EGR 2500 Lab 1 Example PDF

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Group No. _____ FLOW RATE MEASUREMENTS; EXPERIMENTAL UNCERTAINTIES EGR 2500 Laboratory Assignment #1 October 5, 2018 Prepared for: Dr. K. Kobus Submitted by:

Abstract The experiment conducted was to test the accuracy of different flow rate measurements and their uncertainties. The volume collection method, venturi meter, and orifice plate meter were all used to measure the rate at which water was flowing through a certain point. A series of manometers were used in order to measure the pressure differences across different points throughout the venturi and orifice meters. Bernoulli’s equation was used to calculate the flow rates at each meter, but Bernoulli’s equation does not account for multiple factors including friction and viscosity. Because of this, a coefficient had to be found to account for these factors, called the discharge coefficient . We ran the experiment multiple times testing various flow rates measured by the variable area meter. Each method had their pros and cons, but ultimately the volume collection method was the most accurate. The results of the volume collection method most closely matched the variable area meter reading. The error in the other two methods was based heavily on the fact that the manometer heights were not constant (always moving) and the scale on the manometer heights was not very precise. 1. Experimental Flow Rate Measurements

a. Apparatus and Instrumentation: The main tool used to perform this experiment and collect the required data is the Armfield Hydraulic Bench, equipped with a venturi meter, orifice plate, variable area meter, and a manometer bank consisting of eight separate manometers as seen in Figure 1. The only other instrument used was a digital stopwatch to time for the volume collection method. By opening and closing the flow control valve, we were able to adjust the flow rate measured by the variable area meter. The venturi and orifice meters were used to restrict the flow of water and measure the velocity and pressure of the water read on the manometers. The volume collection method can also be used to indirectly measure flow rate. Either by observing how long it takes for a certain amount of water to rise or by observing how much water is collected in a set time. We repeated this experiment 6 times to get a more precise reading of the flow rate. Each time we ran the experiment, the flow control valve was adjusted from 20L/min (read on the variable area meter) and eventually to 4L/min on the last run.. With each run, we measured the flow rate using the volume collection method and recording the height of the manometers on the device. For the volume collection method, the flow control valve was adjusted and the tub drain was plugged to block the water from leaking out. We recorded the amount of time it took for the sink to be filled with 15 liters of water at various flow rates. The manometer heights were also recorded at each flow rate. Manometers 1 and 2 flowed through the venturi meter and manometers 6 and 7 flowed through the orifice plate. a. Measurements, Direct and Indirect: For the venturi meter and orifice plate meter, pressure differences between two specific locations were indirectly measured using the manometer, and flow rate was directly measured using the variable area meter and indirectly measured using a volume collection method. Our calculated and direct measurements were then compared to determine accuracy between all of the methods used.

1

Figure 1 - Schematic of Armfield F1-21 Flow Meter Demonstration Unit

Orifice Plate Meter

Figure 2

Venturi Meter

Figure 3

Experimental Uncertainty Flow Rate Analysis Uncertainty in our experiment refers to the margin of error that is possible in each method. The ideal flow rate is the flow rate when there is no friction. By using the Bernoulli equation, we are able to calculate the ideal flow rate through a venturi or orifice meter. Actual (corrected) flow rate refers to the ideal flow rate including friction of the water and other forces. Then we can calculate the discharge coefficient which to find the actual volumetric flow rate with friction. The difference between the actual and the ideal flow rates of each method is the uncertainty. Results Table 1: Cross-Sectional Diameters and Manometer Heights Venturi meter

Orifice meter

Upstream Pipe Diameter, D (m)

0.03175

0.03175

Throat Diameter, d (m)

0.015

0.02

Upstream manometer height

h

h

Throat manometer height

h

h

1

2

6

7

2

Table 2: Observations and Direct Measurement Collection Volume Uncertainty = + or - .5 L Collection Time Uncertainty = + or - .3 sec Variable Area Flow Meter: Maximum Flow rate = 20 (L/min)

Uncertainty = + or - .5 (L/min)

Manometer height Uncertainty = + or - 2.5 mm Variable Area Flow Meter

Volume Collection Method

Manometer Heights (mm)

Flow rate (L/min)

Collectio n volume (L)

Collectio n time (s)

