FINAL REPORT SKPU 1711FLUID MECHANICS LABORATORY 2011/2012-SEM 2

EXPERIMENT 4

TITLE OF THE EXPERIMENT FLOW MEASUREMENT DATE OF EXPERIMENT 27TH FEBRUARY 2012

LAB INSTRUCTORASSOC. PROF. ABDUL RAZAK ISMAILSECTION 09GROUP 4NO.TEAM MEMBERSMATRIC NO.

1.MOHD SYUKUR ARIFF BIN MAIDINA11KP0053

2.MOHD RAMZI BIN ABDUL RASIDA11KP0050

3.MOHD AZLIN BIN CHE ALANGA11KP0060

4.FARS MAHMOUD HASSENA11KP4004

5.RAMIN SHIRAZI FIROOZ

TABLE OF CONTENTSContents Page 4.1 INTRODUCTION34.2 LITERATURE REVIEW/THEORY 54.3 METHODOLOGY74.3.1 Apparatus 74.3.2 Experiment Procedures 85 RESULTS 96 DISCUSSION 117 CONCLUSION158 REFERENCES169 APPENDICES 17

4.1 IntroductionA system generally is adapt from the Bernoulli principle. These experiment want to shows that the pressure of the fluid will be decrease when the velocity of the fluid is rises gradually. For an example when the fluid flows from the narrow spaces, the velocity of the fluid will be increase, but the pressure is vice versa to it. In anozzleor other constriction, thedischarge coefficient(also known ascoefficient of discharge) is the ratio of themass flow rateat the discharge end of the nozzle to that of an ideal nozzle which expands an identical working fluidfrom the same initial conditions to the same exit pressures

Objectives of this experiment wanted to showed students on how to determine and compared the coefficient of discharge, Cd for a flow measurements device. For example orifice plate and venturi meter. These measurement is primary important to measure the rate flow of fluid in many system. There are various of flow measuring devices, the one commonly used is being flows into obstacle device. Such flow meters, are depends on the principle that changes in the static pressure or dynamic pressure(pressure drop or head) can be related to the change in the cross-sectional area of the flow. The relationship between flow rate and pressure difference can be showed in Bernoulli equation, that is assuming changes in elevation, work and heat transfer are negligible.For an orifice plate, is a restriction with an opening smaller than the pipe diameter which inserted in the pipe, the typical orifice plate has a concentric, sharp edge opening, as shown in the figure below.

Because of the smaller area of the fluid, the velocity will be rises, causing a vise versa in the pressure that will be decrease. Flow rate can be calculated from the measured pressure drop across the orifice plate, P1-P3. The orifice plate commonly used flow sensor, but it creates a large non-recoverable pressure due to the turbulence around the plate, leading to high energy consumption.Venture meter is similar to an orifice meter, but it is designed nearly eliminate boundary layer separation, and then form a drag. The changes in cross-sectional area in venture tube causes a pressure changes between the convergent section and the throat, and the flow rate can be determined from the drop of pressure. Whenever it is more expensive than an orifice plate, the venture tube introduce lower non-recoverable pressure drops.

4.2 TheoryVenturi meterThe Bernoulli equation can be applied to by referring point 1 and 2. The analysis for the equation for flow rate can be derived:

where:Qththeoretical volumetric flow rate (m3/s)A1cross sectional area at 1 (m2 )A3cross sectional area at 3 (m2 )h1height of manometer column 1 in meters (m )h3height of manometer column 3 in meters (m )

The discharge coefficient defined as the ratio of the actual flow rate, Qact over theoretical flow rate Qth : Coefficient of discharge, Cd = Qactual / Qtheoritical

This equation can be written as:Log Qact = Log n + a Log To find the the n and hence Cd experimentally, using a graph Log Qact vs Log

Orifice meterFor the orifice plate diagram, the Bernoulli equation can be applied at point 1 and 3. From the analysis, the equations for flow rate can derived as:Volumetric flow rate:

where:Qththeoretical volumetric flow rate (m3/s)a cross-sectional area of plate (m2 ) m ratio of cross-sectional area of plate to pipe, (a/A)h difference in height of manometer column (m)

Discharge coefficient defined as the ratio of actual volume flow rate to theoretical volume flow rate :Coefficient of discharge, Cd = Qactual / Qtheoritical

4.3 Methodology 4.3.1 Apparatus The apparatus consists of manometer at in the middle of the water outflow level and the variable head outlet tank. The orifice meter or the venturi meter is placed in between the both outflow water level and the variable head outlet tank. Besides to the outlet pipe have outlet pipe that was for control the water level in the variable head outlet tank. Water is supplied from the lab faucet (supply valve) to the inlet of the apparatus via a hose. Water flowing through the nozzle strike the flat plate and deflects from the flat plate and falls to the base of the clear Plexiglas tube where it exit and drain in the sink.

