributions.

OBJECTIVE: To investigate the flow round 90 deg bend in a duct of rectangular section, using pressure tapings along the walls to establish pressure distributions.

APPARATUS: Flow Around a Bend AF15A transparent bend of l00 mm x 50 mm cross-section is attached to the contraction; pressure tappings in the wall are grouped and identified as follows:1. Inner wall – 10 tappings2. Outer wall – 10 tappings3. 45° radial section – 9 tappings4. Reference at inlet – 1 tappingThese may be rapidly connected to the multitube manometer in groups, using the quickrelease couplings, and readings taken. Experiments which may be carried out include:1. Measurement of the pressure distribution along the curved inner and outer walls.2. Measurement of the radial pressure distribution and comparison with that predicted assuming free vortex velocity distribution.

AF15 Flow around a Bend


42

Due to the presence of boundary layers along the duct walls, the fluid mechanics of such flows are sometimes extremely complicated. Separation may be produced where the pressure rises in the direction of flow, as illustrated in Fig. 1 (a). This shows a duct of increasing cross-sectional area in which the flow decelerates with an accompanying rise of pressure. Separation of flow from one wall is shown, followed by a region of severe turbulence in which there is mixing between the main flow and the region of recirculating flow (often called the separation bubble) near the wall. Ultimately the main flow reattaches to the wall. The turbulent mixing leads to loss of total pressure, the size of this loss depending on the extent of the .separation. It should be emphasized that the flow shown in the figure is schematic only.

(b) Formation of secondary flow in a bend

Fig. 1. Separation and Secondary Flow in Ducts(a) Schematic representation of a separating and reattaching flow


43

The Fig. 3 shows the dimensions of the bend and the positions of the pressure tappings. There is a reference pressure tapping 0 on the side face near the entry, and three sets of tappings; one set of 10 along the outer curved wall, one set of 10 along the inner curved wall and a set of 9 along a radius of the bend. Air from the contraction section is blown along the duct and is exhausted to atmosphere.

THEORYThe separation line is rarely steady. The size of the separated zone often fluctuates violently, and in some cases the separation is intermittent. Separation might occur over more than one surface and would not normally take place uniformly over one side as shown for illustrative purposes in the figure. A further complication arises from secondary flow which is again due to boundary layer effects. Fig. 1 (b) shows one example of the formation of a secondary flow in a gently-curving duct of rectangular cross-section. The curvature of the flow is accompanied by a pressure gradient which rises across the section from the inner to the outer wall. The pressure gradient extends over the whole section, so that the boundary layers on the upper and lower walls are subjected to the same pressure gradient as the main flow. But because the streaming velocity in the boundary layer is less than in the main part of the flow, the curvature of the streamlines in the boundary layer is more severe, as indicated in the figure. This gives rise to a net inward-directed flow adjacent to the upper and lower walls, which sets up a secondary flow in the form of a double rotation, superposed on the main stream. The motion emerging from the curve in the duct is therefore a pair of contra-rotating spirals, the strength of which depends on the amount of curvature and on the thickness of the boundary layer.

Fig. 2 Assumed Velocity Distribution in Bend Simple theory of flow in a bend

In this experiment, we investigate the flow round a 90° bend in a duct of rectangular section, using pressure trappings along the walls to establish pressure distributions. Fig. 2 indicates flow approaching a bend with a uniform velocity U. Within the bend we shall assume a free vortex distribution of velocity, given by

(1)


44

where u is the streaming velocity at radius r from the centre of curvature of the bend. Separation and secondary flow will be neglected. The constant C may be found by applying the equation of continuity as follows:-

(2)

where b is the width of the section of the duct. Substituting for u from equation (1)

and performing the integration leads to the result

(3)

so the velocity distribution is, in dimensionless form,

(4)

The corresponding pressure distribution may be found by assuming that Bernoulli's

equation may be applied between the upstream section and a section within the bend,

viz:

(5)

where po is the static pressure upstream and p is the pressure at radius r in the bend. It is

convenient to express p in the form of a dimensionless pressure coefficient cp where, (6)

Where,

From equation (5) this may be written

(7)

which may be evaluated for any radius r by substituting the appropriate value of u/U obtained from equation (4). A comparison with measured values of cp may be made as indicated below.

PROCEDURE The pressure tappings along the outer wall, the reference tapping 0 and the

pressure tapping in the air box are all connected to the manometer.

P

p0pi

p= pi Tappimgs pressures (i=1 to 10)P= air box pressurepi= tappings pressure


45

The air speed is adjusted to a value slightly below the maximum, as indicated by the air box pressure, and the pressures are recorded. (The setting of air speed slightly below the maximum is to ensure that the same setting may be repeated in later tests).

The tappings on the inner wall are then connected in place of the ones on the outer wall.

The air box pressure is adjusted to the previous value and a further set of readings are recorded.

Finally the procedure is repeated with the third set of pressure tappings. In the following table record the pressure relative to atmosphere datum and the pressure coefficients cp are calculated from equation (6).

Fig. 3. Dimensions of Bend and Positions of Pressure TappingsAir box pressure P 630 N/m2

Reference tapping pressure p0 80 N/m2


46

OBSERVATION

Table 1.0 Data Measured Pressure

Tapping no. Outer wall Inner wall Radial wall

Pi mm H2O

Pi mm H2O

Pi mm H2O

Pi mm H2O

Pi mmH2O

Pi mmH2O

1

2

3

4

5

6

7

8

9

10

Table 1 Measured Pressure and Pressure CoefficientsTapping no. Outer wall Inner wall Radial wall

P(N/m2)

Cp P(N/m2)

Cp P(N/m2)

Cp

1 90 0.02 70 -0.02 -265 -0.632 145 0.12 40 -0.02 -265 -0.633456789 35 -0.08 10 -0.13 295 0.3910 0 -0.15 0 -015 - -

Taken technical dataNote:-Write down pressures in manometer with respect to atmosphere and convert the readings to gauge pressures in Pascal have and then calculate the pressure coefficient CpBased on pressure Pascal’s


47

CALCULATION

Velocity pressure of uniform flow along duct P - Po = = 550 N/m2,

where, Air box pressure PReference tapping pressure p0

And velocity:

)(2 0pPU

From Fig. 3, the inner and outer surfaces of the bend have radiur1 = 50 mmr2 = 100 mm

From equation (4) the velocity distribution across the section according to the

free vortex assumption is therefore

where r is expressed in mm. In Table 2 we compute this ratio and the corresponding value of cp from equation (7) for a number of values of r.

Table 2 Calculated Pressure Coefficients

Figure 4 shows the distribution of measured pressure coefficient over the curved walls and compares the measured and calculated values across the radial section. It may be seen that the pressure across the inlet section is nearly uniform.

P

p0


48

RESULTS AND DISCUSSION As the flow approaches the bend, the pressure on the inner wall falls rapidly and on the outer wall rises rapidly to values which remain substantially constant round most of the curve. This indicates that the curvature of the flow is also likely to be substantially constant. The distribution of Cp over the radial section follows the calculated curve quite closely, indicating that the assumption of a free vortex velocity distribution made in equation (1), together with the assumption that Bernoulli's equation applies to the flow, give a fairly accurate distribution of the pressure field. The measured pressure distribution varies rather less steeply than calculated, indicating a vortex strength C somewhat less than given by equation (3).