20

15

44.42

17

15

14

h1

Change in Density

h2

h3

h4

h5

h6

389

176

327

304

227

235

49.81

385

220

335

313

237

15

58.17

375

255

337

321

10

15

71.5

360

292

334

7

15

87.0

350

310

4

15

146.4

338

321

h7

h8

Ventur i

Orifice

86

133

2087.4

1460.2

244

131

165

1617

1107.4

244

249

167

173

1176

803.6

323

252

254

209

222

666.4

441

352

326

256

257

230

239

392

264.6

330

326

289

260

249

252

166.6

107.8

Table 3: Calculations of Collected Data Venturi Meter: D = 0.03175 Orifice Meter: D = 0.03175 Variable Area Flow Meter

d = 0.015 d = 0.02

Volume Collection Method

Uncertainty (L/min) (L/min)

Cd,v = 0.6 Cd,o = 0.98

Uncertainty (L/min) (L/min)

Venturi Meter

Orifice Meter

Relative uncertainty (%)

Ideal

Corrected

Ideal

(L/min)

(L/min)

(L/min)

% Difference with

Corrected (L/min)

Variabl e Area

Venturi

Orifice

20

1

20.26

0.86

4.25

22.22

21.78

35.10

21.06

1.30

7.22

3.86

17

1

18.07

0.73

4.06

19.56

19.17

30.57

18.34

6.09

5.91

1.49

14

1

15.47

0.60

3.87

16.68

16.35

26.04

15.62

9.99

5.50

0.97

10

1

12.59

0.46

3.69

12.56

12.31

19.29

11.57

22.91

2.27

8.39

7

1

10.34

0.37

3.57

9.63

9.44

14.94

8.96

38.57

9.17

14.30

4

1

6.15

0.21

3.42

6.28

6.15

9.54

5.72

42.33

0.08

7.17

3

4

Discussion of Results There was a lot of room for error in this experiment. The volume collection method could be off because of human error in the delay to start or stop the timer. If the instrument itself were to have a built in timer that would automatically start and stop when the tank had 15 L, that could eliminate some or all of the error. Both the venturi meter and orifice plate could have an error because the manometer heights were not stable or very precise. By calculating in the uncertainties and errors of these methods, we are able to determine which is the most accurate flow rate measurement tool. We had assumed that the volume collection method would be the least accurate because the timer was not operated by machine or instrument, but ultimately that method proved to be the most accurate. The results of the volume collection method were found to be the closest to the actual flow rate. The orifice plate meter had very similar uncertainties to the venturi meter, but was slightly more accurate in the end. As for unusual trends in the data, the percent error increased as the volume decreased for the percent difference of the variable area meter while the venturi and orifice differed and had a much smaller percentage. This could just be error in the calculations or error in the experiment, but it was consistent with the multiple trials we ran.

Formulas Used/Calculations Volume Collection Flow Rate: (15L/t(sec))*60sec Venturi: Ad = pi(.015)2/4 = 1.767x10^-4 Au = pi(.03175)2/4 = 7.917x10^-4 Orifice: Ad = pi(.02)2/4 = 3.142x10^-4 Au = pi(.03175)2/4 = 7.917x10^-4 Heights: ㅿP= gㅿh, Venturi ㅿ  h = (h1-h2) Orifice ㅿ  h = (h6-h7) V-ideal Venturi: (1.767x10^-4)sqrt((2ㅿP)/(1000(1-1.767x10^-4/7.917x10^-4)^2)*60000  5

V-actual Venturi: (.98)(1.767x10^-4)sqrt((2ㅿP)/(1000(1-1.767x10^-4/7.917x10^-4)^2)*60000  V-ideal Orifice: (3.142x10^-4)sqrt((2ㅿP)/(1000(1-(3.142x10^-4/7.917x10^-4)^2)*60000  V-actual Venturi: (.6)(3.142x10^-4)sqrt((2ㅿP)/(1000(1-1.767x10^-4/7.917x10^-4)^2)*60000  Variable Volume Collection Method Uncertainty: V = V/t dV = (dV/dV)dV + (dV/dt/)dt = (1/t/60)ㅿ  V  + (V/(t/60)^2)ㅿ  t/60  Relative Uncertainty: (Uncertainty/Volume Flow Rate)*100 % Difference with the Volume Collection Method: abs(Vc-V)/((Vc+V)/2)

