Fluid Mechanics and Hydraulics...

A Manual for the

Fluid Mechanics and Hydraulics Laboratory

Course Number: CE0931363

Version 1.2 Spring 2010-2011

Khaldoun Shatanawi, PhD Department of Civil Engineering

Faculty of Engineering and Technology University of Jordan

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TABLE OF CONTENTS

Item Page

LAB SAFETY AND CLEANLINESS 3

REPORT WRITING 4

PLAGIARISM INFORMATION 5

EXPERIMENTS

1 CENTER OF PRESSURE ON A SUBMERGED PLANE SURFACE 6

2 IMPACT OF A JET 11

3 TURBULENT PIPE FLOW 16

4 HEAD LOSS IN PIPE LINES 21

5 VENTURI AND ORIFICE METERS 25

6 STEADY UNIFORM FLOW IN OPEN CHANNELS 31

7 SPECIFIC ENERGY AND CRITICAL DEPTH 36

8 THE HYDRAULIC JUMP 45

9 SLUICE GATE 49

10 FLOW OVER A RECTANGULAR AND VEE NOTCHES 54

11 THE CENTRIGUAL PUMP AND PUMP IN SERIES 58

12 THE AXIAL FLOW PUMP 62

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LAB SAFETY AND CLEANLINESS Students are required to handle equipments safely and avoid being victims of hazardous situations. Equipment in the lab is delicate and each piece is used extensively each semester, so if you notice any equipment that is broken or not working probably, you need to notify the lab instructor, who is trained to fix and calibrate the equipments. Do not try to do it yourself, you could injure your self or cause more damage to the equipment. The layout of the equipment in the lab involves resolving a variety of conflicting problems. These include student traffic flow, emergency facilities, exit door locations, etc. Do not change the location of any equipment unless specified otherwise. Distance between adjacent pieces of equipment is determined by locations of floor drains, and by the need to allow enough space around the apparatus of interest.

The lab should always be as clean or cleaner than it was when you entered. Cleaning the lab is your responsibility as a user of the equipment. The lab contains equipment that uses water or oil as the working fluid. In some cases, performing an experiment will inevitably allow the fluid to get on the equipment and floor. If no one cleaned up their working area after performing an experiment, the lab would not be a comfortable or safe place to work in. It’s your responsibility to clean your area after you use the equipment.

4

REPORT WRITING The reports submitted for the Mechanics of Fluid and Hydraulic Laboratory require a formal laboratory report unless specified otherwise. The report should be written in such a way that anyone can duplicate the performed experiment and find the same results as the originator. Reports are due one week after the experiment was performed, unless specified otherwise. The report should be well organized and neatly done. A poorly written report might lead the reader to think that little care went into writing the report or performing the experiment. The calculations shown in the report should contain accurate results; this is done by rechecking the calculations until accuracy can be guaranteed. Formal laboratory format required are as follows:

1. Title Page The title page should contain the title and number of the experiment, the date the experiment was performed, experimenter's name and experimenter's partners' names.

2. Objective This is one of the most important parts of the laboratory report because everything included in the report must somehow relate to the stated object. The objective should be shown as a clear statement.

3. Theory A complete analytical development of all important equations used in the experiment should be presented, with showing how are these equations used in generating the results.

4. Procedure Outline exactly how the experiment was performed. Consider that the procedure that is presented in this current manual might slight be different than what is actually done in the lab, as the lab instructor might make some changes as needed to obtain accurate data. Including schematic drawings of the experimental setup is a plus. If the experiment cannot be duplicated, the experiment shows nothing.

5. Results A data measured must be presented. A formal analysis of the data with tables and graphs is a must. Graphs must be drawn neatly following a consistent format. The outcome of the experiment should be clearly presented. Show how data were used to generate the results by sample calculation.

6. Discussion and Conclusion This section should clearly give an interpretation of the results explaining how the objective of the experiment was accomplished. Also recommend any changes necessary to better accomplish the object. Answer all questions shown at the end of the experiment description as those could be tools to use in discussion and conclusion section.

5

PLAGIARISM INFORMATION (Academic Integrity Policy)

You are attending the Faculty of Engineering and Technology at the University of Jordan in order to learn a field of study and become a professional engineer. Professionals do their own work. They do not copy or borrow work from others, if they do, they will probably get fired. Now, Plagiarism is the lazy way to produce work; you are using someone else’s ideas, figures, tables, charts, diagrams and so forth, even if you recreate or reformat the material, instead of your own. In other words, plagiarism includes the copying of a language, structure, or ideas of someone else’s work, and giving the credit to your self by claming it’s your own work. However, the whole reason you came to university is to learn, and we measure that learning by having you write, in your own words, what you understand. Copying or reproducing previous year’s reports or parts of it, or any report of a fellow student is considered plagiarism, and is not allowed under any circumstances. If any plagiarism case is suspected, all reports involved will get a zero grade on that report. If a student is caught more than once, he/she will receive an F in the course. You should do your own work.

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EXPERIMENT # 1

CENTER OF PRESSURE ON A SUBMERGED PLANE SURFACE

Dams, weirs and water gates are examples of submerged surfaces used to control the flow of water. As submerged surfaces are found in many engineering applications, it is important to have a working knowledge of the forces that act on submerged surfaces. The determination of the magnitude of hydrostatic forces and its point of application is important in the design and is called the center of pressure. Objective: To verify the location of the center of pressure on a plane submerged surface, and to compare the experimental and the theoretical center of pressure. Apparatus: The apparatus are shown in Figures 1.1 and 1.2.

Transparent rectangular water tank that supports a counter balance arm. The counter-balance arm has an adjustable weight at one end and a weight pan at

the other end. Toroidal float: a = 10 cm, b = 7.5 cm, d = 10 cm, and L = 30 cm.

The circular arc top and bottom faces are centered on the pivot so that the resultant hydrostatic force at every point passes through the pivot axis and does not contribute to the moment.

Figure 1.1 Center of Pressure Apparatus

7

mWater Surface

L

yd

F

b

a

CP

Pivot

y/3

Figure 1.2 Schematic Diagram of the Center Point Pressure Appartus-Partial Submersion

Theory: A plane surface located beneath the surface of a liquid is subjected to a pressure due to the height of liquid above it. Increasing pressure varies linearly with increasing depth resulting in a pressure distribution that acts on the submerged surface. The analysis of this situation involves determining a force which is equivalent to the pressure, and finding the location of this force. The point force equivalent to the distributed hydrostatic forces and the location of the force action can be calculated from the following formula:

cggAhF Eq (1) where - density of liquid g - gravitational acceleration A - the area of the submerged plane surface

cgh - distance from the free surface to the centre of gravity of the submerged plane surface

The line of action of the force is normal to the surface and acts through a point known as the center of pressure. For a vertical plane surface, the center of pressure is at a point whose distance below the centroid is given by the formula:

cgcgcp Ah

Ihh Eq (2)

where cph - distance from the free surface to the centre of pressure of the submerged

surface I - the second moment of area (moment of inertia) of the plane surface area

about the horizontal axis

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Partial Submersion: In the case of partial submersion for a rectangular plane (shown in Figure 1.2), we have the following:

2

yhcg ; byA ;

12

3byI

where y - fluid depth b - Toroid float width

From Eq (1) we get:

2

2

1gbyF

where F - Force of float From Eq (2) we get the theoretical center of pressure:

62

12

2 2

3 y

by

byyhcp

yhcp 3

2

Eq (3)

The hydrostatic moment is balanced in this experiment by the moment of the gravitational force due to the mass placed in the balance pan. That is:

mgLM Eq (4) where m - mass placed in balance pan L - distance from the pivot point to the balance pan suspension rod axis

The moment M due to the force F about the pivot is given by:

)(

2 cgcp hhy

daFM

where a - distance from the suspension rod to the top of the float face d - height of the float face

The center of pressure found experimentally could be calculated using:

ydaF

mgLhcp Eq (5)

Complete Submersion: In the case of complete submersion for a rectangular plane (shown in Figure 1.3), we have the following:

9

2

dyhcg ; bdA ;

12

3bdI

From Eq (1) we get:

2

dygbdF

From Eq (2) we get the theoretical center of pressure:

cgcgcgcp h

d

bdh

bdhh

12

12 23

cgcg

cp hh

dh

12

2

Eq (6)

m

Water Surface

L

yd

F

b

a

CP

Pivot

Figure 1.3 Schematic Diagram of the Center Point Pressure Appartus- Complete Submersion

The moment M due to the force F about the pivot is given by:

)(

2 cgcp hhd

aFM

The center of pressure found experimentally could be calculated using:

ydaF

mgLhcp Eq (7)

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Procedure: 1. Make sure that the given values for a , b , d and L are correct. 2. Level the tank, using the adjustable feet in conjunction with the spirit level. 3. Adjust the counter-balance weight until the balance arm is horizontal. This is

indicated on a gate adjacent to the balance arm. 4. Pump water to the Perspex tank until the water is level with the bottom edge of

the toroid, and take the Vernier reading. 5. Place a mass on the balance pan. 6. Raise the water surface in the tank until the balance arm is horizontal again. 7. Note the water level which restores the balance arm to its balanced position using

the Vernier gauge. 8. Add masses to the balance plan in increments of 50 grams, and repeat steps 6 and

7. Experimental Data Sheet

NoMass (gm)

Depth ( y ) (mm)

1 50

2 100

3 150

4 200

5 250

6 300

7 350

8 400 Report: The report should include sample calculations; compile collected data and calculated results in tabular form with column headings.

