# Flow Measurement Lab

FlowMeasurement Lab

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Summary

Thisexperiment aims at calibrating two differential pressure flow meters(orifice and Venturi meter) and a rotameter. The experiment is usedin conjunction with a water bench. While conducting the experiment acomplete the table of data is provided, further there is drawing of asketch of the flow rig. The experiment winds by calculating therequired cross-sectional areas. Also a diagram of the apparatus andthese calculations in your report are given. There is calculation ofthevolumetricflowrateQ(m3/s)usingthemassofwatercollected,thetimetakenandthedensityofwater.Further, a plot of Qagainsttherotameterreadingis providedtogiveacalibrationgraphand thecalibrationcoefficientcalculated.

Thisexperiment aims at providing the students with the opportunity tocalibrate the two differential pressure flow meters and therotameter. The flow meters in this case include the orifice andVenturi meter. This experiment is used together with a water bench.The water bench itself is made of four critical elements. Theelements include sump, a pump, a bench and a weighing tank. The sumpis put on the floor and serves to hold the water supply that is usedin the experiment. The pump that is in place draws water from thesump and then delivers it through a valve on top of the bench to theexperimental apparatus. The bench element used in this experiment ismade from GRP and has a lip around it to help in preventing spillage.Within the center of the bench there is a hole where the water thatexist the apparatus goes through. The water then falls into theweighing tank and gets back to the sump. To prevent the water fromleaving the weighing tank, the lever is turned just in front of theweighing tank. By doing this, the plug is essentially put into thehole in the tank and allows the water to get storage up in theweighing tank.

Method

1. Open the water bench pump and through opening the valve that is on top of the bench, water is allowed into the apparatus. Through the flow control valve that is on top of the apparatus, there is increase of flow through the equipment up to the point where the top of the rotameter reads approximately 18-20 cm.

2. Make sure that all the air in existence are removed from the apparatus and ensure that water in all the piezometers is within the calibrated scale. The tubes with the extreme values should be tubes 1 and 6. If water in the piezometers are not within the scale then it is necessary that the flow is reduced till it gets within the scale.

3. Record the readings from the rotameter and the manometers. The recorded readings should be from 1,2, 5 and 6 that correspond to the pressure at the points on both the Venturi and the orifice meters on the form that is attached with this sheet.

4. When all is set up for the measurement of the flow rate, turn the lever that is on the front of the weighing tank till it points vertically down. This activity automatically closes the plug in the weighing tank, that is filled at the moment.

5. Upon realizing that the arm that has balance weight starts moving up, start the stopwatch when it hits the stop.

6. Place a 5kg weight on the balance arm that will automatically get to the bottom stop

7. Upon the filling up of the weighing tank with 15 kg of water, the weighing tank will also gain unbalance and the balancing arm will start to rise.

8. When getting to the top, stop the stopwatch

9. At this point, turn the lever on the front of the weighing tank and it is horizontal to allow water to drain out and do away with the weight.

10. In the data table, kindly note the time that is on stopwatch and the weight of water that is collected

11. Make the reading on rotameter as it is adjusted 2 cm steps. Carry out the procedure again.

ANALYSIS

1. On the following page, complete the table, draw a sketch of the flow rig and calculate the required cross-sectional areas. Include a diagram of the apparatus and these calculations in your report.

1. Carry out the following calculations and analysis. Include your working and the three graphs required in your report.

1. Rotameter

1. Calculate the volumetric flow rate Q (m3/s) using the mass of water collected, the time taken and the density of water.
1. Plot Q against the rotameter reading to give a calibration graph, calculate the calibration coefficient.

1. Venturi Meter and Orifice Plate Meter

Q Cd A1

2gh

2

1

A

⎟1

⎝A2 ⎠

where for the Venturi meter, A1 and A2 are calculated from the following diameters:

 Water Bench 3 Venturi Meter D1 = 26mm D2 = 16mm Orifice Plate Meter D5 = 51.9mm D6 = 20mm

Therefore, if you plot Q against for both cases, the gradient of the resulting straight-line graphs will be:

Cd A1

2g

2

1

A

⎟1

⎝A2⎠

and youmaythencalculatethevalueofCdforbothdevices.Commentonthevaluesyouobtain.

