UNIVERSITI TEKNOLOGI MARA FAKULTI KEJURUTERAAN KIMIAChemical Engineering Laboratory I (CPE 453)NAME:SHEH MUHAMMAD AFNAN BIN SEH HANAFI STUDENT NO:2013210382GROUP:EH2213AEXPERIMENT: BERNOULLIS THEOREM DEMONSTRATION UNITDATE PERFORMED:25th NOVEMBER 2014SEMESTER:3PROGRAMME CODE:EH221SUBMIT TO:SIR RUSMI ALIAS

NO.TitleAllocated Marks (%)Marks

1Abstract5

2Introduction5

3Aims5

4Theory5

5Apparatus5

6Methodology/Procedure10

7Results10

8Calculations10

9Discussion20

10Conclusion10

11Recommendations5

12Reference5

13Appendix5

TOTAL MARKS100

Remarks:Checked by:

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TABLE OF CONTENTSCONTENTPAGE

Abstract 2

Introduction3 4

Objectives4

Theory5 7

Apparatus7

Experimental procedure8 9

Result 10 12

Calculation13 15

Discussion16 17

Conclusion18

Recommendation19

Refrences20

Appendices21

ABSTRACTThis experiment is aimed at investigating the validity of Bernoullis equation when applied to a steady flow of water in tapered duct and to measure the flow rate of steady flow rates. Based on (Bernoullis theorem, 2011) relates the pressure, velocity, and elevation in a moving fluid the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar.For this experiment, by using the FM 24 Bernoullis Apparatus Test Equipment is to demonstrate the Bernoullis theorem. The experiment was conducted in order to find the time taken to collect 3L of water, the volumetric flow rates of the water, the pressure difference at all manometer tube at different cross section. The time to collect 0.003 m3 water is recorded based on the different flow rate for each experiment. The combination of venture meter complete with manometer tube and hydraulic bench were used. During the experiment, water is fed through a hose connector and the flow rate can be adjusted at the flow regulator valve at the outlet of the test section. The venture can be demonstrated as a means of flow measurement and the discharge coefficient can be determined the results show the reading of each manometer tubes increase when the pressure difference increases. From the reading of height can be calculated the data by applied the Bernoulli equation to fin the velocity of the fluid moving.The pressure level and velocity reading for part A to E of the tube is recorded. From Bernoulli theory, the relation between the increase and decrease in the pressure value is inversely proportional to its velocity. Bernoulli's Principle tells that as the fluid flows more quickly through the narrow sections, the pressure actually decreases rather than increases. Thus, it proves the validity of Bernoullis theorem

INTRODUCTIONBernoulli's Principle is a physical principle formulated that states that "as the speed of a moving fluid increases, the pressure within the fluid decreases. Bernoulli's principle is named after the Swiss scientistDaniel Bernoulli. Bernoulli's principlestates that for anin viscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressureor a decrease in thefluid'spotential energy.Bernoulli's principle is named after the Swiss scientistDaniel Bernoulliwho published his principle in his book Hydrodynamicain 1738.( Wikipedia, 2013)Bernoulli's principle can be derived from the principle ofconservation of energy.Bernoullis Principle can be demonstrated by the Bernoulli equation. The Bernoulli equation is an approximate relation between pressure, velocity, and elevation. As a fluid passes through a pipe that narrows or widens, the velocity and pressure of the fluid vary. As the pipe narrows, the fluid flows more quickly. Surprisingly, Bernoulli's Principle tells that as the fluid flows more quickly through the narrow sections, the pressure actually decreases rather than increases. Bernoulli's principle can be explained in terms of the law of conservation of energy. As a fluid moves from a wider pipe into a narrower pipe or a constriction, a corresponding volume must move a greater distance forward in the narrower pipe and thus have a greater speed. Meanwhile, Continuity equation is about in physics is anequationthat describes the transport of aconserved quantity. Continuity equations are a stronger, local form ofconservation laws. (Wikipedia, 2013). However, Bernoullis Principle can only be applied under certain conditions. The conditions to which Bernoullis equation applies are the fluid must be frictionless (in viscid) and of constant density; the flow must be steady , continuous, incompressible, non-viscous fluid flow, the total energy or total head remains constant at all the section along the fluid flow provided there is no loss or addition of energy.