1. Calculation: compute the following: a. Force on the plain surface of the float b. Theoretical center of pressure ( cph )

c. Experimental center of pressure ( cph )

d. Percentage of error between the theoretical and experimental values of cph

2. Why isn’t the buoyant force taken into account? 3. Why isn’t the weight of the toroid and the balanced arm taken into account? 4. Results and Discussion: In the results section; discuss results, sources of error,

and possible discrepancies with theoretical data.

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EXPERIMENT # 2

IMPACT OF A JET

When a jet of fluid strikes a stationary object it exerts a force on that object. This force can be measured if the object is connected to a spring balance or scale. The measured force can be related to the velocity and flow rate of the fluid. The applications on the impact of jets are found in water turbines which are used to generate power. In the type of water turbine referred to as a Pelton wheel, one or more water jets are directed tangentially to the vanes. The impact of the water on the vanes generates a torque on the wheel, causing it to rotate and to develop power. Objective: To study the force developed by a jet stream of water, as it hits a target and changes direction, and relate it to the change of momentum when the jet strikes the vane. Apparatus: The jet impact apparatus are shown in Figures 2.1 and 2.2. The jet apparatus consists of a vertically upward directed jet nozzle, 10 mm in diameter, a spring-damped impact and weighing assembly, and two interchangeable target vanes of a flat plate and a hemispheric cup with deflection angles a of 90°, and approximately 180°, respectively. The whole apparatus is enclosed in a transparent tank with removable top. The vane is supported by lever which carries a jockey, of 600 gm, and restrained by a spring. The lever maybe set to a balanced position and then adjusting the knurled nut above the spring. The apparatus outlet is connected to a weighting water tank.

Figure 2.1 Impact of a Jet Apparatus

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Figure 2.2 Schematic Diagram of the Impact of a Jet Appartus

Theory: Newton’s second law states that the sum of the external forces on a control volume must equal the time rate of change of momentum. Reynolds transport theorem describes this relation for a deformable control volume. By assuming that the flow is constant with time, and has a uniform density and velocity across the inlet and outlet, a one dimensional momentum equation can be applied. The flow is deflected by an angle, when the fluid, perpendicularly, strikes a vane. The fluid leaves with a new velocity inclined at the angle to the original axis of flow. The one dimensional momentum equation used to calculate the force acting of the fluid and equal to the rate of change of momentum is expressed as:

oj uuQF cos1 Eq (1) where

jF - force on the jet on the original axis of flow

- density of fluid

ou - fluid velocity by which the jet strikes the vane

1u - fluid velocity after the strike

- fluid angle of inclination to the original axis of flow The force on the vane is equal and opposite of the force on the jet, it can be calculated by:

cos1uuQF o Eq (2)

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where F - force on the vane For the case of a flat plate, β = 90º, so that cos β = 0. It follows that:

oQuF Eq (3) For the case of a hemispheric cup, β = 180º, so that cos β = -1. It follows that:

1uuQF o Eq (4) If we neglect the effect of change of peizometric pressure and elevation on jet speed, and the loss of speed due to friction over the surface of the vane, then ou = 1u . Resulting in a

maximum possible value of force on the hemispherical cup being twice the force on a flat plate.

oQuF 2 Eq (5) The impact of the jet maybe measured by moving the jockey weight along the lever a distance Y until the tally shows that the lever has been restored to original (zero) balanced position. Taking moments about the pivot of the lever which is 150 mm away from the center of the vane gives the force exerted on the vane.

YWF 150.0 Eq (6) where F - force on the vane (experimental) in Newton W - weight of jockey weight = (0.60 × 9.81) in Newton Y - distance the jockey is moved to restore balanced position in meters

The velocity at exist of the nozzle is given by:

A

Qu Eq (7)

where u - velocity at nozzle exist Q - fluid flow rate A - cross sectional area of the nozzle = 42D , D is the nozzle diameter

The velocity at which the jet strikes the vane is given by:

gsuuo 222 Eq (8) where g - gravitational acceleration s - height of the vane above nozzle tip = 0.035 m

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Procedure: 1. Level the apparatus and set the lever to the balanced position (as indicated by the

tally), with the jockey weight at its zero setting. 2. Note the weight of the jockey, and the following dimensions: diameter of the

nozzle, height of the vane above the tip of the nozzle when the lever is balanced, and distance from the pivot of the lever to the centre of the vane.

3. Admit water through the supply valve and increase the flow to maximum. 4. The force on the vane displaces the lever; note the location of the jockey which

restates the lever to its balanced position by sliding the jockey weight along the lever.

5. The flow rate is established by collection of water over a timed interval. 6. Further observations are then made at a number reducing flow rates. About eight

readings should suffice. 7. The experiment should be run twice, first with the flat plate and then with the

hemispherical cup. 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. Diameter of nozzle, D = 10.0 mm Cross sectional area of nozzle, A = πD2/4 = 78.5 mm2 = 7.85 × 10−5 m2 Height of vane above nozzle tip s = 35 mm = 0.035 m Distance from centre of vane to pivot of lever = 150 mm Mass of jockey weight, M = 0.600 kg Weight of jockey weight, W = 0.600 × 9.81 = 5.89 N Experimental Data Sheet

No Volume

(L) Time

(s) Y

(mm) Q

(m3/s) 1

2

3

4

5

6

7

8

15

Report: The report should include sample calculations; compile collected data and calculated results in tabular form with column headings.

1. Calculation: compute the following: a. Theoretical forces on the vane b. Actual forces on the vane c. Efficiency ( the ratio between the actual and theoretical forces)

2. Plot the forces on the vane versus the rate of momentum of jet for the flat plate and hemispherical cup, on the same plot. (compare slopes, and explain)

3. What forces are neglected in the analysis, and how significant are they? 4. If the experiment were to be repeated with the vane in the form of a cone with an

included angle of 60°, derive an expression for the force, and explain how would you expect the results to appear if plotted against the rate of momentum of the jet.

5. Results and Discussion: In the results section; discuss results, sources of error, and possible discrepancies with theoretical data.

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EXPERIMENT # 3

TURBULENT PIPE FLOW

The Reynolds number is a dimensionless ratio of inertia forces to viscous forces and is used in identifying certain characteristics of fluid flow. The Reynolds number is extremely important in modeling pipe flow. It can be used to determine the type of flow occurring: laminar or turbulent. Under laminar conditions the velocity distribution of the fluid within the pipe is essentially parabolic and can be derived from the equation of motion. When turbulent flow exists, the velocity profile is “flatter” than in the laminar case because the mixing effect which is characteristic of turbulent flow helps to more evenly distribute the kinetic energy of the fluid over most of the cross section. Objective: To investigate the velocity profile in fully developed turbulent flow using a total head tube. Apparatus: The laminar/ turbulent pipe flow apparatus are shown in Figures 3.1 and 3.2. The working fluid is oil to facilitate tests at low Reynolds numbers. The oil-line unit is essentially a closed loop through which fluid is circulated continuously by a constant-speed gear pump. The oil is drawn from the reservoir and delivered, by way of the lower horizontal pipe, to a perspex settling chamber. From there it passes through a bell-mouth entry into the upper horizontal test pipe. The aluminum pipe has an inside diameter of 19 mm, and an overall length of about 6 m. An adjustable flow distributor exists on the upstream of the pipe to induce turbulence to the flow. Upon leaving the test pipe as a free jet, the fluid is collected in a perspex catch basin, weighted, and thence returned to the reservoir. The pressure gradient is determined by a series of 18 numbered wall pressure taps connected to a manometer. The velocity profile is given by transverses with total head tubes in two directions at right angles in a common transverse plane, near the down stream end.

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Figure 3.1 Laminar/Turbulent Pipe Flow Apparatus

Figure 3.2 Schematic Diagram of the Laminar/Turbulent Pipe Flow Appartus Theory: The fluid velocity profile across the diameter of a pipe can be plotted and measured by means of the pitot traversing gear. Figure 3.3 shows a cross section of a pipe with a pitot tube installed.

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L

dY

Q

h

H

m

NO.10 NO.18

NO.20

g

Static head Total headOil

Figure 3.3 Schematic Diagram of the Pitot tube

OST hhh Eq (1) where

Th - total head

Sh - static head

Oh - dynamic head in m of oil

The velocity V at any given radius r is given by the following formula:

OghV 2 Eq (2)

where V - velocity g - gravitational acceleration

Pressures in the apparatus are measured by a mercury manometer. The corresponding head of oil can be calculated as follows:

Oil

OilmmO hh

where mh - dynamic head in m of mercury = 1820 hh

m - density of mercury at 20º C = 13550 kg/m3

Oil - density of oil at 20º C = 840 kg/m3 Therefore, the actual velocity at any distance (Y ) from the pipe wall is given by:

19

12

Oil

mmghV

For turbulent flow (Re > 4000), the theoretical velocity distribution is given by the following universal logarithmic velocity distribution formula:

C

YVV log75.5 Eq (3)

where V - theoretical velocity at any distance (Y ) from the pipe wall V - shear velocity Y - distance from the pipe wall C - velocity constant

Note that:

Oil

OV

V

C11.0

Oil

where O - shear stress at the pipe wall

- kinematic viscosity - dynamic viscosity

The shear stress at the pipe wall can be calculated from:

OilLO hL

gd 4

Eq (4)

where d - inside diameter of the pipe = 0.019 m L - length of the pipe between pressure tapping No. 10 and No 18. Y - distance from the pipe wall Lh - head loss between two points in the pipe in m oil (No. 10 & 18)

Procedure:

1. Run the apparatus for few minutes to warm up the motor and ensure steady flow conditions.

2. Withdraw the two pitot traverse heads and bleed air from the selling chamber and from all the manometer leads to avoid errors in pressure measurements.