Rememberbeforeyoucalculatethevaluesof tochangehfrommmtom.Similarly, yourareasshouldbeinm2,notmm2.

0.98*(5.3066*10-4)[ sqrt (10/ (5.3066*10-4m2/ 2.01088*10-4m2)]

0.63*(2.11448*10-3m2)[sqrt (10/ (2.11448*10-3m2/3.14*10-4m2)]

Tableof Data

Completethissheetandincludetheseresultsinyourreport

 Mass of water collected (kg) Time of collection (sec) Rotameter reading (cm) Flow rate Q (m3/s) h1 (mm) h2 (mm) h5 (mm) h6 (mm) h1-h2 = h5-h6 = Äh1-2 (m) Äh5-6 (m) 0.16256913 34.11 17.7 0.000163 315 95 300 29 0.22 0.271 0.12858816 36.22 16.7 0.000129 300 111 290 50 0.189 0.24 0.09935661 38.21 15.6 0.000099 290 125 280 75 0.165 0.205 0.05972891 44 13.8 0.000060 280 135 270 105 0.145 0.165 0.04462026 47 12.8 0.000045 273 155 260 140 0.118 0.12 0.03286064 50 11.8 0.000033 260 171 256 150 0.089 0.106 0.02443451 53 10.9 0.000024 255 177 251 158 0.078 0.093 0.01448687 63 9.7 0.000014 249 185 245 168 0.064 0.077 0.00682667 75 8 0.000007 241 200 239 176 0.041 0.063 0.00294544 89 6.4 0.000003 235 210 235 188 0.025 0.047

Sketchdiagram offlow righere

A-Bench valve

B-Flow Control valve

C- Centrifugal pump

D-Venturi meter

E-Rotameter

F-Orifice meter

G-8 bank manometer

H- Sump tank

I-Air bleed screw

J-volumetric tank

Calculatecross-sectionalareashere:

VenturiMeter A1= [3.14(r^2)] A2= [3.14*(0.008)^2]

[3.14*(0.013)^2]=5.3066*10-4m22.01088*10-4m2

OrificePlateMeter A5= A6=

[3.14*(0.02595)^2] = 2.11448*10-3m2[3.14*(0.01)^2] = 3.14*10-4m2

GraphRotameter

 Flow rate Q (m3/s) h1-h2 = h5-h6 = Äh1-2 (m) Äh5-6 (m) sqrt h1-h2 sqrt h5-h6 0.000163 0.22 0.271 0.4690416 0.5205766 0.000129 0.189 0.24 0.4347413 0.4898979 0.000099 0.165 0.205 0.4062019 0.4527693 0.000060 0.145 0.165 0.3807887 0.4062019 0.000045 0.118 0.12 0.3435113 0.3464102 0.000033 0.089 0.106 0.2983287 0.3255764 0.000024 0.078 0.093 0.2792848 0.304959 0.000014 0.064 0.077 0.2529822 0.2774887 0.000007 0.041 0.063 0.2024846 0.250998 0.000003 0.025 0.047 0.1581139 0.2167948

Graph1

Graph2

CalculatedValues

 Calibration coefficient of Rotameter Gradient of graph of flow rate Q (m3/s) against h (where the units of h are m) for the Venturi Meter 1.1014*10-3 Gradient of graph of flow rate Q (m3/s) against h (where the units of h are m) for the Orifice Pate Meter 1.093*10-3 Discharge Coefficient Cd for Venturi Meter 0.98 Discharge Coefficient Cd for Orifice Plate Meter 0.63

Discussionof errors

Whenconducting an experiment, one has to include the experimentaluncertainty, which is also referred to as experimental error of theresults. Within the scientific bounds, an error does not refer to ablunder or mistake rather it is refers to the uncertainty thataffects all the existing measurements.