The Bernoulli equation: . + + z = total head=constant (Equation 2.11)Where, = Pressure Head (m) = Velocity or kinetic head (m) (v=Q /A= m/s )Z = Potential head (Height above some assumed level)

OBJECTIVE1. To investigate the validity of the Bernoulli equation when applied to the steady flow of water in a tapered duct. 2. To measure the flow rates with venture meter and to demonstrate Bernoulli. 3. To find the time taken to collect 3L of water, the volumetric flow rates of the water, the pressure difference at all manometer tube, velocity, dynamic head and also the total head4. To determine a steady, continuous, incompressible, non-viscous fluid flow, the total energy or total head remains constant at all the section along the fluid flow provided there is no loss or addition of energy.

THEORYThe FM 24 Bernoullis Apparatus Test Equipment is used to investigate the validity of the Bernoulli equation when applied to the steady flow of water in tapered duct. The apparatus consists of a clear acrylic duct of varying circular cross section, known as a Venturi. The duct has a series of wall tapings that allows measurement of the static pressure distribution along the converging duct, while a total head tube is provided to traverse along the center line of the test section. The venture meter is connected to the manometer with pipes. Wall pressure tapings are provided along the converging and diverging portions of the venturi to measure the static pressure distribution. The reading of the manometer from manometer 1 to manometer 5 shows the pressure head and manometer 6 shows the static head. Flow rate and pressure in the apparatus may be varied independently by adjustment of the flow control valve, and the bench supply control valve.

Tapping PointDistance (mm)Diameter (mm)

A6026

B8321.6

C10516

D148.620

E166.422

F215216

From table above show the positions in mm of the pressure tappings and the dimensions of the cross-section. From this related figure, point A to F is the same along the venture meter. This data is use for to apply in Bernoulli equation and Continuity Equation. The test section is arranged so that the characteristics of flow through both a converging and diverging section can be studied. Water is fed through a hose connector and is controlled by a flow regulator valve at the outlet of the test section. The venturi can be demonstrated as a means of flow measurement and the discharge coefficient can be determined. The tapping point from A to F where the distance from point A to F is increase and the diameter is different for each of them. The common form or bernoullis equation, where is valid at point along a streamline when gravity is constant is the liquid is incompressible which density is constant, along a stream line, the liquid is non-viscous, the flow is steady and the velocity of the liquid is less than the critical velocity for the liquid and there is no loss of energy due to friction.

Bernoullis equation may be written as;

Where,

The terms on the left-hand-side of the above equation represent the pressure head (h), velocity head (hv ), and elevation head (z), respectively. The sum of these terms is known as the total head (h*). According to the Bernoullis theorem of fluid flow through a pipe, the total head h* at any cross section is constant (based on the assumptions given above). In a real flow due to friction and other imperfections, as well as measurement uncertainties, the results will deviate from the theoretical ones. (Kostic, 2001)In our experimental setup, the centre line if the cross sections lies on the same horizontal plane, taken as our datum, z = 0. As all the z value is equal to zero, the equation can be represented as:

This represents the total head at a cross section.In this experiment, the pressure head is denoted as hi and the total head is denoted as h*I, where I represents the cross sections at different tapping points. A1Volume flow rate = A5 Where, A1= and A5=Velocity measurement The velocity of the flow is measured by measuring the volume of the flow, V, over a time period, t. Thus gives the rate of volume flow: Qv = V/t m3/s, which in turn gives the velocity of the flow through a defined are :-

v =

Continuity equation For an incompressible fluid, conservation of mass requires that volume is also conserved. A1V1 = A2V2