3. Record the readings of the manometer connected to the pressure tapping No. 10, No. 18 and measure the flow rate by timing the collection of oil (30 kg) in the weighting tank.

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4. Adjust the micrometer, connected to the total head tube, to measure at distance Y= 1 mm from the pipe wall

5. Record the readings of the manometer connected to the pressure tapping No. 18 and No. 20.

6. Perform a velocity traverse by adjusting the micrometer and varying Y, and record the manometer reading connected to tap No. 18 and No. 20 at each distance.

Distance between tapping 10 and 18 (L) = 4.014 m Inside diameter of upper tube (d) = 0.019 m Weighted oil = 30 kg = 9.5 × 10-3 Pa.s

Experimental Data Sheet

Time = Head loss between tapping 10 and 18 (hL(10-18)) =

1 2 3 4 …. n

Y (mm)

h18 (mm)

h20 (mm)

hm (mm)

Vmeasured (m/s)

Vtheoretical (m/s) Report: The report should include sample calculations; compile collected data and calculated results in tabular form with column headings.

1. Calculation: compute the following: a. Measured velocity profile b. Theoretical velocity profile c. Plot and compare both profiles

2. Find the distance (Y) at which Theoretical and mean velocities are equal. 3. Results and Discussion: In the results section; discuss results, sources of error,


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EXPERIMENT # 4

HEAD LOSS IN PIPE LINES

Fluids are usually transported through pipes. The frictional losses within the pipe causes pressure drops (head loss). These head losses are a function of various geometric and flow parameters including pipe diameter, length, internal surface roughness and type of fitting. The head loss must be known to determine the pump requirements, if existed on the pipe system, and to study the behavior of the traveled fluid. Head losses that occur in straight pipes and ducts are knows as major losses, while the losses that occur in the system components (fittings) are known as minor losses. Even though, the minor losses can be significant compared to the major losses (i.e. when a valve is closed or nearly closed the minor loss is infinite), this experiment will only deals with the losses that are caused through friction between the pipe and the fluid. The flow is classified as laminar or turbulent depends on whether Reynolds number is greater or less than a critical value. The Reynolds number is extremely important in modeling pipe flow. Objective: To study head loss and friction factor, due to frictional effects (major losses), for laminar and turbulent flow in a smooth pipe over a range of Reynolds number. Apparatus: The laminar/ turbulent pipe flow apparatus are shown in Figures 4.1 and 4.2. The working fluid is oil to facilitate tests at low Reynolds numbers. The oil-line unit is essentially a closed loop through which fluid is circulated continuously by a constant-speed gear pump. The oil is drawn from the reservoir and delivered, by way of the lower horizontal pipe, to a perspex settling chamber. From there it passes through a bell-mouth entry into the upper horizontal test pipe. The aluminum pipe has an inside diameter of 19 mm, and an overall length of about 6 m. An adjustable flow distributor exists on the upstream of the pipe to induce turbulence to the flow. Upon leaving the test pipe as a free jet, the fluid is collected in a perspex catch basin, weighted, and then returned to the reservoir. The pressure gradient is determined by a series of 18 numbered wall pressure taps connected to a manometer. The velocity profile is given by transverses with total head tubes in two directions at right angles in a common transverse plane, near the down stream end.

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Figure 4.1 Laminar/Turbulent Pipe Flow Apparatus

Figure 4.2 Schematic Diagram of the Laminar/Turbulent Pipe Flow Appartus

Theory: Reynolds number is a dimensionless ratio of inertia forces to viscous forces and is used in identifying certain characteristics of fluid flow. It can be computed by:

VD

Re Eq (1)

where Re - Reynolds number V - velocity of the flow D - Pipe inside diameter - fluid density - dynamic viscosity

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The head loss due to wall friction is usually computed using Darcy-Weisbach equation:

g

V

D

LfhL 2

2

Eq (2)

where Lh - head loss

f - friction coefficient L - length of the pipe carrying the flow g - gravitational acceleration

The Darcy-Weisbach friction coefficient is a function of relative pipe roughness, ratio of the pipe surface roughness to its diameter, D , and Reynolds number. For commercial pipes this relation is found in what is known as Moody diagram, which conveniently depicts the variation of friction coefficient over the whole range of Reynolds numbers, and involves relative roughness as a parameter. The Moody Diagram represents one of the major working tools of applied fluid mechanics. In the case of laminar flow (i.e., Re ≤ 2000) the pipe roughness is not a factor, and the friction coefficient can be determined analytically by Hagen-Poiseuille law as:

Re

64f Eq (3)

However, in cases where the flow in hydraulically smooth pipes (i.e., glass, copper, and plastic tubing) is turbulent (4,000 ≤ Re ≤ 100,000), Blasius equation can be used to compute the friction coefficient (an approximation of the von Karman-Prandtl smooth-pipe law):

25.0Re

316.0f Eq (4)

For other cases 2000 < Re < 4000 (transitional flow), or when the turbulent flow is traveling in a rough pipe; Moody diagram must be used to compute the friction coefficient. This may require an iterative solution where a flow rate is guessed, f estimated and than a new flow is calculated. Procedure:

1. Run the apparatus for few minutes to warm up the motor and ensure steady flow conditions.

2. Withdraw the two pitot traverse heads and bleed air from the selling chamber and from all the manometer leads to avoid errors in pressure measurements.

3. Record the readings of the manometer connected to the pressure tapping No. 10, No. 18 and measure the flow rate by timing the collection of oil (30 kg) in the weighting tank.

4. Repeat step number 3 for different flow rates, and make sure that you take several readings for flow in both turbulent and laminar conditions.

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Distance between tapping 10 and 18 (L) = 4.014 m Inside diameter of upper tube (d) = 0.019 m Weighted oil = 30 kg = 9.5 × 10-3 Pa.s Experimental Data Sheet

Oil Mass (kg)

Time (s)

Q m3/s

V m/s

Lh Hg

Lh Oil


1. Calculation: compute the following: a. Experimental head loss b. Experimental friction coefficient c. Theoretical friction coefficient

2. Prepare a log-log plot of your results, i.e., f vs Re (called Stanton diagram). 3. Plot on the same graph the theoretical curves from the equations. 4. Results and Discussion: In the results section; discuss results, sources of error,


25

EXPERIMENT # 5

VENTURI AND ORIFICE METERS

The turbine type meter, the rotameter, the orifice meter, the venturi meter, the elbow meter and the nozzle meter are some of many different meters used in pipe flow. Each meter works by its ability to alter a certain physical characteristic of the flowing fluid and then allows this alteration to be measured. The measured alteration is then related to the flow rate. This experiment will only deals with venturi and orifice meters. In the venturi meter, the fluid is led through a contraction area called the throat. While in the orifice meter the fluid is led to a concentric square edged circular hole in a thin plate that is clamped between the flanges of the pipe. Objective: To investigate and evaluate the operation and characteristics of venturi and orifice flow meters and to determine their coefficients of discharge, through actual results and comparison with theoretical calculations. Apparatus: The flow meter loop apparatus are shown in Figures 5.1 and 5.2. The apparatus is a flow loop with a venturi meter, a square-edged orifice meter, a pump, and a collection tank. The pressure taps around the flow loops are connected before the inlets and at the constriction points of the meters, so that it would be possible to measure pressure differentials at different points around the loop. All pressure tappings are connected to a bank of manometers. Flow of water through the test section is provided by the pump of the hydraulics bench, and the discharge is measured by accumulating flow over a period of time in the volumetric metering tank of the bench.

Figure 5.1 Venturi and Orifice Meter Flow Apparatus

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Orifice Meter Air Bleed Screw

Flow Control Valve

Outlet Pipe

Inlet Pipe

Venturi Meter

Variable Area Meter

Manometer Bank

Figure 5.2 Schematic Diagram of the Venturi and Orifice Meter Flow Apparatus Theory: The venturi meter is constructed as shown in Figure 5.3. It contains a constriction known as the throat. When fluid flows through the constriction, it must experience an increase in velocity over the upstream value because of the smaller cross sectional area at the throat when compared to the upstream pipe. The velocity increase is accompanied by a decrease in static pressure at the throat. The difference between upstream and throat static pressures is then measured and related to the flow rate. The greater the flow rate, the greater the pressure drop. The pressure difference can be found as a function of the flow rate.

Figure 5.3 Schematic Diagram of a Venturi meter A standard square-edged orifice meter is shown in Figure 5.4. The orifice meters consist of a throttling device (an orifice plate) placed into the flow. The accurately machined and drilled plate is mounted between two flanges with the hole concentric with the pipe in which it is mounted. The throttling device creates a measurable pressure difference from

27

its upstream to its downstream side. Pressure taps, one before and one after the orifice plate, are connected to a manometer to measure the pressure drop. The measured pressure difference is then related to the flow rate.