Fig. 4. Distribution of Pressure Coefficient cp Over Walls

Downstream of the bend, the wall pressures readjust until at the duct exit the pressure is substantially constant across the section. It is, however, a little lower than the reference pressure at inlet, and this difference represents a pressure loss round the bend. It is convenient to express this loss p in terms of the velocity pressure 1/2 U2 in the uniform approaching flow by the expression

K=

(9)

where K is the dimensionless loss coefficient. In this case we find, from the

change in Cp from the inlet to the outlet sections, the value

K=0.15 (10)

p = p0-p10_outlet


49

CONCLUSION The distribution of pressure over the curved walls of a 90° bend of rectangular section has been established by pressure plotting. The pressure coefficient is negative and almost constant round the inner wall, and positive and almost constant round the outer wall. Across the 45° cross-section the pressure distribution may be predicted with reasonable accuracy by assuming free-vortex velocity distribution over the section. The value of loss coefficient K is 0.15 for this bend.

Questions for Further Discussion

1. Do you consider that there is likely to be any separation of flow anywhere in the bend, and can you suggest any way by which this might beinvestigated?

2. Do you consider that there might be any secondary flow in the stream,downstream of the bend, and can you suggest how this might beinvestigated?

3. It has been proposed to measure flow rate Q in a duct system placingpressure tappings on the inner and outer walls at the 45° section of anyconvenient 90° bend which occurs in the line of the duct, and measuringthe differential pressure p between the tappings. Using equations (2)to (5) show that Q is given by

where b, r and r2 are defined on Fig. 2

Noting that the measured pressures do not quite agree with the theoretical values, this equation may be modified to

in which Cd is a discharge coefficient. Show that Cd is given by


50

and hence find Cd from the experimental results. (Cd = 1.06)


p (p5inner - P5outlet) Pressure tappimgs (5) at the inner and outer walls at the 450 section


51

Practical Lab # 6. Measurement of drag and lift of an aerofoil at different angles of attack

INTRODUCTIONWhen a solid body is placed in a fluid flow and a nonsymmetrical situation occurs the direction of the force on the body does not coincide with the direction of the (undisturbed) flow. This principle makes flying possible. Discussion of lift and drag starts usually with the introduction of an airfoil. (x is the direction of the horizontal flow, z is vertical)The airfoil is tilted with respect to the (undisturbed) flow direction, defined by the angle of attack; α. the airfoil experiences a force FR. The airfoil cross section of an airplane wing is long in the direction perpendicular to the plane of the drawing and the flow can be considered as two-dimensional. In this practice you should obtained the form experimental the values of the components of the force FR

OBJECTIVE: To measure the drag and lift of an aerofoil at different angles of attack

APPARATUS:HM 170 Air Flow Bench (wind tunnel)

Technical DescriptionThe educational wind tunnel HM 170 (figure 1) is a so-called "Eiffel type" of open subsonic wind tunnel. With this type of tunnel, the air is taken from the atmosphere and returned to the atmosphere. A carefully designed nozzle shape guarantees the constant distribution of velocity within the closed measurement section. Velocities of around 100km/h are reached. A flow rectifier at the inlet ensures a low degree of turbulence. The wind tunnel consists of the following components: inlet hopper with flow rectifier, nozzle, measurement section, diffuser and fan. The nozzle, inlet hopper and the measurement sections are mounted on a guide rail and can be moved in order to access the measurement section. An axial fan with guide wheel is used which is characterized by its low noise level and high efficiency. The fan is mounted on rubber elements to minimize vibration during operation. It is driven by a speed-controlled motor with frequency converter. The fan is connected permanently with the diffuser. An electronic 2-component force transducer permits the measurement of resistance and buoyant forces at various objects. The measured values are displayed on a measuring amplifier. It is also possible to process the data via PC-data acquisition (available as an accessory). A slanted tube manometer is used to display the current air velocity at the inlet into the measurement section.


52

Figure 1. Specification

[1] Open wind tunnel on mobile carriage[2] Experimental set-up lxwxh 2890x860x1670mm, 250kg [3] 450mm Plexiglas measurement section, cross-section of flow 292x292mm[4] Inlet hopper, nozzle and diffuser made of FRP[5] Speed-controlled fan motor with frequency converter[6] Electron. 2-components force transducer with measuring amplifier and digital display [7] Flow rectifier

Technical DataMeasurement sectionCross-section wxh: 292x292mmLength: 450mmMax. wind velocity: 28m/sFanPressure difference: 500PaMax. volumetric flow: 9000m³/hMotor output: 2.25kWMax. rotational speed: 2850rpm2-component force transducerMeasuring range: 0...5N and 0...10NSlanted tube manometer0...500Pa


53

THEORYWhen a solid body is placed in a fluid flow and a nonsymmetrical situation occurs the direction of the force on the body does not coincide with the direction of the (undisturbed) flow. This principle makes flying possible. Discussion of lift and drag starts usually with the introduction of an airfoil. (x is the direction of the horizontal flow, z is vertical)

The airfoil (e.g. the cross section of an airplane wing) is long in the direction perpendicular to the plane of the drawing and the flow can be considered as two dimensional. The airfoil is tilted with respect to the (undisturbed) flow direction, defined by the angle of attack,α. the airfoil experiences a force FR. Considering an airplane it is very useful to decompose the force FR into components FL and FD perpendicular and parallel to the flow direction. FL is the lift force, it carries the plane, and by definition it does not do work. FD is the drag force, the resistance to be balanced by the propulsion force generated by the engines. The net power required is the product of drag force times flow velocity. The lift and drag forces are expressed as:

2DD

2LL

uAC5.0F

uAC5.0F

with: FL and FD = lift and drag force CL and CD = lift and drag coefficient ρ = density of the fluid A = projected area of the airfoil with e.g. 1m length perpendicular to the plane of the

drawing u = velocity of the undisturbed flow

Note that the expression for FL and FD differ only in CL and CD. The designer of an airplane tries to maximize CL and to minimize CD. CL and CD are dependent on the angle of attack. For an enormous number of airfoil profiles CL and CD have been measured or calculated. Usually the CL drops sharply and CD increases strongly at α = abt.150. The force on the airfoil is the result of the integration of pressure around the perimeter.

FRFL

FD

angle of attack α

direction of fluid flow

z

x

Figure 2. Angle fo attack


54

When not an airfoil but a flat surface with zero thickness is placed in a flow a lift and drag force can be distinguished as well.

An aerofoil is shaped so that air flows faster over the top than under the bottom. There is, therefore, a greater pressure below the aerofoil than above it. This difference in pressure produces the lift.Angle of Attack is the difference between where the wing is pointed and the direction of the air flowing over the wing as shown in this schematic. As the force is the resultant of the pressure on the surface the direction of the force cannot be different from perpendicular to the surface (shear forces neglected). This includes that CD

and CL cannot be independent of each other. Between the two the next relation exists:

tanC

C

L

D

When a curved surface with zero thickness is placed in a flow the force on every surface element is perpendicular to that element but as the angle of attack varies and also the pressure distribution not much can be said over the position and the direction of the resulting force. See Figure. But when the curvature is small as with a rowing blade, the situation cannot be very different from a flat plate. Assume now that the forces are in the horizontal plane as is the case with rowing. For an elaboration of the idea see section 5. CD and CL as function of the angle of attack.

direction of fluid flow

Figure 3. Forces diagram

FR

FD

FL

z

x

direction of fluid flowFD

FRFL

Figura 4. Flow direction


55

From the explanation above follows: the distinction between lift and drag is not of a physical nature but it is a functional one (carrying and resisting) or a geometrical one (perpendicular and parallel to the flow direction) but the observation made before that the lift force does not do work is of importance. In other words, the lift force does not waste energy.