VENTURI/ORIFICE METERPUMP SWITCHCONTROL VALVEMANOMETERWATER OUTFLOW LEVELOUTLET PIPEFLOW MEASUREMENT APPARATUSWATER VOLUME INDICATORWATER RESERVOIR VALVECONSTANT HEAD INLET TANKVARIABLE HEAD OUTLET TANK

Figure 4.3.1 orifice meter and venturi meter

4.3.2 Procedure

1. The apparatus was set up as shown in the figure. The outlet pipe variable head outlet tank had to elevate. The pump then had to turn on until the water start to flow into the pipe at the constant head inlet tank.2. The flexible tubing to the manometer have to connect, then ensured that connection are free from air bubbled or air pack in the flexible tube during the flowing of the water.3. By adjusting the outlet pipe at the variable head outlet tank, we could determine the height of water at variable head outlet tank. The height will be constant, so at that time we have to record the pressure reading on the manometer. For orifice plate meter, we have to take the H1, H2, and H3, H4. This is for D and D/2, upstream and downstream. For venture meter, took the reading H1 and H2 only.4. After the reading had taken, closed the water reservoir/sump valve to obtain flow rate (Q), and when the volume attained at 2 liters, start the stopwatch until the volume of water reached at 7 liters. The total volume of the water is 5 liters.5. Next, used 3 different height of water for further reading. Follow step 3 and 4. Both procedures can be performed simultaneously when the height of the water became constant.6. Finally closed the controlled valve during the completion and then turned off the pump switch. Remembered did not to forget to clean all the apparatus that had been used, and dry it.

4.4 ResultTable below show the data for venturi meter and orifice plate meter respectively.

Venturi meterVolume water collected(Litre)Time (second,s)H1(mm)H2(mm)(m)Qtheo(m3/s)x 10-3Qact(m3/s)x 10-3Cd,theoLog

LogQactual

5.030.074983420.1560.140.171.21-0.01-3.77

5.024.754882640.2240.170.201.18-0.65-3.70

5.022.064541780.2760.190.231.21-0.56-3.64

5.020.13452900.3620.220.251.14-0.44-3.60

D1 = 20.4 mm D3 = 10.0 mm

Orifice plate meterThese orifice has two different method of pressure drop measurement cross the orifice plate.i. Upstream pressure point where the orifice plate equal to the diameter of the test pipe (D) and downstream pressure is where its distance is equal to radius of pipe (D/2)ii. Both upstream and downstream pressure/tapping point at the corner are positioned immediately perpendicular to the orifice plate.

D = 22.0 mm and D/2 = 12.0 mm

Pressure heads at D and D/2 tappings

Volume water collected (litre)Time (second,s)h1 @ D(mm)h2 @ D/2(mm)(m)Qtheo(m3/s)x 10-3Qact(m3/s)x 10-3Cd,theo

5.0295403700.1700.0930.1721.849

5.0275003100.1900.0980.1851.888

5.0235002400.2600.1150.2171.887

5.0204901800.3100.1260.2501.984

Pressure heads at the upstream and downstream corners corner tappings

Volume water collected (litre)Time (second,s)h3 @ up-stream(mm)h4 @down-stream(mm)(m)Qtheo(m3/s)x 10-3Qact(m3/s)x 10-3Cd,theo

5.0295052900.2150.1050.1721.638

5.0274952900.2050.1020.1851.814

5.0234902800.2100.1030.2172.107

5.0204702800.1900.0980.2502.551

Example of Calculationa) Venturi MeterFor the first data, i) Time t = 31.16 sii) Volume v = 5 liter = 0.005 m3iii) Qactual = 0.005m3/31.16 = 0.1605x 10-3 m3/siv) H = h1 - h2= ( 497 -343 ) mm = 0.154 mv) Qtheo = 7.854x10-5 [ 2(9.81)( 0.410) (1-(7.854x10-5 /3.2685x10-4)2 ] = 0.15663 x 10-3 m3/s

vi) Cd = Q actual Q theo = 0.2073 x10-3 0.72568 x 10-3 = 0.2857vii) log Qactual = log 0.2073 x 10-3 = -0.6834viii) log H = log 0.410 = -0.3872 Value for the next data also use the same method as above.

b) Orifice Plate Meter Pressure Heads at D and D/2 tappings For the first data, i) Time t = 84 s ii) Volume v = 5 liter = 0.005 m3 iii) Qactual = 0.005 m3 84 s = 0.0595 x 10-3 m3/s iv) H = h1 - h2 = ( 525 - 360 ) mm = 0.165 m

v) Qtheo = 452.3893 [2(9.81) 0.165) (1-(452.3893/546.6321)]

= 0.4598 x 10-3 m3/svi) Cd = 0.0595 x 10-3 0.4598 x 10-3 = 0.1294

Value for the next data also use the same method as above.

Pressure Heads at the Upstream & Downstream Corners Corners Tappings i) Qactual = 0.0595 x 10-3 m3/sii) H = h3 - h4 = ( 526 -362 ) mm = 0.164 m iii) Qteori = 452.3893 [2(9.81) 0.164) (1-(452.3893/546.6321)]

= 0.4584 x 10-3 m3/siv) Cd = Qactual Qtheo = 0.0595 x 10-3 0.4584 x 10-3 = 0.1298 Value for the next data also use the same method as above.