Figure 5.4 Cross Sectional View of the Orfice meter

The Bernoulli equation applies to steady, incompressible flow along a streamline with no heat or work interaction. One form of the Bernoulli equation is

2

222

1

211

22Z

g

V

g

PZ

g

V

g

P

Eq (1)

where 2,1P - static pressures at points 1 and 2 respectively

2,1V - flow velocities at points 1 and 2 respectively

2,1Z - heights at points 1 and 2 respectively, relative to a common datum level

- density of the fluid g - acceleration due to gravity

From continuity, the flow rate is related to the cross sectional area and flow velocity by:

2211 AVAVQ Eq (2) where Q - volume flow rate

2,1A - cross sectional areas of the flow at points 1 and 2 respectively

Because the venturi and orifice flow meters are oriented in a horizontal position, 21 ZZ , the heights cancel out. By combining Eq (1) and (2), Bernoulli's equation then reduces to:

gHAA

AAQTheo 2

22

21

21

Eq (3)

where H - pressure head difference between point 1 and 2 (differential manometers readings across the entry and throat of the meter = 21 hh

for the venturi, and 76 hh for the orifice meter)

28

To take into account frictional energy losses, a discharge coefficient, C , can be added to the equation. This coefficient depends on the pipe geometry and is different for both the venturi and the orifice flow meters. Therefore, the actual discharge can be calculated by:

TheoAct CQQ Eq (4) where C - discharge coefficient (can be obtained by experiment)

For a well design venturi the coefficient of discharge, C , is about 0.98, while for the orifice flow meter it’s about 0.63. On the manometer board, the following can be obtained at each flow rate.

1. Venturi reading Manometer 1 - Manometer 2 2. Loss in Venturi Manometer 1 - Manometer 3 3. Loss in variable area meter Manometer 4 - Manometer 5 4. Orifice plate reading Manometer 6 - Manometer 7 5. Loss in orifice plate Manometer 6 - Manometer 8

Procedure:

1. Record the dimensions of the venturi and orifice meter given on the plates mounted on the apparatus.

2. With the outlet valve open, turn on the pump to admit water to the apparatus through the opened inlet supply valve.

3. Bring the flow meter apparatus into equilibrium by partly closing the outlet valve so that water is driven into the manometer tubes. Then carefully, close both valves so that the flow is stopped while keeping the water levels in the manometer within the range of the manometer scale (between 220-240 mm H2O). The manometers require time to equilibrate so be patient.

4. Level the apparatus by adjusting the leveling screws until the manometers each read the same value.

5. By adjusting the flow control valve on the apparatus, set the flow to 5 l/min and measure the actual flow rate, using the timed volume collection method, (i.e. Qactual= volume/time.)

6. Read and record the pressure heads for manometers 1, 2, and 3, for the venturi meter and 6, 7 and 8 for the orifice meter.

7. Repeat steps 5 and 6 for variable flow rates, minimum of 10, between 5 and 22 l/min as instructed by the lab instructor.

To be performed by the student or instructor whenever needed:

1. In order to disperse air from the orifice plate, partially close and then open the flow control valve several times (never close the flow control valve completely). Leave the flow control valve at a setting so no air bubbles are found downstream of the orifice meter at the lowest flow reading (5 L/min).

2. Set the flow so the variable meter float is pegged out, and open the air bleed screw so water flows through the manometer taps removing the air from the tubing and manometers (It may be necessary to open the bench control valve to

29

help remove all the air). After all the air is removed adjust the bench control valve so the float is pegged out.

3. Close the air bleed screw, connect the hand pump to the fitting and pressurize the pump with one stroke of the handle. Open the air bleed screw cautiously and slowly pump air into the manometer to adjust the water column heights in the manometer so they are all on scale, then close the air bleed screw. The manometers require time to equilibrate so be patient. If any of the manometer readings are off scale, decrease the flow to 22 L/min to bring them back on scale. The system should be ready.

For the venturi meter Upstream pipe diameter = 31.75 mm, hence A1 = 7.92 x 10-4 m2 Throat diameter = 15 mm, hence A2 = 1.77 x 10-4 m2 Upstream taper = 21º inclusive Downstream taper = 14º inclusive For the orifice meter Upstream pipe diameter = 31.75 mm, hence A1 = 7.92 x 10-4 m2 Orifice diameter = 20 mm, hence A2 = 3.14 x 10-4 m2 Experimental Data Sheet Manometer Readings (pressure head in mm H2O) Variable

Area Flow

(l/min)

Volume of

water (L)

Time (sec)

Actual flow rate (m3/sec)

1 2 3 6 7 8

The data above is NOT pressure, but pressure head. Convert to cm. 1ml = cm3. Report: The report should include sample calculations; compile collected data and calculated results in tabular form with column headings.

1. Calculation: compute the following: a. Average coefficients of discharge for both the venturi and orifice meter for

all flow rates.

b. Plot H (horizontally) versus QAct (vertically) and H versus QTheo on the same graph for each of the venturi and orifice meter and find the slope.

c. Plot C versus QAct for each of the venturi and orifice meter.

30

2. For each flow rate, estimate head losses (losses in energy), through the venturi and orifice by using the appropriate manometer relationships. Plot the venturi and orifice head losses, separately, versus dynamic head on one graph. (dynamic head on the x-axis, head losses on the y-axis.) Use QAct in your calculations.

3. Draw a picture of the apparatus such that the venturi, variable area, and orifice meters are along a common datum. Carefully add an Energy Line (EL) and Hydraulic Grade Line (HGL) by using all available information. Note that head loss produces a change in the EL. Label all pertinent distances.

4. Which meter in your opinion is the best one to use? 5. Which meter incurs the smallest pressure loss? Is this necessarily the one that

should always be used? 6. Which is the most accurate meter? 7. What is the difference between precision and accuracy? 8. Results and Discussion: In the results section; discuss results, sources of error,


31

EXPERIMENT # 6

STEADY UNIFORM FLOW IN OPEN CHANNELS

Uniform flow occurs when the flow velocity is the same magnitude and direction at every point in the fluid, while steady flow is one in which the conditions (velocity, pressure and cross-section) may differ from point to point but do not change with time. Steady uniform flow is an idealized concept for open channel flow and is difficult to obtain, even in laboratory flumes. However, for many applications, the flow is steady and the changes in width, depth or direction are so small or occur over a long distance that the flow can be considered uniform. Therefore, steady uniform flow conditions do not change with position in the stream or with time. Objective: To observe the characteristics of uniform flow in open channel and to determine the Manning’s n and the Chezy’s C, and the Darcy- Weisbach friction factor, f. Apparatus: The apparatus are shown in Figures 6.1. The open channel flow apparatus consists of a long tiltable rectangular laboratory perspex channel. It’s equipped with a downstream sluice gate to control the passage of the fluid. A pair of guide rails is positioned above the channel to carry the depth gauges used to measure the depth of flow. A hand wheel is used to tilt the channel bed to the desired slope and a slope scale is attached to the apparatus to verify the adjusted slope. The water is pumped from a sump tank (reservoir) and discharged to the inlet chamber. After passing through the channel, water passes by an adjustable overshot weir to a discharge tank. A flow meter measures the discharge.

Figure 6.1 Open Channel Flow Apparatus – Uniform Flow

32

Theory: In uniform flow conditions, the cross section of the channel and velocities are constant along the channel length. This means that 1y and 2y are equal, and 1V and 2V are equal as well. Also, the channel bed, water surface, and energy line are parallel to one another. Assuming the short reach of length L along the channel between points 1 and 2 is uniform flow with water cross section area A , the body of water contained in the reach is in static equilibrium since there is neither acceleration nor deceleration to the flow. Summing the forces along the reach, the hydrostatic forces, 1F and 2F balance each other, sine there is no change in the depth y between points 1 and 2. The only forces that acts on the reach on the direction of flow, is the gravity component, which is resisted by

the average boundary shear stress o , acting over the PL , where P is the wetted

perimeter of the section (see Figure 6.2). Thus:

PLFWF 021 sin Eq (1)

where 2,1F - hydrostatic pressure forces at points 1 and 2

W - weight of fluid contained in the reach = gAL - angle between the channel bed and horizontal

o - average boundary shear stress

P - wetted perimeter of the section L - length of reach A - water cross section area

L

F

F

y

y1

2Wsin

w

E.L.

E.L.E.L.

1

2

Figure 6.2 Uniform Flow in Open Channel

In this experiment we will assume that oSS , since the angle is small (<5.7º) which

follows that tansin , where S is the slope of the energy line or the energy gradient,

33

and oS is the channel bed slope. However, if is greater than 5.7º, a distinguishing in

the difference between S and oS must be made.

L

hS L sin Eq (2)

where Lh - loss in energy between points 1 and 2

Substituting Eq (2) in Eq (1) and solving for o , yields:

SgRSP

Ag h 0 Eq (3)

where hR - hydraulic radius of he section

We also know that:

2

2

0

VC f Eq (4)

where fC - friction coefficient

V - flow velocity Solving for Eq (3) and (4), and by taking oSS , we get:

oh SRf

gV

8 Eq (5)

where f - conventional friction factor (Darcy-Weisbach friction factor) = fC4

The Chézy equation, used widely for open channels and pipes under pressure, suggests

that the velocity in open channel varies by oh SR . This led to the equation known by his

name:

oh SRCV Eq (6)

where C - Chezy coefficient = f

g8

Applying the continuity equation VAQ , for a rectangular channel, Chézy equation becomes:

2/12/1oh SCARQ Eq (7)

34

Manning found that CChézy is only a function of the roughness of the wall but it is related to the hydraulic radius. He found by experiment that the value of C in Chézy equations varied by almost 6/1

hR . Manning’s equation, one of the best and most widely used

equations for uniform flow in open channels. in SI units is:

2/13/21oh SAR

nQ Eq (8)

where n - friction factor (known as Manning’s n) The Chézy coefficient can be found by:

6/11R

nC Eq (9)

Procedure:

1. Adjust the channel to horizontal position. 2. Insert the sluice gate at the end of the channel and make sure that it’s in closed

position. 3. Start the pump and allow the flow to run through the channel until the channel is

half full, and then turn off the pump and close the inlet valve. 4. In the middle of the channel set the depth gauges 2 m apart. Calibrate the gauges

by taking their readings when they hit the bottom of the channel. 5. Using the hand wheel, tilt the channel bed so that the gauge at the downstream

end reading is 0.5 cm greater than the upstream gauge reading, and find the slope of the channel bed and compare it to the slope given on the channel scale.