Figure 5. Polar diagram is a graph showing the relationship between the drag and lift coefficients

PROCEDURE

1. Mount the aerofoil model in the middle of the working section (take care of the lever arm of 310 mm of the force balance)

2. Set the force at the measuring amplifier to zero with the help of offset potentiometer.3. Started the wind tunnel. After the desired wind speed is reached set the aerofoil to the

zero angle of attack. All angles will be measured with reference to this angle position.4. Measurement the drag and lift at different setting angles.

Make sure that the model is secured in respective position when the tunnel is on! 5. At high angles, the vibration of the aerofoil indicates flow turbulence.

If the vibration amplitude is high stop the experiment.

OBSERVATION Table 1 . Data No Angle of attack Lift force(Fl) in N Drag force(Fd) in

NLift coefficient (Cl) Drag coefficient(Cd)

1 0

2 3

2 6

3 9

4 11

5 13

6 15

7 17

8 19

Area of the holder rod is 0.000125m2 Drag coefficient for cylindrical rod is 1.1 Length of the aerofoil 100mm

Figure 5. Aerofoil


56

CALCULATION, RESULTS AND DISCUSSION

1. Calculate drag and lift coefficients of an aerofoil2. Draw a graph showing the variation of lift and drag with variation in angle of attack

at the same graph3. Draw Cd vs. angle of attack and Cl vs. angle of attack in one graph4. Draw the polar diagram.

The graphs below (figure 6) shows how lift and drag changes with the angle of attack for a typical wing design.

Where the curve crosses the Drag axis is where the wing is generating zero lift. Notice the angle of attack at that point is a negative value. That means a typical wing has to point down to get to zero lift. Notice, also, there is some drag at zero lift. There is, truly, no free lunch.As the nose of the wing turns up, angle of attack increases, and lift increases. Drag goes up also, but not as quickly as lift. Think about the last time you took a trip on an airplane. During take-off an airplane builds up to a certain speed and then the pilot

“rotates” the plane; that is, the pilot manipulates the controls so that the nose of the plane comes up and, at some angle of attack, the wings generate enough lift to take the plane into the air. Since an airplane wing is fixed to the fuselage, the whole plane has to rotate to increase the wing's angle of attack.A wing is fairly efficient. You get a lot of lift without much drag—until you get to about 12 degrees angle of attack on this curve. Then drag goes way up, without creating much more lift. As the angle of attack increases from 12 to 19 degrees for this particular design, there isn’t much increase in lift but you have a lot more drag. We say the wing is “stalled” when lift decreases at increasingly higher angles of attack.The shape of this curve is why you read about airplane crashes during stormy takeoffs and landings. Under conditions of low speed and high lift, the plane is rotated up there near the top of the curve. If the plane has to climb and the pilot tries to bring the nose up, he gets more drag and not much more lift. What he really needs is more airspeed. A few years ago most airlines changed their procedures and you don't see planes landing at high angles of attack any more.Front wings on racecars are fabricated so the angle of attack is easily adjustable to vary the amount of downforce needed to balance the car for the driver. You see that happening at pit stops during a race. Rear wings are also adjusted by changing the angle of attack but that takes too much time for a pit stop. Sometimes you'll see a team change a Gurney flap during a pit stop and that's the next Race Tech story coming soon.

Figure 6. Lift and drag coefficients


57

CONCLUSION You should be the comparison the drag and lift of an aerofoil at different angles of attack, according to the result obtained and its analysis.



58

Practical Lab # 7 Comparison of losses in nozzle and diffuser type duct flows

OBJECTIVEComparison of the lost in nozzle and diffuser type duct flows using a venturi-meter and determine the coefficient CD of venturi-meter.

INTRODUCTIONSpecial Tubes a variety of special forms of the pitot tube have been evolved. Folsom (loc. cit.) gives a description of many of these special types together with a comprehensive bibliography. Included are the impact tube for boundary-layer measurements and shielded total-pressure tubes. The latter are insensitive to angle of attack up to 40. Chue [Prog. Aerosp. Sci., 16, 147–223 (1975)] reviews the use of the pitot tube and allied pressure probes for impact pressure, static pressure, dynamic pressure, flow direction and local velocity, skin friction, and flow measurements.

A reversed pitot tube, also known as a pitometer, has one pressure opening facing upstream and the other facing downstream. Coefficient CD for this type is on the order of 0.85. This gives about a 40 percent increase in pressure differential as compared with standard pitot tubes and is an advantage at low velocities. There are commercially available very compact types of pitometers, which require relatively small openings for their insertion into a duct.

APPARATUS Venturimeter, large flask and measurement cylinder.

The pitot-venturi flow element is capable of developing a pressure differential 5 to 10 times that of a standard pitot tube. This is accomplished by employing a pair of concentric venturi elements in place of the pitot probe. The low-pressure tap is connected to the throat of the inner venturi, which in turn discharges into the throat of the outer venturi. For a discussion of performance and application of this flow element, see Stoll, Trans. Am. Soc. Mech. Eng., 73, 963–969 (1951).


59

THEORYVenturimeter is advice used for measurement rate of a fluid flowing through the pipe. It consists in three parts:

A short converging part Throat Alverging tube

Venturi Meters The standard Herschel-type venturi meter consists of a short length of straight tubing connected at either end to the pipe line by conical sections (see Figure). Recommended proportions (ASME PTC, op. cit., p. 17) are entrance cone angle 1 21 2, exit cone angle 2 5 to 15, throat length one throat diameter, and upstream tap located 0.25 to 0.5 pipe diameter upstream of the entrance cone. The straight and conical sections should be joined by smooth curved surfaces for best results.The practical working equation for weight rate of discharge, adopted by the ASME Research Committee on Fluid Meters for use with either gases or liquids, is

w= q1. 1 = CD

. Y. A2 2 gc ( p1-p2). 1

1 4

w= q1. 1 = CD

. Y. A2 2 gc ( p1-p2). 1

where A2 cross-sectional area of throat; CD coefficient of discharge, dimensionless; gc

dimensional constant; p1, p2 pressure at upstream and downstream static pressure taps respectively; q1 volumetric rate of discharge measured at upstream; w weight rate of discharge; Y expansion factor, dimensionless; ratio of throat diameter to pipe diameter, dimensionless; and 1 density at upstream pressure and temperature.

Figure _ Herschel-type venturi tube.