APPARATUS

1. Pad of Manometer tubes2. Venturi tube3. Air bleed screw4. Water inlet5. Pump and Pump switch 6. Stopwatch7. Water hosts and tubes8. Water tank equipped with valves, Control Valve and measuring tube9. Hypodermic tube10. Hydraulic Bench 11. Union12. Air Bleed Screw13. Discharge water14. Sump tank15. Volumetric Tank

PROCEDURESGeneral Start-up ProceduresThe Bernoullis Theorem Demonstration (Model: FM 24) is supplied ready for use and only requires connection to the Hydraulic Bench (Model: FM110) as follows:1. The clear acrylic test section was ensured installed with the converging section upstream. The unions tightened and checked. 2. The apparatus located on the flat top of the bench.3. A spirit level was attached to the baseboard and the unit was level on the top of the bench by adjusting the feet.4. The water was filled into the volumetric tank of the hydraulic bench until approximately 90% full.5. The flexible inlet tube was connected using the quick released coupling in the bed channel.6. The flexible hose was connected to the outlet and it directed into the channel.7. The outlet flow control partially opened at the Bernoullis Theorem Demonstration Unit.8. The bench flow control valve, V1 fully closed then the pump switched on.9. V1 was gradually opened and water allowed filling until all air has been expelled from the system.10. All the trapped bubbles was checked in the glass tube or plastic transfer tube. To remove air bubbles, the air were bleed out using a pen or screw driver to press the air bleed valve at the top right side of the manometer board.11. Water flowing into the venturi and discharge into the collection tank of hydraulic bench.12. The water flow rate proceeds to increased it. When all the water flow was steady and there were no trapped bubbles, the discharge valve closed to reduce the flow to the maximum measurable flow rate.13. Water levels in the manometer were in different heights.14. V1 and outlet control valve adjusted to obtain the flow through the test section and the static pressure profile observed along the converging and diverging sections is indicated on its respective manometers. The total head pressure along the venture tube being measured by traversing the hypodermic tube.Note: the manometer tube connected to the tapping adjacent to the outlet flow control valve is used as a datum when setting up equivalent conditions for flow through test section.15. The actual flow rate measured by using the volumetric tank with a stop watch.

General Shut Down Procedures1. Water supply valve and venturi discharge valve closed.2. The water supply pump closed.3. Water drain off from the unit when not in use.

Procedure

1. The general start up procedures was performed.2. Before conducting the experiment, all the manometer tubing was checked to make sure air-bubbles free whether they are properly connected to the corresponding pressure taps. The discharge valve was adjusted to a high measurable flow rate3. After the level stabilized, the water flow rate was measured using volumetric method and record the manometer reading.4. The hypodermic tube that was connected to manometer #H was gently slide so that its end reaches the cross section of the venturi tube at #A. After some time, the readings from manometer #H and #A were noted. The reading shown by manometer #H is the sum of the static head and velocity heads, total head (h*), because the hypodermic tube is held against the flow of fluid forcing it to a stop (zero velocity). The reading in manometer #A measures just the pressure head (hi) because it is connected to the venturi tube pressure tap, which does not obstruct the flow thus measuring the flow static pressure.5. Step 5 was repeated for other cross sections (#B, #C, #D, #E and #F).6. Steps 3 to 6 were repeated at least with three other decreasing flow rates by regulating the venture discharge valve.7. The actual flow Q from the volumetric flow measurement method was obtained.8. The velocity was calculated using the Bernoullis equation where ViB =9. The velocity were also calculated using the continuity equation where, ViC = 10. The difference between the two velocities was calculated.