Giventhat errors are inevitable, the best thing that one carrying out anexperiment can do is to ensure that errors occurring are negligibleand as reasonable as possible and allow them to have the rightestimates as possible.

Experimentalerrors are divided into two categories and they often are theindeterminate, which are known to be random and the determinate,which are systematic in nature. Normally, the indeterminate errorsexist in almost every other experimental measurement. No methodexists to determine the size or even the sign of an error in anyparticular measurement. Often, the size of indeterminate errors canbe reduced through having several repeated measurements and thencalculating the averages of the values. The average value is normallytreated as the best representation of the true value that exists. Ininstances where measurements have somewhat smaller indeterminateerrors then they can be said to have high precision. Often, thedeterminate errors have the same size as well as algebraic sign forany given measurement and the size as well as the sign of errors canbe determined. A common case of determinate error is the bias fromprocedure or instruments used and often this arises frommiscalibrated scale or instrument. If measurements have smallindeterminate errors and small determinate errors then they are saidto have high accuracy. Often the term precision is confused withaccuracy but precision does not necessarily mean precision andprecise measurement can in one way or another be inaccurate if thereis determinate error.

Errorin the Difference between Two Measurements

Theerror in the difference between the two measurements is an error thatoccurs while doing the experiment. In looking at the error in thedifferences between the two values calculated using the sameequations and pegged on the same quantities, which are measured usingthe same setup of the experiment and method, there are high chancesthat error in the difference will contain the indeterminate errorswhile the determinate errors will cancel out (Sun, 2010). In the samecase as our experiment, it then occurs that the precision and not theaccuracy of the measurement is important. Given that the main resultsfrom the measurements in our experiment are the change in thefriction factor from the measurements without and with the particles,the determinate errors thus drop out of the calculations and what isleft out is the indeterminate errors. Notably, it is critical toidentify the different error sources as either indeterminate ordeterminate before calculating the error in the differences betweenthe two measurements.

Errorfrom Measuring Instruments

Theother error that occurs is that from the measuring instruments and itemerges when using the instruments to measure quantity. Thisexperimental error is normally given in the instruction manual thatis supplied by the manufacturer. In the different instruments usedlike venturi, orifice plate and rotameter the manual is attached andhelps in the distinction of accuracy and precision a process that isnormally referred to as repeatability of the measurement. Often, therepeatability has a smaller value compared to accuracy(McCabe, Smith and Harriott, 1993).The error in this experiment was minimized by installation and properuse of the instruments. While doing the experiment, the measurementfrom the manufacturer was used to help estimate the error in thequantity measured using this instrument.

Conclusion

Inthe experiment, the venturi is being used as flow meter and theaverage velocity of the fluid in the throat is normally calculatedusing the Bernoulli equation. The volumetric flow that is used inthis experiment is the average velocity. From our experiment, theco-efficient discharge is 0.98, which means that the venturi is welldesigned. The co-efficient discharge, which is the empiricalparameter, helps in making the flow rates calculated be the same asthe observed flow rates.

Themanner in which the orifice meter operates is similar to that ofventuri meter. For the venturi meter the coefficient discharge isintroduced while for the orifice meter there is calibration of thecoefficient of discharge (Goldstein,1996).The value from our calculations is 0.63, is dependent on the positionof the pressure taps, and often is a function of the diameters of theorifice hole and pipe.

References

Goldstein,R., 1996.&nbspFluidmechanics measurements.CRC Press.

McCabe,W.L., Smith, J.C. and Harriott, P., 1993.&nbspUnitoperations of chemical engineering&nbsp(Vol.5, p. 154). New York: McGraw-Hill.

Sun,Z., 2010. Mass flow measurement of gas–liquid bubble flow with thecombined use of a Venturi tube and a vortex flowmeter.&nbspMeasurementScience and Technology,&nbsp21(5),p.055403.