For the flow of gases, expansion factor Y, which allows for the change in gas density as it expands adiabatically from p1 to p2, is given by


60

for venturi meters and flow nozzles, where r p2 /p1 and k specific heat ratio cp /cv. Values of Y computed from Eq. (10-21) are given in Fig. 10-16 as a function of r, k, and .For the flow of liquids, expansion factor Y is unity. The change in potential energy in the case of an inclined or vertical venturi meter must be allowed for. Equation is accordingly modified to give

m= q1. = CD

. A2 [2 gc ( p1-p2) + 2 g. ( Z1-Z2)]. 1 4

where g local acceleration due to gravity and Z1, Z2 vertical heights above an arbitrary datum plane corresponding to the centerline pressure reading locations for p1 and p2

respectively.

Value of the discharge coefficient CD for a Herschel-type venturi meter depends upon the Reynolds number and to a minor extent upon the size of the venturi, increasing with diameter. A plot of CD versus pipe Reynolds number is given in ASME PTC, op. cit., p. 19. A value of 0.984 can be used for pipe Reynolds numbers larger than 200,000.

For flow measurement of steam and water mixtures with a Herschel type venturi in 2a- n-and 3-in-diameter pipes, see Collins and Gacesa, J. Basic Eng., 93, 11–21 (1971).A variety of short-tube venturi meters are available commercially. They require less space for installation and are generally (although not always) characterized by a greater pressure loss than the corresponding Herschel-type venturi meter. Discharge coefficients vary widely for different types, and individual calibration is recommended if the manufacturer’s calibration is not available. Results of tests on the Dall flow tube are given by Miner [Trans. Am. Soc. Mech. Eng., 78, 475–479 (1956)] and Dowdell [Instrum. Control Syst., 33, 1006–1009 (1960)]; and on the Gentile flow tube (also called Beth flow tube or Foster flow tube) by Hooper [Trans. Am. Soc. Mech. Eng., 72,1099–1110 (1950)].

The use of a multi-venturi system (in which an inner venturi discharges into the throat of an outer venturi) to increase both the differential pressure for a given flow rate and the signal-to-loss ratio is described by Klomp and Sovran [J. Basic Eng., 94, 39–45 (1972)].

PROCEDURE Check if all valves are in right position. Switch on the hydraulics bench. Take differential manometers reading for each point. Set the flow and close valve exit in the reservoir of the hydraulic bench. Take reading of flow rate, by take the time and volume of liquid Repeat the procedure for different flow rates.


61

OBSERVATIONTable: Data Collected

Pieszometric Xn (mm) Dn (mm) Hn(mm of H2O (Cp)a (Cp)a

A -12 26B 7 32.2C 19 18.4D 33 16.10E 48 16.79F 63 18.47G 78 20.10H 93 21.84J 108 23.58K 123 25.21L 143 26.00 Taken technical data

CALCULATE AND ANALYSISWith the data that you took in the carry out practical for different piezometer position it canbe calculated the coefficient Cp for each position, for the actual condition and for theoretical calculation.

For actual condition the coefficient can be calculate by:

Where,

and the actual flow rate will be:Q= Volume of fluid (m3) / Time, sQ= (12.95 x 10-3 m3 ) / (26.4 s )Q= 0.0004905 m3 / s

Q= A1. C1 , C1= Q/ A1

C1= (0.0004905 m3 / s ) / ( 0.7854 . (26x10-3)2)C1= 0.924 m/s = 924 mm/s

A B C ED F G H I J K L

h1 - hn

(C22 / 2g)

Cp a =

(C22 / 2g) = h1 – h2 + (C1

2 / 2g)


62

Where, C1 is the velocity of fluid in section 1, and A1 area the flow in section 1; m2

Then,

Where, h1 = 292 mmh2 = 30 mm

After that it should be calculated the theoretical piezometric head coefficient (Cpht) for each section:

Where: D2 throat diameter D1 inlet diameterExample, for section A:

As D2= 16 mm and D1= 26 mm, but D1= DA, in this section is obtained that,

For section B,

As the relation between D2= 16 mm and D1= 26 mm is:

The same way for each section “A” to “L” you can obtained the (Cpht). The result should be shown in the following table:

(C22 / 2g) = 292 –30 + (9242 / 2(9.51) . 1000)

(C22 / 2g) = h1 – h2 + (C1

2 / 2g)

(C22 / 2g) = 305.5 mm

Cp ht = D2

Dn[ ]4 - D2

D1[ ]4

(Cp ht)A = D2

DA[ ]4 - D2

D1[ ]4

(Cp ht)B = D2

DB

[ ]4 - D2

D1[ ]4

(Cp ht)A = 0

D2

D1[ ] = 0.615

(Cp ht)B = 16 32.2

[ ]4 – (0.615)4

(Cp ht)B = 0.0828


63

Section A B C D - - - - - - - - - - - - L(Cpht)i 0 0.083 - - - - - - - - - - - - - - -

After that you can calculate the Cpa coefficient (Actual piezometric head coefficients),

For section A:

as, h1 =hA , it is obtained,

For section B:

as, which one was calculated before,

Subsequently, the same way you should obtained the values for another section.

The results can be shown as represent in following table,Section A B C D - - - - - - - - - - - - L(Cpa)i 0 0.0131 - - - - - - - - - - - - - - -

For venturi meter the flow rate equation is:Q theoretical = CD

. A2 2 gc ( h1-h2) 1 2

Q theoretical = CD. A2 2 gc ( h1-h2)

1 4

where, D2 / D1 = 0.016/0.026 = 0.615 h1: it is taken in inlet of the venturi and h2 in throat.

h1 - h2

(C12 / 2g)

Cp a =

h1 - ha

(C22 / 2g)

Cp a =

(Cpa)A = 0

h1 - hB

(C22 / 2g)

(Cp a) = 292 - 288

305.5 =

(C22 / 2g) = 305.5 mm,

(Cpa)B = 0.0131

1

2

h


64

Then the theoretical flow rate can be calculated without CD as,

Q theoretical = 0.7854 (0.016) 2 (9.81) (292 – 30) 1 4 1000

Q theoretical = 0.0005786 m3/ s

Actual flow rate as was calculated before is,

Qactual= 0.0004905 m3/ s

The relation between actual flow rate (Qactual) and theoretical flow rate (Q theoretical) we can obtain the discharge coefficient of venturi meter.

CD= Qactual / Q theoretical = 0.0004905 / 0.0005783

CD= 0.85 that is the coefficient of discharge of the venturi meter, for this condition.

RESULTS AND DISCUSSION After realized the calculated and analysis, we can realize the analysis theses results and the discussion of it. Through the analysis of the calculate data and you can construction the graph that may help you for obtained the comparison of calculated values. Now, we can graph the length of venturi meter (mm) vs. pressure along the length of the venturi meter (mm of water) and the different coefficients vs. the length, as shown in the following figures:

CONCLUSION In this point, you should realize the analysis about the results, reflect on the calculation, analysis of the result, discussion point, and take in maid the loss in the venture meter tube and how influence is the present of frictional losses about the flow. You should do the analysis of conclusion about the chart of results.

0

0.2

0.4

0.6

0.8

1

-5 15 35 55 75 95 115 135

Length, mm

Cp

a, C

ph

t

(Cp)a

(Cth)a

050

100150200250300350

0 20 40 60 80 100 120 140

Length, mm

Pre

ssu

re, m

m o

f w

ater


65

Practical Lab # 8. Finding pressure distribution over an aerofoil at different velocity and angles

INTRODUCTIONThe airfoil is tilted with respect to the (undisturbed) flow direction, defined by the angle of attack,α. the airfoil experiences a force FR. The airfoil cross section of an airplane wing is long in the direction perpendicular to the plane of the drawing and the flow can be considered as two dimensional. In this practice you should obtained the form experimental the values of the components of the force FR , but in this case we consider pressure distribution over an aerofoil at different velocity and angles.