RESULTExperiment 1Volume (L)3 L

Average Time (s) to collect 20.99 s

Q, Flow Rate (/s)1.429 x /s

Cross sectionUsing Bernoulli equationUsing Continuity equationDifference

#h* = hH(mm)hi(mm)ViB = (m/s)Ai = (m2)Vic =

(m/s)ViB - Vic(m/s)

A1541440.4430.0005310.2690.174

B1521400.4850.0003660.3100.095

C1491040.9390.0002010.7110.228

D1461240.6570.0003140.4550.202

E1451290.5600.0003800.3760.184

F1421320.4430.0005310.2690.174

Experiment 2Volume (L)3 L

Average Time (min) to collect 23.345 min

Q, Flow Rate (/s)1.285 x /s

Cross sectionUsing Bernoulli equationUsing Continuity equationdifference

#h* = hH(mm)hi(mm)ViB = (m/s)Ai = (m2)Vic =

(m/s)ViB - Vic(m/s)

A1761650.4650.0005310.2420.223

B1661530.5050.0003660.3510.154

C1541090.9390.0002010.6390.300

D1381160.6570.0003140.4090.248

E1251100.5420.0003800.3380.204

F1201100.4430.0005310.2420.201

Experiment 3Volume (L)3 L

Average Time (s) to collect 33.498

Q, Flow Rate (/s)8.958 x /s

Cross sectionUsing Bernoulli equationUsing Continuity equationdifference

#h* = hH(mm)hi(mm)ViB = (m/s)Ai = (m2)Vic =

(m/s)ViB - Vic(m/s)

A1731620.4650.0005310.1690.296

B1701570.5050.0003660.2450.260

C1651200.9390.0002010.4460.493

D1631410.4320.0003140.2740.158

E1571420.2940.0003800.2260.068

F1521420.4430.0005310.1690.274

CALCULATIONSExperiment 1:Flow rate of water = 1.429 x /sSample Calculation (cross section A):Bernoulli equation:ViB = ViB = ViB = 0.443 m/sContinuity equation:Ai = Ai = Ai = 5.31 x 10-4 m2Vic = Vic = Vic = 0.269 m/sTherefore, the difference is = ViB - Vic = 0.443 m/s 0.269 m/s = 0.174 m/sThe step are repeated but use data for B, C, D ,E ,F for flow rate 1 only to get difference.

Experiment 2:Flow rate of water = Sample Calculation (cross section A):Bernoulli equation:ViB = ViB = ViB = 0.465 m/sContinuity equation:Ai = Ai = Ai = 5.31 x 10-4 m2Vic = Vic = Vic = 0.242 m/sTherefore, the difference is = ViB - Vic = 0.465 m/s 0.242 m/s = 0.223 m/sThe step are repeated but use data for B, C, D ,E ,F for flow rate 2 only to get difference.

Experiment 3:Flow rate of water = Sample Calculation (cross section A):Bernoulli equation:ViB = ViB = ViB = 0.465 m/sContinuity equation:Ai = Ai = Ai = 5.31 x 10-4 m2Vic = Vic = Vic = 0.169 m/sTherefore, the difference is = ViB - Vic = 0.465 m/s 0.169 m/s = 0.296 m/sThe step are repeated but use data for B, C, D ,E ,F for flow rate 3 only to get difference.