6. Start the pump and adjust the sluice gate at the end of the channel and the flow rate to obtain uniform flow depth in the middle of the channel as instructed by the lab instructor (i.e. depth of flow about 1 cm) and wait few minutes to ensure uniform flow conditions.

7. Measure the flow rate and depth. 8. Repeat step 7 for different flow rates as instructed by the lab instructor. 9. Repeat step 7 for different slopes and different flow rates as instructed by the lab

instructor.

35


No Lh (mm)

Q (m3/s)

y(mm)

V (m/s)

1

2

3

4

5

6

7

8 Report: The report should include sample calculations; compile collected data and calculated results in tabular form with column headings.

1. Calculation: compute the following: a. Chézy coefficient C from Eq (7)

b. Manning’s n from Eq (8) c. Darcy- Weisbach friction factor, f from Eq (5) d. Reynolds number, Re

2. Plot the following for all cases: a. Clog versus hRlog (confirm Eq (9) and find the average value of n )


Part A 36

EXPERIMENT # 7 PART A

SPECIFIC ENERGY AND CRITICAL DEPTH

USING SLUICE GATE

In the laboratory, open channel flow experiments can be used to simulate flow in a river, in a spillway, in a drainage canal or in a sewer. Such modeled flows can include flow over bumps or through dams, and flow through a venturi flume or under a partially raised sluice gate. This experiment involves making appropriate measurements for flow under a sluice gate, and relating flow rate to critical depth. The flow rate, critical depth, and specific energy are determined theoretically and experimentally. Objective: To analyze the energy relationships in the transition of flow from subcritical flow to supercritical flow in an open channel. Apparatus: The apparatus are shown in Figures 7.1a. The open channel flow apparatus consists of rectangular laboratory perspex channel, 4 m wide. A centrifugal pump draw water from a sump tank (reservoir) and discharges it through the discharge line to a flow meter and then to the head tank (inlet chamber), which incorporate an over flow to return excess water to the sump tank and a stilling device to provide satisfactory conditions in the working section. A sluice gate is installed at the upstream end of the apparatus working section, while a tail gate is provided at the downstream end. A pitot tubes (total head) and a piezometers (static pressure tapping) are used to record measurements from the working section. After passing through the channel, water passes by an adjustable overshot weir to a discharge tank. A flow meter measures the discharge.

Figure 7.1a Open Channel Flow Apparatus with Sluice gate

Part A 37

Theory: Flow in a channel is modeled in terms of a parameter called the specific energy head of the flow, E. For any cross section shape, the specific energy head at a particular section is determined as the energy head referred to the channel bed as datum. The specific energy head is the sum of the depth of flow and the velocity head, assuming that the slope of channel, and head loss is zero. The specific energy head is defined as:

g

VyE

2

2

Eq (1)

where E - specific energy head of flow y - depth of flow V - flow velocity g - gravitational acceleration

Applying the continuity equation ( VAQ , where A is the wetted cross sectional area), and for a rectangular channel, the total specific energy can be expressed as:

22

2

2 bgy

QyE Eq (2)

where Q - volume flow rate b - channel width

A plot of the specific energy head versus the flow depth is called the specific energy diagram (shown in Figure 7.2a). For a constant discharge Q , there are two different y values for a given specific energy head E . These are known as alternate depths. The two alternative depths represents two totally different flow regimes; slow and deep on the upper limp of the curve and fast and shallow on the lower limp of the curve. In the figure, it can be seen that at a point the specific energy is minimum and only a single depth occurs. At this point the flow is critical. The flow for which the depth is less than critical is supercritical flow, and the flow for which the depth is greater than critical is subcritical. Supercritical velocity is greater than critical velocity, and subcritical velocity is less than critical velocity.

Figure 7.2a Specific Energy Diagram

Part A 38

A relation for critical depth in a wide rectangular channel can be found by differentiating E of Eq (2) with respect to y for which E is minimum, Thus:

23

2

1bgy

Q

dy

dE Eq (3)

and when E is minimum, cyy and 0dy

dE, Eq (3) can be reduced to:

232 bgyQ c or 3/1

2

2

gb

Qyc Eq (4)

where cy - critical depth (at that point E is minimum)

Substituting Q in Eq (2) by Eq (4), for the condition of minimum specific energy head, we get:

cc yEE2

3min or min3

2Eyc

where minE - minimum specific energy head at critical flow

Also, the discharge is maximum when cyy , therefore, Eq (4) can be used to solve for

maximum discharge, that is 23max bgyQ c .

Procedure:

1. Adjust the channel to horizontal position and start the pump. 2. Allow the flow to run through the channel for few minutes to ensure stability. 3. Insert a sluice gate and, initially, adjust its opening, gatey to 20 mm.

4. Adjust the inlet valve so that 1y = 220 mm. (This will result in a constant discharge).

5. Measure the average Q by taking several readings, and measure the flow

corresponding 1y , 2y , and 2E . 6. Repeat step 5 as you gradually raise the sluice gate as instructed by the lab

instructor (i.e. Adjust the sluice gate to an opening of 50 mm and a 1y value of 20 mm)

7. Adjust the flow as instructed by the lab instructor (i.e. 1y is 180 mm and then

readjust to 1y is 150 mm) and repeat step 5.

Part A 39

No gatey

(mm) 1y

(mm) 2y

(mm) 2E

(mm) Calculated 1E

(mm) Calculated 2E

(mm)

1

2

3

4

5

6

7


1. Calculation: compute the following: a. Specific energy head at the head tank, 1E

b. Critical depth, cy

c. Minimum specific energy head, minE 2. Plot the following:

a. The specific energy head E versus the flow depth y , and determine cy

and minE and compare to the calculated results.

b. Measured 2E versus calculated 2E 3. Results and Discussion: In the results section; discuss results, sources of error,

and possible discrepancies with theoretical data. 4. What is the significance of Froude number?

Part B 40

EXPERIMENT # 7 PART B

SPECIFIC ENERGY AND CRITICAL DEPTH USING RAISED BED

In the laboratory, open channel flow experiments can be used to simulate flow in a river, in a spillway, in a drainage canal or in a sewer. Such modeled flows can include flow over humps or through dams, and flow through a venturi flume or under a partially raised sluice gate. This experiment involves making appropriate measurements for flow over a locally raised bed (hump), and relating flow rate to critical depth. The flow rate, critical depth, and specific energy are determined theoretically and experimentally. Objective: To study the effects of a streamlined hump on the flow and to analyze the energy relationships in the transition of flow from subcritical flow to supercritical flow in an open channel. Apparatus: The apparatus are shown in Figures 7.1b. The open channel flow apparatus consists of rectangular laboratory perspex channel, 4 cm wide. A centrifugal pump draw water from a sump tank (reservoir) and discharges it through the discharge line to a flow meter and then to the head tank (inlet chamber), which incorporate an over flow to return excess water to the sump tank and a stilling device to provide satisfactory conditions in the working section. A sluice gate is installed at the upstream end of the apparatus working section, while a tail gate is provided at the downstream end. Three pitot tubes (total head) and three piezometers (static pressure tapping) are used to record measurements from the working section. After passing through the channel, water passes by an adjustable overshot weir to a discharge tank. A flow meter measures the discharge.

Figure 7.1b Open Channel Flow Apparatus with a Hump

Part B 41

Theory: Flow in a channel is modeled in terms of a parameter called the specific energy head of the flow, E. For any cross section shape, the specific energy head at a particular section is determined as the energy head referred to the channel bed as datum. The specific energy head is the sum of the depth of flow and the velocity head, assuming that the slope of channel, and head loss is zero. The specific energy head is defined as:

g

VyE

2

2

Eq (1)

where E - specific energy head of flow y - depth of flow V - flow velocity g - gravitational acceleration

Applying the continuity equation ( VAQ , where A is the wetted cross sectional area), and for a rectangular channel, the total specific energy can be expressed as:

22

2

2 bgy

QyE Eq (2)

where Q - volume flow rate b - channel width

In the case of a humped channel bottom, critical depth does not always occur, and all depths are controlled by the tailgate. When the flow upstream of the hump is subcritical, there will be a slight depression in the water surface over the hump. This depression is caused by the decrease in 2y that occurs with the drop in the specific energy 2E , for a

constant flow rate. The decrease in 2y exceeds the decrease in 2E and therefore a depression in the water surface over the hump occurs (See Figure 7.2b). Further increase in hump height creates further depression of the water surface over the hump until finally the depth of the hump becomes critical, and is called critical hump height criticalZ . If the

hump height is increased beyond critical height, critical depth remains at the hump and the depth upstream of the hump increases until it gains sufficient energy to be able to flow with the same flow rate. This is called damming action, where the flow downstream of the hump is supercritical, and the flat top hump acts as broad crested weir. Before reaching minE conditions, 1y is independent of 2Z , however, after reaching the minimum

conditions 1y is independent of the tail water condition.