OBJECTIVETo measure the pressure distributions on an aerofoil

APPARATUSHM 170 Air Flow Bench Win Tunnel, it was presented in before practice; the same way is use in this case.

Wind Tunnel and HM 170.09 Drag Model "Aero Foil"

Instruments: Manometer, an aerofoil mode with pressure topping on bottom and copper surfaces. Dial gage of pressure.

Technical DescriptionThe aerofoil drag model is intended for usage in the measuring section in the HM 170 Educational Wind Tunnel. The model consists of an aerofoil section made of plastic and mounting bracket made of corrosion-resistant steel. The aerofoil is painted red and is fitted with guide panels at the ends. These ensure that the flow is optimally aligned with the aerofoil. The model is placed in a 2-component force transducer, this indicates the drag force and lift as a measured value when the body is placed in a flow.

Figure 1. Aerofoil

Specification[1] Drag model for experiments on bodies in flows[2] Aerofoil made of plastic, profile NACA 15, lxwxh 100x100x15mm[3] Bracket made of corrosion-resistant steel, d=4mm


66

[4] Force transducer section up to the middle of the model 239mm[5] Model painted in RAL 3000

Technical DataProfile: NACA 15

Dimensions and Weightl x w x h: 100 x 15 x 289 mmWeight : ca. 0.3 kg

THEORYDrag CoefficientA dimensionless value that allows the comparison of drag incurred by different sized and different shaped bodies.

The force on an object due to aerodynamic drag can be calculated using:

where

F = aerodynamic drag force [N]

Cd = drag coefficient

A = frontal area [m2]

ρ = density of fluid [kgm-3]

v = velocity of object relative to fluid [ms-1]

Figure 2. Forces Diagrame

PROCEDURE First we mount the model in the middle of the working section. Then we connect all the pressure topping along the length of bottom and top surfaces

of the aerofoil model to the manometer. And the we set the aerofoil at 10 0C of angle of attack.

After that we measure initial atmospheric pressure acting on the aerofoil before starting the wind tunnel.


67

Finally we started the wind tunnel and measured the pressure at different portion along the aerofoil length.

OBSERVATIONThe measurement to realize should be taken as is shown in the following table:

Table 1. DataThe data collected Calculated as tabulatedX P Patm (Pa) P x_gange (Pa) Cp

in cm of H2O in Pascal 12.n

CALCULATIONSubsequently we shown the example, how we can calculate of the pressure and Cp we can carry out it known the experimental values. To measure pressure distribution in aerofoil, calculate the pressure coefficient.

CP= [ (Px)y – (P)y ] / 0.5 . . U2

Where: (Px)y – Gange pressure at x distance of the aerofoil(P)y - Gange pressure of free stream - Density of airU - Free stream velocityCP - Pressure coefficient

(Px)y = Px_gange - Patm

= Patm / RT Patm- 0.82 mbar R = 287 = 0958 kg/ m3 T= 25 0C = 298 K


68

RESULTS AND DISCUSSION Show the result with help of the graph same as is shown in the following figure 3, with the values calculated.

Figure 3. ResultCONCLUSION You should be boarding the aspect in relation with behavior the Cp and pressure in different positions of the aerofoil.


Cp

X


69

Practical Lab # 9. Assessments of the variance of lift and Drag on an aerofoil via flaps and slats

INTRODUCTIONThe airfoil is tilted with respect to the (undisturbed) flow direction, defined by the angle of attack, α. the airfoil experiences a force FR. The airfoil cross section of an airplane wing is long in the direction perpendicular to the plane of the drawing and the flow can be considered as two dimensional. In this practice you should obtained the form experimental the values of the components of the force FR , but consider assessments of the variance of lift and Drag on an aerofoil via flaps and slats.

OBJECTIVETo find but the effect of flaps and soft on lift and drop control.

APPARATUSHM 170 Air Flow Bench Win Tunnel, it was presented in before practice; the same way is use in this case.

Instruments: Potentiometer Aerofoil models Measurement amplifier Measurement drag an lift force Thermometer

THEORYAn aerofoil is shaped so that air flows faster over the top than under the bottom. There is, therefore, a greater pressure below the aerofoil than above it. This difference in pressure produces the lift.

Figure 1. Aerofoil

The lift generated by a wing is based on the principle that the pressure in a fluid decreases as its velocity increases (Bernoulli′s Principle)

The aerofoil is long in the direction perpendicular to plane of the drawing and the flow can be considered as two dimensional the aerofoil is filled by the angle to the flow direction, defined by the angle of attack, the aerofoil express a force Fr.


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Considering un aero plane it is very useful to decompose the force Fr in component FL and FD perpendicular and parallel to the flow direction FL is the lift force, it carries the plane and by definition it darts not do warp. FD is the drag force, the resistance to be balanced by the propulsion force generated by the engines.The net power required is the product of drag force times flow velocity. The lift and force are expressed (the same way that in before practice) as:

FL= 0.5 C L. .A. C2

FD= 0.5 .C D. A. C2

Where:FL, FD – Lift and drag force.C L ,C D - Lift and drag coefficient.- Density A- Projected areaAn aerofoil is sloped so that air flows faster aver the top than under bottom. There is, therefore a greater pressure below the aerofoil than above it.

Angle of attack is the difference between where the wing pointed and the direction of the air flowing aver the wing.Some values of drag coefficient according to values of Re, shape and area:Circular flat plate

Cd = 1.12 Re ~ 106

A = πd2/4

Sphere Cd = 0.45 Re < 2x106

A = πd2/4

Cd = 0.2 Re > 2x105

A = πd2/4

Solid Hemisphere Cd = 1.17

Re = 103

A = πd2/4

Solid Hemisphere Cd = 0.38

Re = 103

A = πd2/4


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PROCEDURE We mounted the aerofoil models in the middle of the working section by tubing care

of the lever arm of 310 mm of the force balance. Then you adjusted the force at the measurement amplifier to zero with the help of the

off set potentiometer. What we done next it that the wind tunnel started and after the derived wind speed is

reached we settled the aerofoil in the zero angle. This is achieved by turning the holder until the model is directed to zero angle of attack.

After that we measured the drag and lift force at but the measured valve of the drag and lift force is there the condition of four different cases which are aerofoil with but having both the flaps and slats aerofoil having or with flaps, and our up measured for the aerofoil with having slats and aerofoil with both the flaps and the slats. The determination of the force is done by the variation of angle at different position.

At high angle the vibration of the aerofoil is team turbulence. It the vibration amplitude in high stop the experiment.


No. Angle of attack With not slats and flaps

(case 1)

With flaps (case 2) With slats (case 3) With slats and flaps

(case 4)

D L D L D L D L

1. 0 Measurement 0.02 0.1 0.06 -0.27 0.04 0.02 0.08 -0.3

Replica 0.02 0.1 0.06 -0.27 0.04 0.02 0.08 -0.3

2. 5 Measurement

Replica

3. 15 Measurement

Replica

4. 19 Measurement

Replica

Temperature = 26 0C

You can take replicas as in each carry out experiment for obtained more exactly result en performance of the practical.