DISCUSSIONFor this experiment, Bernoullis theorem demonstration apparatus along with the hydraulic bench were used. This instrument was combined with a venturi meter and the pad of manometer tubes which indicate the pressure of hA until hF . A venturi is basically a converging-diverging section (like an hourglass), typically placed between tube or duct sections with fixed cross-sectional area. The flow rates through the venturi meter can be related to pressure measurements by using Bernoullis equation. From the result , it is been observed that when the pressure difference increase, the flow rates of the water increase and thus the velocities also increase for both convergent and divergent flow.As fluid flows from a wider pipe to a narrower one, the velocity of the flowing fluid increases. This is shown in all the results tables, where the velocity of water that flows in the tapered duct increases as the duct area decreases, regardless of the pressure difference of each result taken. Bernoullis equation used to calculate the velocityFrom the experiment, to calculate the velocity using the continuity equation as it relates with area. The velocity was calculated with ViC =, where is the volumetric flow rate and is cross sectional area of pipe. From the data, the value of the volume flow rate is calculated based on the 3L volume collected per time in second .After calculated the value is to be for the fast rate for flow rate 1, for the medium flow rate for flow rate 2 and finally for slow flow rate for flow rate 3 by using the Bernoullis equation for velocity The velocity calculated using the Bernoullis equation is higher compare than velocity calculated using the continuity equation. This is because the condition of the velocity taken, for Bernoullis equation, the velocity at stagnation point where the maximum velocity is taken at center of pipe meanwhile for the continuity equation where the velocity is taken by the average velocity. From analysis of the results, it can be concluded that the velocity of the water decrease as the water flow rate decrease. The differences of velocity at cross section are from applying the different equation that is Bernoulli equation and Continuity equation. From the data, it can be conclude that, the diameter of tube influence the differences in velocity of water flow. Based on the calculation made after the experiment, it can be concluded that the diameter of the tube will affect the differences in velocity as a bigger tube will cause the differences in velocity become bigger while the smaller tube cause the velocity differences between ViB and Vic to be smaller.From this experiment there are also happen the major and minor losses in the pipe. The major factor contributed to this loss is sudden expansion and enlargement across the point A to point F. Next, the friction factor also contributed in reducing the pressure inside the pipe. Therefore, it can be concluded that the Bernoullis equation is valid when applied to steady flow of water in tapered duct and absolute velocity values increase along the same channel. Although the experiment proof that the Bernoullis equation is valid for both flow but the values obtain might be slightly differ from the actual value. There are some errors on the results due to happen during the experiment is done. As for parallax error, the observer must have not read the level of manometer properly, where the eyes are not perpendicular to the water level on the manometer. Thus, possibility that the eye position of the readers is not parallel to the scale. Besides that, the error also occurs due to manometer reading which not steady due to water flow through the pipe not properly in stable state.

CONCLUSIONThe increasing velocity of fluid is flowing from a wider to narrower tube and the velocity will decrease in the opposite case regardless of the type of flow and the pressure difference. As the velocity for all cases increases the dynamic head values are also seem to be increased. The pressure depends on the velocity of the flow while velocity is dependent on the diameter of the tube also. Increasing the flow rate leads to increasing the velocity at any point thus will cause the pressure drop. But there are some errors occurred in the results. There might be due to some errors occurred during the experiment. However, the results can be improved if some precautions are taken during the experiment for example the eyes level must be placed parallel to the scale when manometer readings are taken. Besides that, the valve is also need to be controlled slowly to stabilize the water level in the manometer. Furthermore, before conducting the experiment, make sure all the bubble inside the manometer tubes is remove completely .This is due to influence taking the reading of manometer and it also effect the pressure inside the manometer include the velocity flow. The second objective which is to measure flow rates and both static and total pressure heads in a rigid convergent and divergent tube of known geometry for a range of steady flow rates is achieved. As thepressure difference increase, the time taken for 3L water collected increase and the flow rates of the water also increase.Thus, as the velocity of the same channel increase, the total head pressure also increase for both convergent and divergent flow.

RECOMMENDATION Before start running the experiment, make sure the trap bubbles must be removed from manometer tubes to get accurate data by press air bleed valve lightly to allow fluid and trapped air to escape out. Then, the valve must be control carefully to maintain the constant values of the pressure difference as it is quite difficult to control. When taking the reading at manometer, the eye position of the observer must be parallel tothe water meniscus to avoid parallax error. During taking the reading at manometer, the time taken must be accurate with the rising of water volume to avoid error. Beside that, the experiment should be repeat several times to get average values.

REFRENCE

1. Bernoulli's Theorem" from The Wolfram Demonstrations Project retrieved from http://demonstrations.wolfram.com/BernoullisTheorem/ 2. Bernoullis Theorem Demonstration, , Date accessed at 11 November 2013 from http://www.solution.com.my/pdf/FM24(A4).pdf3. Bernoulli Principle ,Date accessed at 11 November 2013 from http://en.wikipedia.org/wiki/Bernoulli's_principle4. Continuity equation Date accessed at 11 November 2013 from http://en.wikipedia.org/wiki/Continuity_equation

APPENDIX

Bernoullis Apparatus Test Equipment

FM 24 Bernoullis Apparatus Test Equipment

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