Part B 42

yy y21 3

E.L E.L

z2

Q

Figure 7.2b Schematic Diagram of a Humped Channel Bottom A plot of the specific energy head versus the flow depth is called the specific energy diagram (shown in Figure 7.3b). The condition of the flow is represented by the solid line with arrows showing how the flow changes from subcritical to supercritical. At the location on the hump the height is 2Z , and the energy head is 2E . For a constant discharge Q , there are two different y values for a given specific energy head E . These are known as alternate depths. The two alternative depths represents two totally different flow regimes; slow and deep on the upper limp of the curve and fast and shallow on the lower limp of the curve. In the figure, it can be seen that at a point the specific energy is minimum and only a single depth occurs. At this point the flow is critical. The flow for which the depth is less than critical is supercritical flow, and the flow for which the depth is greater than critical is subcritical.

Figure 7.3b Specific Energy Diagram As water flows over the hump, the initial specific energy head 1E is reduced to a value E by an amount equal to the height of the hump. So at any location along the hump, the

Part B 43

specific energy head is 21 ZE , where 2Z is the elevation above the channel bed. A relation for critical depth in a rectangular channel can be found by differentiating E of Eq (2) with respect to y for which E is minimum, Thus:

23

2

1bgy

Q

dy

dE Eq (3)

and when E is minimum, cyy and 0dy

dE, Eq (3) can be reduced to:

232 bgyQ c or 3/1

2

2

gb

Qyc Eq (4)

where cy - critical depth (at that point E is minimum)

Substituting Q in Eq (2) by Eq (4), for the condition of minimum specific energy head, we get:

cc yEE2

3min or min3

2Eyc

where minE - minimum specific energy head at critical flow

Procedure:

1. Adjust the channel to horizontal position and start the pump. 2. Adjust the tailgate height as instructed by the lab instructor (i.e. 75 mm). 3. Allow the flow to run through the channel for few minutes to ensure stability. 4. Adjust the inlet valve so that as instructed by the lab instructor (i.e. 1y = 110 mm)

This will result in a constant discharge. 5. Measure the average Q by taking several readings, and measure the flow

corresponding 1y , 2y , 3y , 1E , 2E , and 3E .

6. Repeat step 5 as you gradually raise the bed in 5 mm increments, maintaining the flow rate constant, as instructed by the lab instructor.

7. Adjust the flow as instructed by the lab instructor, and repeat step 5.

Part B 44


No Q

(m3/s) 2Z

(mm) 1y

(mm) 2y

(mm) 3y

(mm) 1E

(mm) 2E

(mm) 3E

(mm) 1

2

3

4

5

6

7


1. Calculation: compute the following: a. Specific energy head at each section b. Critical hump height, citicalZ

c. Critical depth, cy

d. Minimum specific energy head, minE

e. 21 ZE and compare with 2E and minE 2. Plot the following:

a. The specific energy head E versus the flow depth y , and determine cy

and minE and compare to the calculated results.

b. 1E versus 2Z

c. 2E versus 2Z 3. Results and Discussion: In the results section; discuss results, sources of error,

and possible discrepancies with theoretical data. 4. How is the second term in Eq (2) related to Froude number, and what is the value

of the Froude number in the experiment?

45

EXPERIMENT # 8

THE HYDRAULIC JUMP

When spillways or other similar open channels are opened by the lifting of a gate, liquid passing below the gate has a high velocity and an associated high kinetic energy. Due to the erosive properties of a high velocity fluid, it may be desirable to convert the high kinetic energy (e.g. high velocity) to a high potential energy (e.g., a deeper stream). The problem then becomes one of rapidly varying the liquid depth over a short channel length. Rapidly varied flow of this type produces what is known as a hydraulic jump. Objective: To study the force and energy conditions in a hydraulic jump. Apparatus: The apparatus are shown in Figures 8.1. The open channel flow apparatus consists of rectangular laboratory perspex channel, 4 cm wide. A centrifugal pump draw water from a sump tank (reservoir) and discharges it through the discharge line to a flow meter and then to the head tank (inlet chamber), which incorporate an over flow to return excess water to the sump tank and a stilling device to provide satisfactory conditions in the working section. A sluice gate is installed at the upstream end of the apparatus working section, while a tail gate is provided at the downstream end. Three pitot tubes (total head) and three piezometers (static pressure tapping) are used to record measurements from the working section. After passing through the channel, water passes by an adjustable overshot weir to a discharge tank. A flow meter measures the discharge.

Figure 8.1 Open Channel Flow Apparatus

46

Theory: The short transition from fast flow to slow flow is accompanied by considerable energy loss and is known as the hydraulic jump. Figure 8.2 shows a side view of the hydraulic jump. It also shows the upstream flow depth ( 1y ), the downstream flow depth ( 2y ), and

the pressure distribution upstream ( 1P ) and downstream ( 2P ).

E.L

E.L

Sluice Gate

Subcritical

PV

P V y

1 1

22

y1

2

Figure 8.2 The Hydraulic Jump The location of the hydraulic jump is determined by the fast flow control on the upstream side and the slow flow control on the downstream side, in association with energy losses due to viscous resistance which also affect the depths in the fast and slow lengths. The friction forces acting are neglected because of the short length of the channel involved and therefore the only significant forces are hydrostatic forces. No analysis can be based on the equality of the total heads at both sides of the jump. However, a force balance of the control volume would include only the pressure forces. Applying the momentum equation in the flow direction to the volume of fluid gives:

122211 QVQVAPAPFX Eq (1)

where XF - the sum of external forces on the body of fluid in the horizontal direction

A - rectangular cross section area = by (where b is the channel width) P - pressure on the centroid of the cross section - density of fluid Q - flow rate

1V - flow velocity upstream the jump

2V - flow velocity downstream the jump

Pressure in the above equation represent the pressure that exists at the centroid of the cross section, where for rectangular horizontal channel the vertical depth to the centroid

ch equals 2

y , therefore,

2

ygP and cghF . Also, the flow q per unit width can

be used ( bqQ ) where b is the width of the channel. The above equation becomes:

47

1222

11

22VVqy

gyy

gy Eq (2)

where 1y - depth of the fluid upstream the jump

2y - depth of the fluid downstream the jump

g - gravitational acceleration q - flow rate per unit width

Since the flow rate is constant before and after the jump the continuity equation shown below is used:

QVAVA 2211 , thus qVyVy 2211 Eq (3) By substituting for 2V and and q from Eq (3) in Eq (2) and by rearranging and solving Eq (2) yields:

0)(2

)( 22

21

2

21

12

1 yyg

y

yyV Eq (4)

After simplifying the above equation and by solving for 1

2

y

y by the quadratic formula,

keeping only the positive roots, yields:

21

1

21

1

2 8112

11

81

2

1Fr

gy

V

y

y

Eq (5)

where 1Fr - Froude number at point 1 = 1

1

gy

V

The depths 1y and 2y are known as the conjugate depths. As y increases with distance downstream of the sluice gate, its conjugate depth decreases. The jump occurs where the conjugate depth 2y , coincides with the slow flow depth which is controlled in this case

by the tailgate. The head loss ( Lh ) caused by the jump is the drop in energy, therefore:

g

Vy

g

VyEEhL 22

22

2

21

121 Eq (6)

For rectangular channels, the head loss associated with the hydraulic jump can be computed by:

21

312

4 yy

yyhL

Eq (7)

48

Procedure: 1. Adjust the channel to horizontal position and start the pump. 2. Allow the flow to run through the channel for few minutes to ensure stability 3. Insert a sluice gate and, initially, adjust its opening as instructed by the lab

instructor (i.e. 20 mm). 4. Adjust the inlet valve as instructed by the lab instructor (i.e. 1y = 230 mm). 5. Create a hydraulic jump in the center of the working sections by adjusting the tail

gate. 6. Measure Q , and it corresponding 1y , 2y , 1E , and 2E using the attached ruler. 7. By adjusting the sluice gate and tail gate, vary the upstream height, downstream

height, and record the measurements on the different jumps. Experimental Data Sheet

No Q

(m3/s) 1y

(mm) 2y

(mm) 1E

(mm) 2E

(mm) 1

2

3

4

5

6

7


1. Derive the applicable equations in detail and substitute appropriate values to verify the predicted downstream height and lost energy (compare the measured upstream height to the calculated downstream height).

2. Compute ch , and verify that 21 yhy c .

3. Calculation: compute and plot relevant graphs, such as: a. 2

cghF and yhc

b. chE and chy

c. Froude number ( 1Fr ) and 12 yy d. Momentum diagram. A momentum diagram is a graph of liquid depth on

the vertical axis versus momentum on the horizontal axis. 4. Results and Discussion: In the results section; discuss results, sources of error,


49

EXPERIMENT # 9

SLUICE GATE

A sluice gate is a device used to measure and control flow in an open channel. Sluice gates are commonly used to control water levels and flow rates in rivers and canals. They are also used in wastewater treatment plants and to recover minerals in mining operations. Water depths can be measured upstream and downstream of the sluice gate to calculate the hydrostatic pressure force. By measuring the flow rate, the momentum equation can be applied to calculate the horizontal force acting on the sluice gate. This experiment involves making appropriate measurements for flow under a sluice gate. Objective: To apply Bernoulli equation to determine the discharge underneath a gate and determine the coefficient of discharge, and to use the momentum equation to calculate the thrust force on a gate. Apparatus: The apparatus are shown in Figures 9.1. The open channel flow apparatus consists of rectangular laboratory perspex channel, 4 cm wide. A centrifugal pump draw water from a sump tank (reservoir) and discharges it through the discharge line to a flow meter and then to the head tank (inlet chamber), which incorporate an over flow to return excess water to the sump tank and a stilling device to provide satisfactory conditions in the working section. A sluice gate is installed at the upstream end of the apparatus working section, while a tail gate is provided at the downstream end. Three pitot tubes (total head) and three piezometers (static pressure tapping) are used to record measurements from the working section. After passing through the channel, water passes by an adjustable overshot weir to a discharge tank. A flow meter measures the discharge.