72

Aph = 0.000125 m2

CALCULATIONDrag Coefficient:A dimensionless value that allows the comparison of drag incurred by different sized and different shaped bodies.

The force on an object due to aerodynamic drag can be calculated using:

where

F = aerodynamic drag force [N]

Cd = drag coefficient

A = frontal area [m2]

ρ = density of fluid [kgm-3]

v = velocity of object relative to fluid [ms-1]

Top of FormAerodynamic Drag

drag coefficient Cd0.45

frontal area, A 0.002 m2

density of fluid, ρ 0.985 kgm-3

velocity, v 5 ms-1

aerodynamic drag force, F 0.0110812 N

You can find the software on line for calculate the drag force following Internet site : http://www.diracdelta.co.uk/science/source/d/r/drag%20coefficient/source.html

With equation,P/ = RT , we have = Pjimma / R T = 0.82 .105 Pa / 287 J/kg. 299 K = 0.955 kg/m3

FD h = Cb h Aph ( C2 / 2) = 9.45 x 10-4 N

FDac = FDmeam - FD h

= FDmeam - 9.45 x 10-4 N

FDmeam = CDmean Ap ( C2 / 2)

Where:


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Ap= 0.01 m2

C= 12 m/sCDmean = 1.1Pjimma = 0.82 barrT= 26 0C

For example, With not slats and flaps, when angle of attack is =00

C L= FL/ Ap. (0.5 . C2) = (0.1/0.01) ( 0.5 . 0.955 . 144)

C L= 0.145C D= (FD - FDh) / ( Ap

. (0.5 . C2) = (0.02- 9.45 x 10-4 N ) / ( 0.01 . 0.5 . 0.955 . 144)C D= 0.02776Then realize the same calculate for each angle of attack with slats and flaps, and the same calculation should be realized with flaps, with slats or with slats and flaps for each angle of attack.

RESULTS AND DISCUSSION You should be present the result in different charts or table (table 2) for different situation and angle of attack, we advise it the following form:

Table 2. ResultsCase 1, 00 50 150 190

CL

CD

Case 2, 00 50 150 190

CL

CD

Case 3, 00 50 150 190

CL

CD

Case 4, 00 50 150 190

CL

CD

Whit theses result that you have obtained of the calculates in each experiment to realized, you can show in the graph CL vs , and CD vs , and realize the comparative analysis over theses resulted obtained.


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0.8

0.6

0.4

0.2

0

-0.2

-0.4

Cd_case 2

Cd_case 3

CL_case 4

CL_case 1

Figure 2. Result CL vs , and CD vs

CONCLUSION With the result of the before point you should arrive to the conclusion on the influence of the employment of one or another model in these carried out experiment.



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Practical Lab # 10. Verification of Bernoulli’s equation

INTRODUCTIONThe experiment demonstrates the use of a Pitot-static tube, and investigates the application of Bernoulli's theorem to flow along a convergent-divergent passage.

OBJECTIVE: The continuity equation and the energy equation (Bernoulli) can be checked in experiments:· Measurement of the dynamic pressure component on constriction of the flow cross-section· Measurement of the static pressure component, related to atmospheric pressure.

APPARATUS:Air Flow Bench, it was presented in practice number 2.Description of Apparatus A duct of rectangular section is fitted to the exit of the contraction which leads from the air box, and liners placed along the inside walls of the duct produce a passage which contracts to a parallel throat and then expands to the original width. The shape of this convergent-divergent passage is indicated on fig. 3.1, from which it may be noted that the convergent portion is shorter than the divergent portion. Air is blown through the passage, and a probe may be traversed along the centre line to measure the distribution of total pressure P and static pressure p. This probe is a Pitot-static probe. Pressure tappings are connected from the air box and from the Pitot-static probe to a multitube manometer.

Figure 1. Arrangement of Apparatus for Experiment on Bernoulli's Equation


76

THEORYThe aim of the experiment is to measure the distribution of total pressure P and static pressure p along the duct and to compare these with the predictions of Bernoulli's equation. Consider how the equation is applied to the present case. Fig. 2 shows the duct as a stream tube.According to Bernoulli's equation the total pressure P, defined by

P = + P (1)

should be constant along this tube, provided the flow is steady and that the air is incompressible and in viscid. If Po denotes the total pressure in the air box, then we should expect the measured value of P along the passage to be everywhere the same asPo, if Bernoulli's theorem is valid for this motion.Now the total pressure P is measured with comparative ease by an open-ended tube facing the flow. Fig. 2 shows a streamline starting from the air box, passing along the duct, and arriving at the mouth of the Pitot tube. The motion is arrested at this point, so that in equation (1) the local value of u

Figure 2. Measurement of Total and Static Pressure

is zero. The pressure recorded by the Pitot tube is therefore the local value of total pressure P. If Bernoulli's equation applies along the whole length of the streamline from

the air box, then P should everywhere be the same as the initial total pressure Po. The value of Po may be found easily from a pressure tapping in the wall, since the air velocityin the box is so slight as to make the difference between total pressure and static pressure

quite negligible.


77

The variation of static pressure p may be measured by the static pressure tube. Fig. 2 shows a further streamline emanating from the air box and flowing close to the surface of the probe. Provided that the holes in the surface of the probe are placed far enough from the tip of the tube as to be unaffected by the disturbance in this locality (which means in practice about 6 tube diameters away from the tip) then the flow is undisturbed by the holes, which therefore measure the undisturbed pressure, viz. static pressure p. To compare the measured values of p with the result of calculations we must use the continuity equation as well as the Bernoulli equation. Taking the flow as one-dimensional, viz. assuming the velocity over any chosen cross-section to be uniform over that section, then the continuity equation for incompressible flow gives the volume flow rate as

Q=uA = utAt (2)

(The suffix t indicates conditions at the throat). The velocity distribution

along the duct may thus be written in the form of the ratio

(3)

and since the depth of the duct is constant, cross-sectional area is proportional _ to

width, so

(4)

The velocity ratio following from continuity may therefore be calculated simply from the dimensions of the convergent-divergent passage. This nowmay be compared with the velocity ratio inferred from pressure distribution

using Bernoulli's theorem. For equation (3.1) gives the local velocity as

(5)

and in particular the velocity ut at the throat is

(6)

so from equations (5) and (6)

(7)

The right-hand side of this equation may be evaluated from the measured pressure distribution and compared with the values from equation (3.4)


78

PROCEDUREThe experimental set-up is placed in the measuring section of the Air Flow Bench. The set-up consists the contraction which leads from the air box, and liners placed along the inside walls of the duct produce a passage which contracts to a parallel throat and then expands to the original width, a Pitot. Air is blown through the passage, and a probe may be traversed along the centre line to measure the distribution of total pressure P and static pressure p. This probe is a Pitot-static probe. Pressure tappings are connected from the air box and from the Pitot-static probe to a multitube manometer.