4.5 Discussion

The graph is plotted. By comparing this equation of Log Qact = Log H + Log n, where n = with the graph plotted, is linearly increasing to and the graph obtained is a linear graph. This proved that the graph plotted is correct. Next, the gradient from the equation is 0.5 while the gradient obtained from the graph is 0.5461. The theoretical gradient value and the gradient value obtained from the graph are slightly different. While the y-intercept obtained from the graph is -3.3432. From y-intercept, we are able to calculate the value for as below:

Log n = = -3.3432-3.3432 = Log = 0.9672Average = = 1.0648

However, the calculated and average values are slightly different. Thus, the overall result that we obtained for venturi meter is incorrect. This is due to some errors made while conducting the experiment and also errors that might come from the apparatus been used in experiment. This will further discuss in question (v).

The graph of Qact against h for method D and 1/D and method upstream and downstream is plotted.

Theoritically,

,

thus the graph can also be expressed as

Qact =MX+c, m =.

For the D and 1/2D tappings method, the m=1.3539, therefore;

=1.3539 = 1.3539 = 1.3539 =1.081For method D and 1/2D, the average coefficient discharged Cd is, Average = = 1.750For method upstream and downstream, the average coefficient discharged Cd is,Average = = 1.570The value of both average coefficient discharged Cd for method D and 1/2D and upstream and downstream is different to each other which are 1.750 and 1.570. The different value is can be caused by some errors that done during the experiment such as the reading of outlet pipe that is not perpendicular to our eyes. Other error is might be come from the apparatus.

Based on the experimental results, venturi meter have more losses compared to orifice meter. This venturi meter losses should be low due to steam line shape of the diffuser however our experimental data deviate from the fact. From the observation, venturi meter have lower Cd compared to orifice meter. So, venturi gives less accurate measurement because its coefficient of discharge, Cd is lower compared to orifice meter.

Based on the experimental results, which flow meter gives more accurate measurement. Briefly explain your choice.

Based on the result obtain from experiment, the most accurate flow meter reading is venturi meter. Because the ratio of the actual flow rate / theoretical flow rate for average is just marginally exceeding 1. This show that the reading data got during experiment is not accurate data .Compared to orifice plate meter which is ratio is exceeded 1 by a large margin, this show that there might be some errors when conducting the experiment as the actual flow rate is so much different from theoretical flow rate.

Source of Errors and Limitations in the ExperimentSystematics error like error with the apparatus. The flexible tube have an air buble inside it. Therefore, it will affect the reading of the height of the manometer.The surface of the manometer ruler is not clear. It confius the reader want to read the scale. As a result, the reading was not precise.Human error also one of the errors happen in the experiment. There is limitation in the time response in human, the observer may not start and stop the stopwatch simultaneously when the water level is reaching.

Recommendations

1. The parallax error can be reduced by putting a white paper behind the ruler to make the water meniscus be seen more clearly 2. Before start the experiment, we have to ensure that the air bubble in the flexible tube completely null. So it will gave the precise readings.3. Make sure the scale of the ruler is in good condition. So the readers would get the precise readings.4. The rate of flow of water must be in a steady flow for a constant velocity at nozzle.5. All the apparatus is made sure in good condition before the experiment start.In order to obtain a more accurate result, some repetition while taking the reading can be done and average value is calculated.

4.6 ConclusionThe objective of this experiment was to determine and compared the coefficient of discharged, Cd for a series of flow measuring devices.

The following conclusions can be drawn from this experiment: 1- As it can be observed from the data obtained that, the logarithm value for Qactual is directly proportional with the increasing logarithm value for h2- The experimental slopes of graphs are seen to be deviate from the theoretical value Cd.3- The coefficient discharged,Cd can be measured by the slope of the Qactual versus 4- The height of the manometer reading will be effect the coefficient discharged, Cd5- Qtheoritical is inversely proportional to coefficient discharge, Cd. so the higher the Qtheoritical, the lower the Cd.

However, this experiment involved with some errors which affect the accuracy of the result, hence, a group suggested some recommendations to get more accuracy during handling this experiment.

4.6 References

1. R. L. Daugherty and J. B. Franzini,Fluid Mechanics, 6th ed. (New York: McGraw-Hill, 1965). pp. 338-349.

2. http://mysite.du.edu/~jcalvert/tech/fluids/orifice.htm

3. http://en.wikipedia.org/wiki/Orifice_plate

1.

4.7 Appendices1. Cross sectional area = 2 = x 0.012 = 3.14159 x 10-4 m2

2. Flow rate theoretical, = (3.14159 x 10-4) = 8.8823 x 10-4 m3/s

3. Diffrences height, h = height 1, h1 height 2, h2 = 0.481 0.084 = 0.397 m

4. Coefficient discharged, Cd = Qactual / Qtheoritical = 0.2222 / 0.2258 = 0.9841

5. Logarithm Qactual = Log Qact = Log 0.2222 = -3.6532

6. Logarithm = Log = Log 0.397 = -0.4012