Figure 9.1 Open Channel Flow Apparatus – Sluice Gate

50

Theory: The discharge underneath a sluice gate is an example of converging flow where there is negligible friction loss and Bernoulli equation is applicable. The total head at section 1 and 2 in Figure 9.2 is equal to:

2

222

1

211

22Z

g

V

g

PZ

g

V

g

P

Eq (1)

where 2,1P - static pressures at points 1 and 2

2,1V - flow velocity at points 1 and 2

2,1Z - heights at points 1 and 2, relative to a common datum

g - gravitational acceleration - density of the fluid

E.L

Sluice Gate

y

1y

2

E.L

V2ygate

Figure 9.2 Flow Under a Sluice Gate Assuming a horizontal bottom where 21 ZZ , and by applying the continuity equation ( VAQ , where A is the wetted cross sectional area), for a rectangular channel:

222

2

2221

2

122 bgy

Qy

bgy

Qy Eq (2)

where Q - volume flow rate

2,1y - depth of flow at points 1 and 2

b - channel width Solving for the flow rate yields:

1

2

1

2

12

y

y

gybyQi

Eq (3)

51

where iQ - ideal volume flow rate at points 1 and 2

2,1y - depth of flow at points 1 and 2

b - channel width The actual flow rate is less than the ideal flow calculated from Eq (2); this reduction in flow is caused by the viscous resistance between points 1 and 2, and is accounted for by using a coefficient vC . Also, in the case of free flow, the down stream depth 2y maybe

expressed as a fraction of the gate opening gatey by using a coefficient of contraction cC ,

where gatec yCy 2 . Therefore the actual flow rate can be calculated by:

ivcact QCCQ Eq (4) where

actQ - actual flow rate

cC - coefficient of contraction

vC - coefficient to account for the effect of friction and velocity of approach

The above equation can be rewritten as:

1

2

1

1

y

yC

gybyCCQ

gatec

gatecvact

Eq (5)

where gatey - height of the gate opening

Absorbing the effects of flow contraction, friction, velocity of approach, and the downstream depth into an experimental flow coefficient, a simple discharge equation for flow under a sluice gate is obtained:

12gyACQ dact Eq (5)

where dC - coefficient of discharge (sluice coefficient)

A - the area of the gate opening = gateact byA

Values of dC are a function of gatey , and 1y , and are usually between 0.55 and 0.6 for

free flow, but are significantly reduced when the flow conditions downstream cause submerged flow. The force on a sluice gate may be computed by considering the horizontal components of external forces acting on the control volume shown in Figure 9.3. A force balance of the control volume would include the pressure forces, the viscous shear force on the bed and the thrust of the gate. The shearing force is neglected over the short smooth bed of the channel. Applying the momentum equation in the flow direction to the volume of fluid gives:

52

122211 QVQVFAPAPF gX Eq (6)

where XF - the sum of external forces in the horizontal direction

A - rectangular cross section area = hb (where b is the channel width) P - pressure on the centroid of the cross section

gF - force on the gate

- density of fluid Q - flow rate

1V - flow velocity upstream the gate

2V - flow velocity downstream the gate

yF

F

Fy

g1

2

1

2

E.L E.L

Figure 9.3 Forces on a Sluice Gate Pressure in Eq (6) represent the pressure that exists at the centroid of the cross section,

where for rectangular horizontal channel the vertical depth to the centroid equals 2

y ,

therefore,

2

ygP . Eq (6) can be rewritten as:

12

222

21

11

2

1

yyb

QyygbFg

Eq (7)

where 2,1y - depth of flow at points 1 and 2

b - channel width The pressure distribution on the gate is not hydrostatic since for hydrostatic conditions, the pressure must be atmospheric at the upstream water level and at the point where jet springs clear of the gate. However, the thrust force, HF computed by assuming hydrostatic pressure distribution on the gate can be found by:

2212

1yygbFH Eq (8)

where HF - the gate thrust force assuming hydrostatic pressure distribution

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Procedure: 1. Adjust the channel to horizontal position. 2. Insert the sluice gate about 1 m from the inlet end, and adjust its opening, gatey to

20 mm. 3. Lower the downstream to the bottom. 4. Start the pump and allow the flow to run through the channel for few minutes to

ensure stability. 5. Adjust the inlet valve so that 1y = 230 mm. (This will result in a constant

discharge). 6. Measure the average Q by taking several readings, and measure the flow

corresponding 1y , 2y . 7. Repeat step 6 as you gradually raise the sluice gate as instructed by the lab

instructor (i.e. Adjust the sluice gate to an opening between 20 mm and 40 mm) 8. Repeat step 6 by adjusting the flow rate as instructed by the lab instructor while

maintaining 1y at 230 mm and gatey between 20 mm and 40 mm. Experimental Data Sheet

No Q

(m3/s) gatey

(mm) 1y

(mm) 2y

(mm)

1

2

3

4

5

6

7


1. Calculation: compute the following: a. vC , cC , and dC

b. gF , and HF

2. Plot the following for all cases: a. vC and cC versus 1/ yygate

b. Hg FF / versus 1/ yygate

3. Where are sluice gates found and what are they used for? 4. Results and Discussion: In the results section; discuss results, sources of error,


54

EXPERIMENT # 10

FLOW OVER A RECTANGULAR AND VEE NOTCHES

In open channels, flow rate can be regulated or measured by introducing an obstruction into the flow. A simple obstruction, called a weir, consists of a vertical plate extending the entire width of the channel. The plate may have an opening, usually rectangular, trapezoidal, or triangular. Other configurations exist and all are about equally effective. Objective: To observe the characteristics of flow over a rectangular, and Vee notches and to determine their discharge coefficients. Apparatus: The apparatus are shown in Figures 10.1 and 10.2.

Hydraulic Bench Hook and point Gauge Stop watch Rectangular notch, and Vee notch

The Vernier hook and point gauge is mounted on the instrument carrier which is located on the side channels of the molded top. The carrier maybe moved along the channels to the required measurement position. The rectangular notch weir or Vee notch weir to be tested is clamped to the weir carrier in the channel by thump nuts.

Figure 10.1 Flow Over Rectangular and Vee Notch Apparatus

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L

H

Crest of weir

Weir Plate Weir Plate

Crest of weir

L

H

Figure 10.2 Rectangular and Vee Notch Plates

Theory: By applying Bernoulli’s equation, for the conservation, to a flow model of a rectangular notch weir, the theoretical discharge for the total ideal flow can be found by:

2/323

2LHgQi Eq (1)

where iQ - total ideal discharge

g - gravitational acceleration L - rectangular crest length (breath of the rectangular notch) H - height of water above the crest

The actual flow over the weir will be less than the idea flow, because the effective flow area is smaller than LH due to flow drawdown from the top and contraction of the nappe from the crest below (See Figure 10.3). Therefore, the coefficient of discharge is introduced to allow for the differences between the simplified flow model and the ideal flow situation.

2/323

2LHgCQ d Eq (2)

where Q - discharge

dC - coefficient of discharge

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H

P

VelocityDistribution

Roller

Crest

Nappe

Drawdown

Figure 10.3 Flow Over a Rectangular Plate In the case of modeling flow over a Vee notch (triangle weir), the theoretical discharge for the total ideal flow can be found by:

2/5

2tan2

15

8HgQi

Eq (3)

where - vertex angle of the vee notch Introducing the coefficient of discharge, the actual flow over the vee notch can be found using:

2/5

2tan2

15

8HgCQ d

Eq (4)

Note that the Q - H relationship (discharge curve) can be described by an empirical

formula nKHQ , where K and n are constant that depends on the notch shape and dimensions. Therefore:

HnKQ logloglog Eq (5) Procedure:

1. Insert the stilling baffle into the slots in the sides of the channel of the hydraulic bench.

2. Insert the rectangular weir on the upstream side and fit the weir tightly by using thump nuts in order to prevent leakage to occur.

3. On the instrument carrier, place the hook and point gauge on the channels’ side adjacent to the weir plate installed.

4. Start the pump and open the water supply and allow water flow over the weir. (i.e. H is not equal to zero).

5. Adjust the water supply make the water level become steady. Let the water flow over the weir and wait until steady state of flow is reached.

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6. Adjust the Vernier height gauge to a datum reading where its pointer just touches the water surface. Set the reading to be zero so that the bottom of the notch is taken as the datum. Make sure the Vernier does not slide during the experiment until all data have been recorded.

7. Position the top gauge half way between the notch plate and stilling baffle. Open the water supply slowly, wait at least one minute allowing the flow to stabilize. Measure the head (H) by the Vernier.

8. Determine the flow rate by taking the volume of water using the volumetric tank and recording the time.

9. Repeat steps 7 and 8 by using different flow rates; adjust the flow rates so that the measured head (H) increases 1 cm for each flow rate. Make sure that you record 8 readings of flow rate and corresponding head.

10. For flow over a Vee notch, follow same procedures described above except that a Vee notch, instead of a rectangular notch, should be installed to the hydraulic bench.

Breadth of rectangular notch = 3 cm Vertex angle of the Vee notch = 90º Experimental Data Sheet

No Head (mm)

Volume (L)

Time (s)

Flow (m3/s)

1 2 3 4 5 6 7 8


1. Calculation: plot the following: a. Actual Q versus H b. logQ versus log H

c. dC derived from the actual flow versus H

2. Compute the discharge coefficient and head term exponent from the discharge curve and compare to the relationships explained in the theory section.