To measure the distribution of total pressure P and static pressure p along the duct and to compare these with the predictions of Bernoulli's equation, the Pitot tube is set at about 10 mm distance from the surface and the desired wind speed is established by bringing the pressure Po in the air box to

the required value. Now the total pressure P is measured with comparative ease by an open-ended tube

facing the flow. Fig. 3.2 shows a streamline starting from the air box, passing along the duct, and arriving at the mouth of the Pitot tube. The motion is arrested at this point.

The value of Po may be found easily from a pressure tapping in the wall, since the air velocity in the box is so slight as to make the difference between total pressure and static pressure quite negligible.

The variation of static pressure p may be measured by the static pressure tube Readings of total pressure P measured by the Pitot tube are then recorded over the range

of settings should be substantially constant.


No. X, mm P0, N/m2 P, N/m

2 p, N/m2

1 4 800 750 1952 16.5 800 780 353 29 800 785 -130. . . . .. . . . .. . . . .. . . . .16 279 800 780 -9517 304 800 780 25


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CALCULATION

Figure 3. Dimensions of Convergent-Divergent Passage

may vary somewhat from one test rig to another. Any convenient starting value may be chosen, the subsequent calculations being changed accordingly. The values of Bt/B are calculated from the known dimensions of the contraction. For example, in the converging section, when x = 29 mm

B=76- (76- 44) x = 62.7

So Bt/B = 44/62.7 = 0.701and in the diverging section, when x = 204 mm

B=76- (76- 44) x = 59.2

So Bt/B 44/59.2 = 0.74

RESULTS AND DISCUSSIONAir temperature 22°C - 295 KBarometric pressure 1028 mb = 1.028 x 105 N/m2

The profile of the convergent-divergent passage is shown in fig. 3. In table 1.1, measurements of Po, P and p are recorded as the probe traverses along the duct. These pressures are "gauge pressures" i.e. measured relative to atmospheric pressure. Note that the readings of P and p in a single line of the table do not represent the same physical position of the probe, because the static pressure holes lie 25 mm downwind of the tip. By measuring pressures at longitudinal spacings of 12.5 and 25 mm, P and p are obtained at identical stations but at different probe settings. The initial value, x = 4 mm, was a convenient starting point with the particular equipment under test and


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Table 1.1 Total and Static Pressure DistributionsNo. X,

mmP0,

N/m2

P, N/m

2p, N/m

2Bt/B

1 4 800 750 195 0.583 0.5822 16.5 800 780 35 0.643 0.6533 29 800 785 -130 0.701 0.790. . . . . . .. . . . . . .. . . . . . .16 279 800 780 -95 0.613 0.70317 304 800 780 25 0.440 0.653

Fig. 4 and 5 show the results in graphical form. The total pressure P is seen to remain

very close to the air box pressure Po over the whole length of the duct, despite the considerable fluctuation of static pressure p. Bernoulli's equation has therefore been verified for the streamline along the centre of the duct, along which significant

velocity changes take place. The distribution of velocity, measured by the Pitot-static probe, is compared in fig. 5 with the velocity distribution inferred from the continuity equation. In the converging section, the results are almost identical, but in

the diverging section downstream of the throat a steadily increasing discrepancy arises. The air stream is apparently decelerating less quickly than the geometrical shape of the passage would indicate.

It will be seen in a later experiment that a boundary layer forms adjacent to any fixed surface along which air flows, and in this layer the velocity reduces from the free stream value down to zero at the surface. The thickness of the layer increases in the

direction of flow, and it is found experimentally that the growth in thickness is more rapid in regions of rising pressure (i.e. where the main stream is decelerating) than in regions where the pressure is constant. The converse is true; where the pressure falls in

the direction of flow the growth of boundary layer thickness is retarded.

The results presented in fig. 5 are consistent with this concept. In the converging section and the throat, the measured pressures agree closely with those calculated from the variation in duct width so the boundary layer has scarcely any effect. In the diverging section, however, thickening of the boundary layer would give the appearance of the cross-section of the duct enlarging less rapidly than it actually does; the retarded air in the thickening boundary layer presents a partial blockage to the flow.

Fig. 4.


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We may therefore conclude that the experiment as a whole has demonstrated that Bernoulli's equation is sensibly valid along the central streamline of the convergent-divergent duct, since the total pressure has been shown to be virtually constant along its length. The calculated pressure distribution, which depends on the concept of continuity as well as constant total pressure, shows a significant discrepancy from the measured results in the divergent portion, and this may be explained by the growth of boundary layers on the walls of this portion.

Fig. 5.


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QUESTION1. What boundary layer thickness do your results lead you to expect.

Can you infer this from the graph of fig. 5?2. What is the Mach number at the throat of the duct? For approximate

calculation, you may assume that the static pressure and temperaturethere are approximately the same as in the air box. The air velocity atthe throat may be found from the Pitot-static reading, and the acousticvelocity a may be estimated from the equation

in which

: is the ratio of specific heats = 1.4 for air R is the gas constant = 287.2 J/kg

K T: is the absolute temperature in K

3. What difference to the results would you expect if the flow direction were reversed? You may check your prediction by reversing the liners.

4. What suggestions have you for improving the experiment? 5. How might you check whether there is in fact a boundary layer of

significant thickness at exit from the duct? A possible project would beto devise and construct a suitable simple traversing gear for a Pitot tubewhich would measure the velocity distribution. Would it be necessaryto traverse along more than one axis?

CONCLUSION You should realize the analysis according to result and discussion to you will obtain the conclusion of the practice; you can help also with the answer given below.



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Experiment Title: Impact of a Jet

Objective of the Experiment: the objective of the experiment is to: Measure the force generated by a jet of water striking a flat plate and a hemispherical

cup Compare the results with computed momentum flow rate in the jet.

APPARATUS As shown Fig 1, the water supply from the hydraulic bench is led to a vertical pipe, terminating in a tapered nozzle. This produces a water jet which impinges on a vane in the form of a flat plate. The nozzle and vane are contained in a transparent cylinder. An outlet at the base of the cylinder directs the flow to a catch-tank for measuring the flow rate. The vane is attached to a pivoted beam which carries a jockey weight and is restrained by a light spring. The lever may be balanced (as indicated by the tally suspended from it) by placing the jockey weight at its zero position and adjusting the knurled knob above the spring. After this initial adjustment, the force generated by the impact of the jet on the vane may now be measured by moving the jockey weight along the lever until the tally shows that the lever has been restored to its original balanced position. The following quantities are required for data analysis:

Diameter of nozzle = 10 mm Cross-sectional area of nozzle, A = 78.5 mm2 Mass of jockey weight, w = 0.6 kg Distance of vane center to pivot = 0.15 m Height of vane above nozzle-exit, s = 35 mm


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THEORY: FORCE DUE TO THE IMPACT OF A JET Let the mass flow rate in the jet be m. Imagine a control volume V, bounded by a control surface S which encloses the vane as shown. The velocity with which the jet enters the control volume is u1, in the x-direction. The jet is deflected by its impingement on the vane, so that it leaves the control volume with velocity u

2, inclined at an angle β2 to the x-direction.

Now the pressure over the whole surface of the jet, apart from that part where it flows over the surface of the vane, is atmospheric. Therefore, neglecting the effect of gravity, the changed direction of the jet is due solely the force generated by pressure and shear stress at the vane's surface.