58

EXPERIMENT # 11

THE CENTRIGUAL PUMP AND PUMP IN SERIES

The purpose is to convert energy of an electric motor or turbine into velocity or kinetic energy and then into pressure energy of the fluid that is being pumped. The fluid enters the pump impeller along or near to the rotating axis and is accelerated by the impeller, flowing radially outward into a volute chamber, from where it exits into the downstream piping system. It uses a rotating impeller to increase the pressure of the fluid. Centrifugal pumps are commonly used to move liquids through a piping system, especially for large discharges through smaller heads. Objective: To study the performance characteristics of a centrifugal pump, and the performance of pumps in series. Apparatus: The apparatus are shown in Figures 11.1 and 11.2. The centrifugal pump is connected to a pipe that is connected to a water tank. A pressure gage is connected before the pump inlet to measure vacuum or suction pressure at the inlet of the pump. Also, a pressure gauge is connected to the pipe after the pump to measure the discharge pressure at the outlet of the pump. The flow rate is measured by a flow meter. A mechanical variable pitch speed controller is connected to the motor to vary the speed of the pump, and a digital tachometer reads the impellers’ revolution in rpm. The centrifugal pump consists of three parts; an inlet duct, an impeller, and a volute. The apparatus consists of two geometrically similar pumps of 140 mm and 100 mm impeller diameter. The two pumps will be used when conducting the pumps in series part.

Figure 11.1 Center of Pressure Apparatus

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Impeller

Suction Eye

Volute Casing

Vanes

Bearing Rotating Shaft

Impeller Vane

Inlet

Discharge

Casing

Figure 11.2 Cross Section of a Centrifugal Pump Theory: When the pumps starts, the fluid enters the suction nozzle and then into center of the impeller (suction eye). As the impeller rotates, it spins the fluid sitting in the cavities between the vanes outward and provides centrifugal acceleration. As the fluid leaves the eye of the impeller, low pressure is developed, causing continuous flow into the pump inlet. Figure 11.2 shows a cross section of a centrifugal pump indicating the movement of the fluid. Same in the axial flow pumps, the head developed by a pump is determined by measuring the pressures on the suction and discharge sides of the pump. The velocities are computed by measuring the discharge and dividing it by the respective pipes’ cross areas. Therefore, the net head delivered by the pump to the fluid is:

1

211

2

222

22Z

g

V

g

PZ

g

V

g

PH

Eq (1)

where H - head developed by the pump 2,1P - pressure head at the suction side and delivery side of the pump

2,1V - velocity at the suction side and delivery side of the pump

2,1Z - elevation at the suction side and delivery side of the pump - density of fluid g - gravitational acceleration

Note that, in the current apparatus, the pressure head is measured in bars; and 1 bar = 510 (N/m2).

Usually the intake pipe is larger than the discharge pipe. However in the current apparatus the discharge and suction pipes are the same size, therefore the velocity heads cancel out. Also, the assumption is made that both the suction side and delivery side are

60

on the same elevation, resulting in neglecting the elevation head. The net total head can be expressed by:

510

g

PH

Eq (2)

where P - pressure head ( 12 PP ) The total power output, in watts, of the pump is equal to the production of the pump total pressure and the volumetric flow rate:

gQHoutputPower Eq (3) where Q - flow rate

The power input, in watts, from the dynamometer is given by:

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2 NFrinputPower

Eq (4)

where - Torque - angle velocity F - force (measured load on motor in Newton) r - torque arm = 0.178 m N - impeller speed (rpm)

The total power output of the pump is equal to the production of the pump total pressure and the volumetric flow rate:

%,inputPower

outputPowerEfficiencyMechanical Eq (5)

The purpose of connecting pumps in series is to keep the same flow rate, but change the head. This can be used in cases to reduce the initial cost of the pumps, or when the pump can’t deliver the desired head.

Pump 1 Pump 2Q QQ

Figure 11.3 Pumps in Series

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Procedure: 1. Start by making sure that the valve between both pumps is closed, and the outlet

and inlet valve for each pump are fully open. 2. Turn on the power for each pump and set the impellers’ speed to 3000 rpm using

the control knob. 3. For each pump, separately, measure the flow rate, and pressure head before and

after the pump. 4. Partially close the outlet flow valve to reduce the flow rate and record the new

flow rate along with the pressures before and after the pump. 5. Repeat step number 4 for different flow rates, until the flow is minimal. 6. After taking several readings for each pump separately, connect both pumps in

series and repeat step number 4. Experimental Data Sheet

No. Pump 1 Pump 2 Pumps 1 and 2 (Series)

1P 2P 1Q 4P 5P 2Q 1P 5P 2Q

1 2 3 4 5 6 7 8


1. Calculation: compute and plot relevant graphs, such as: a. Q and H for each pump, separately. b. Q and H for setup pump in series. Include and compare both curves for

experimental and theoretical results. 2. Where should the pump be located? 3. When should we use pumps in parallel versus pumps in series? 4. Results and Discussion: In the results section; discuss results, sources of error,


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EXPERIMENT # 12

THE AXIAL FLOW PUMP

An axial flow pump, also known as propeller pump, is a common type of water pump that essentially consists of a propeller in a tube. Axial flow pumps use the propeller action of the impeller’s vanes to draw water into the pump by developing pressure (suction). The fluid is discharged axially; pumping the liquid in a direction that is parallel to the pump shaft. These pumps have the smallest of the dimensions among any of the conventional pumps and are more suited for low heads and higher discharges. Axial flow pumps are usually used as circulation pumps that work in conjunction with sewage digesters or evaporators, high volume mixing applications. They may also be submersible, and are common in irrigation and drainage applications. Axial flow pumps are typically used in high flow rate, low lift applications. Their main advantage is that they can easily be adjusted to run at peak efficiency at low-flow/high-pressure and high-flow/low-pressure by changing the pitch on the propeller. Objective: To study the performance characteristics of an axial flow pump. Apparatus: The apparatus are shown in Figures 12.1 and 12.2. An axial flow pump has a high specific speed and is usually compact in construction; it usually contains three sets of blades, in which the first set is called the inlet guide blades and it exists to allow the fluid to flow axially into the pump, however in this present apparatus, this set of blades does not exists since its constructed to allow fluid to approach in an axial direction. The second set of blades is the rotator blades, where in pumps they are called impellers. Four impellers are placed on a propeller and are set to an angle of 30º that can be adjusted if needed. The third set of blades is the outlet blades which are used to adjust the flow to an axial direction as required by the apparatus setup. A flow meter and pressure gauges are used to measure the flow rate and pressure at various points, respectively. The revelation of the impeller in rpm is measured automatically and shown on a digital tachometer. The engine is connected to a scale force that measures the force in Newton.

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Figure 12.1 The Axial Pump Apparatus

Impeller

Outlet Guide Blade

Q

Figure 12.1 Blades of the Axial Pump

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Theory: The purpose of the inlet blade is to guide the incoming flow axially so that it enters without velocity of whirl. The rotor blades impart a whirl and hence recover the head equivalence of this velocity thus increasing the head down stream of the pump. The head developed by a pump is determined by measuring the pressures on the suction and discharge sides of the pump. The velocities are computed by measuring the discharge and dividing it by the respective pipes’ cross areas. Therefore, the net head delivered by the pump to the fluid is:

1

211

2

222

22Z

g

V

g

PZ

g

V

g

PH

Eq (1)

where H - head developed by the pump 2,1P - pressure head at the suction side and delivery side of the pump

2,1V - velocity at the suction side and delivery side of the pump

2,1Z - elevation at the suction side and delivery side of the pump - density of fluid g - gravitational acceleration

Note that, in the current apparatus, the pressure head is measured in bars; and 1 bar = 510 (N/m2).

Usually the intake pipe is larger than the discharge pipe. However in the current apparatus the discharge and suction pipes are the same size, therefore the velocity heads cancel out. Also, the assumption is made that both the suction side and delivery side are on the same elevation, resulting in neglecting the elevation head. The net total head can be expressed by:

510

g

PH

Eq (2)

where P - pressure head ( 12 PP ) The total power output, in watts, of the pump is equal to the production of the pump total pressure and the volumetric flow rate:

gQHoutputPower Eq (3) where Q - flow rate

The power input, in watts, from the dynamometer is given by:

60

2 NFrinputPower

Eq (4)

where - Torque - angle velocity F - force (measured load on motor in Newton)

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r - torque arm = 0.178 m N - impeller speed (rpm)

The total power output of the pump is equal to the production of the pump total pressure and the volumetric flow rate:

%,inputPower

outputPowerEfficiencyMechanical Eq (5)

Procedure:

1. Make sure all vales are open and turn on the motor in the control cabinet. 2. Turn the control knob to the required speed of 2000 rpm. 3. Set the outlet angles blade to 0º. 4. Set the rotor blade to 30º. 5. Adjust the lower left hand valve for changing the discharge pressure. 6. Record pressures, flow rates, and torque for various discharge pressure for the

given speed. 7. Turn the control knob to 2500 rpm and repeat steps 5 and 6 8. Turn the control knob to 3000 rpm and repeat steps 5 and 6


No. 2000 rpm 2500 rpm 3000 rpm

1P 7P Q F 1P 7P Q F 1P 7P Q F 1 2 3 4 5 6 7 8


1. Calculation: compute and plot relevant graphs, such as: a. Q and H b. Q and outputPower c. Froude number (Q ) and inputPower


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