If this force on the jet in the direction of x be denoted by Fj, then the momentum equation in the x-direction is:

Fi = m(u

2cos β

2 − u

1)…………………………………….…(1)

The force F on the vane is equal and opposite to this, namely: F = m (u

1 − u

2 cosβ

2 ) …………………………………..….(2)

For the case of a flat plate, β2 = 90°, so that cos β2 = 0. It follows that the force on the flat plate, irrespective of the value of u2 is: F = m u

1

For the case of a hemispherical cup, we assume that β2 = 180°, so that cosβ2 = −1, and F = m(u

1+ u

2) …………….……….(3)

If we neglect the effect of change of elevation on jet speed, and the loss of speed due to friction over the surface of the vane, then u

1= u

2, so

F = 2m u1…………………………..(4)

This is the maximum possible value of force on the hemispherical cup which is just twice the force on the flat plate.

Note that the velocity of the jet just before it hits the plate, uo

is somewhat smaller than the

nozzle-exit velocity u1

due to the deceleration caused by gravity. Using conservation of

energy, neglect head loss, and determine uo

by given u1

and the distance of the plate above

the nozzle-exit (s) is 35 mm.

uo2= u

12 - 2gs

uo

= √( u12 - 2gs) ………………..……….(5)

Momentum flow in jet at impact for flat plate is J, J = m uo

.…………………........(6)

Momentum flow in jet at impact for hemispherical cup is J, J = 2m uo

.……........(7)


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The jockey-weight can be slid along the lever by a distance, x (measured from the zero position at the hinge) so that it creates a clockwise moment about the pivot point that will exactly balance the counter-clockwise moment caused by the impact of the jet. Using the balance of moment for the lever:

F*0.15 = w , where w = 0.6kg and x is in meters, g = 9.81m/s2

=4.0 …………………………………………………………………….(8)Where F is the force on the plate required to balance the lever. This measured value Fdetermined from the moment balance (Equation (8)) should closely match the theoretical value J determined from Equation (6 or 7 depending on cases).

PROCEDURE 1. Balance the lever (as indicated by the tally) with the jockey weight at the zero

position. 2. Admit water into the nozzle by adjusting the bench valve. Increase the flow rate to its

maximum value; record the position of the jockey weight, and measure the flow rate using the catch-tank and the stopwatch

3. Record a total of ten different jockey positions (x) for gradually decreasing flow rates (Q), such that the jockey weight is moved to the left in roughly equal distance. [The best way to set the conditions for reduced flow rate is to place the jockey weight exactly at the desired position, and then to adjust the flow control valve to bring the lever to the balanced position. The condition of balance is thereby found without touching the lever, which is much easier than finding the point of balance by sliding the jockey weight. Moreover, the range of settings of the jockey position may be divided neatly into equal steps.]

4. The experiment should be run twice, first with the flat plate and then with the hemispherical cup.

Experimental data: Flat PlateQty(m3) t(s) x(mm) m(kg/s) u

1(m/s) u

0(m/s) J(N) F(N)

Experimental data: Hemispherical cupQty(m3) t(s) x(mm) m(kg/s) u

1(m/s) u

0(m/s) J(N) F(N)


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DATA ANALYSIS AND DISCUSSION 1. Determine u

1from the measured data and then determine u

0from u

1.

2. Plot rate of momentum flow in Jet, J vs. F, Force on vane. Fit a least-squares line to the data. What is the slope?

3. What do you expect the slope to be? What is the correlation coefficient? 4. If the slope of the above graph is different from what you expected, speculate the

possible reasons that cause the discrepancy. 5. Does the linear fit to the data pass through the origin? If not, why not?

Questions for Further Discussion 1. What would be the effect on the calculated value of the vane efficiency of the following

systematic errors of measurement: a. Mass of jockey weight in error by 0.001 kg. b. Distance L from centre of vane to pivot of lever in error by 1 mm. c. Diameter of water jet emerging from nozzle in error by 0.1 mm.

2. What would be the effect on the calculated force on the flat plate if the jet were to leave the plate not absolutely horizontal, but inclined upwards at an angle of 1°?

3. If the experiment were to be repeated with the vane in the form of a cone with an included angle of 60° (half angle 30°), how would you expect the results to appear on Figure J vs F?


87

Title of the experiment: Forced vortex flows

Objective of the experiment:

To plot the shape of a free vortex by measurement of the surface profile co-ordinates,

and thus vortex that Vr = constant where V is the speed and r is the radius of the

vortex

To plot the surface profiles of various forced vortices formed under different speed

conditions.

Verification of the formula 22

2r

gh

for forced vortices where h is the height of

the surface of the water above the datum point, is the vortex angular velocity and

r is the vortex radius.

Measurement of angular velocity of the water

Calculation of angular velocity

S.No Number of revolution Time taken (sec) Angular velocity

t

N2

1 100

2 100

3 100

Hence, from the table the average angular velocity of the water will be

3321

av


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Observed data

S.No Height of the surface )(cmh Distance from the center )(cmr

1

2

3

4

5

6

Height difference from its maxi with respect to distance from the center

S.No Height difference, )(cmh Distance from the center )( 22 cmr

1

2

3

4

5

6

Observed and calculated value of height, radius and 22

2r

gh

S.No )(cmh )( 22 cmr 22

2r

gh

1

2

3

4

5

6

Discussions and results


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BIBLIOGRAPHY

1. Kreith, F.; Berger, S.A.; et. al. “Fluid Mechanics” Mechanical Engineering Handbook Ed., 1999

2. CHHABRA, P. Non-Newtonian_Flow_in_the_Process_Industries, First published 1999

3. Darby. Chemical Engineering Fluid Mechanics, 2nd Ed. Marcel Drekker, 2001.4. Advanced_Fluid_Mechanics__Course_Notes5. KING, R. P. Introduction to Practical Fluid Flow, First published , 2002.6. White, F.M. Fluid Mechanics 4th Ed, McGraw Hill7. Hodges, P. Hydraulic Fluids, Arnold, 19968. Rosabal, J. Hidrodinámica y Separaciones Mecánicas, Editorial Pueblo y Educación,

La Habana, 1998.9. Díaz, A .Manueal de Hidráulica Aplicada, Santiago de Cuba, 1998.10. Skelland, Non-Newtonian Fluids and Heat Transfer, Edition, 1966.11. Incropera, F.P. Introduction to Heat Transfer, Thirth edition, John Wiley & Son, 199612. DIXON, S. L. (1998). Fluid Mechanics, Thermodynamics of Turbomachinery (4th

ed.)13. Hydraulic Lab Manual, Civil Engineering Department, Faculty of Technology, Jimma

Uiversity, 200414. Adrian Bejan. HEAT TRANSFER HANDBOOK. Duke University Durham, North

Carolina, JOHN WILEY & SONS, INC, 2003.15. Fikirta, Marin, Salomon: Note of Curse Lab Thermo Fluid, Department of

Mechanical Engineering, Jimma University. 16. Markland, E: A first curse in air flow , TecQuimpment, England17. http://www.armfield.co.uk/pdf_files/c2.pdf18. http://insideracingtechnology.com/techstart.htm19. http://www.ae.su.oz.au/aero/contents.html20. http://www.grc.nasa.gov/WWW/K-12/airplane/short.html21. Remedios, P at. el: Thermo Fluid Lab Manual, Jimma University, 2007

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