Appendix Raw Experiment Measurement Data

6

Raw and Sample Calculations

7

EGR 2500 – Introduction to Thermal Engineering Fall 2018

Laboratory Assignment #1

Bazinski/DelVescovo/Guessous/Kobus

Flow Rate Measurement and Calibration Figure 1 – Schematic of Armfield F1-21 Flowmeter Demonstration Unit [1] The purpose of this laboratory exercise is to introduce you to different fluid flow rate measurement methods, associated experimental uncertainties and the calibration of orifice plate and venturi meters. Figure 1 shows a schematic of the apparatus used in this experiment. The equipment consists of a venturi meter, variable area meter and orifice plate meter, installed in a series configuration to allow for direct comparison [2]. Pressure taps on either side of each flow meter are connected to an eight-tube manometer bank which allows for measurement of the pressure drop across each flow meter. The apparatus is mounted on an Armfield Hydraulics Bench and flow control valves on the hydraulics bench as well as on the flow meter apparatus are used to control the flow rate through the various flow meters. You will be comparing volumetric flow rate measurements taken using these three types of flow meters, to those determined indirectly using a volume collection method that involves a volume collection and a timer. You will also determine calibration factors, known as discharge coefficients, for the venturi and orifice plate meters.

Figure 2 – Orifice (left) and venture (right) meters restrict the flow in a pipe. Volume flow rate can be related to the pressure drop across the restriction [3]. Background Information: Venturi and orifice plate meters are both restriction-type flow meters whose operation is based on the basic physical principle that in an incompressible fluid, an increase in velocity results in a decrease in pressure. By measuring the pressure drop between the lower velocity, higher pressure section of the meter and the higher velocity, lower pressure section in the throat of the meter, one can experimentally determine the volume flow rate. Using the Bernoulli  equation and 8

the Conservation of Mass e quation, one can show that the ideal flow rate for steady, incompressible and frictionless flow through a venturi or orifice meter may be expressed as: where,

and

(1)

D and d are the diameters at the inlet and the throat of the meter, respectively, ρ is the fluid density, ΔP is the pressure drop across the venturi or orifice meter, and subscripts u and d respectively refer to upstream and downstream. Due to frictional and other effects, the actual flow rate deviates from the value given by equation (1). To account for this deviation, a correction factor known as the discharge coefficient, Cd, is used when determining the actual volume flow rate using a venturi or orifice plate meter, (2) Discharge coefficient values depend on a number of parameters including the downstream to upstream diameter ratio d/D. Typical values are roughly around 0.6 and 0.98 for orifice and venturi meters, respectively [3]. Because the actual flowrate through a restriction will always be less than the ideal flowrate, discharge coefficients for real devices will always have a value less than 1.0. Table 1 lists the dimensions and manometer height readings to be used for the venturi and orifice plate meter calculations. Table 1 – Upstream and downstream diameters to be used in flowrate calculations [1] Another indirect way of determining volume flow rate is using the volume collection method. The volume collection method is an indirect experimental method that can be used to measure volume flow rate by collecting a volume, ∀c of fluid and recording the length of time, t, that it takes to collect this volume. Two approaches can be used: setting a constant collection volume or setting a constant collection time. The volume flow rate can then easily be determined from (3) Experiment Specifications: 1. Turn on the pump and adjust the control valve on the hydraulic bench, the exit valve of the flow meter demonstration unit and the bleed valve on the manometer manifold to bleed off all air bubbles. 2. Conduct steady-flow experiments, for at least 6 different flow rates (indicated by the variable area flow meter) ranging between 4 and 20 L/min. Start at the highest flow rate. 9

3.

4.

5.

6.

7.

8.

At each flow rate, record the collection time needed to collect 15 L in the tank, as well as the eight manometer heights. To do this, close the drain valve at the bottom of the tank of the hydraulics bench. Collect 15 L of water in the tank as indicated by the upper sight scale in the side of the hydraulics bench and record the time required to do so. Derive equations for the uncertainty and relative uncertainty of the indirectly measured volume flowrates using the volume collection method. Express the venturi and orifice meter ideal volume flowrates in terms of the appropriate manometer heights. For each measured flow rate, calculate and tabulate the volume flow rate given by Eq. (3), as well as the uncertainty and the relative uncertainty of the volume collection flow rate values. In the same table, include the ideal venturi and orifice meter flow rates given by Eq. (1). Note that the uncertainty of the variable area flow meter measurements is a constant (5% of flow meter full scale). On one graph, plot the volume collection volume flow rate, versus the ideal venturi and orifice meter volume flow rates. Include error bars for the volume collection values. Next, using appropriate trendlines in Excel, plot best fit curves that will allow you to determine the discharge coefficients for the venturi and orifice plate meters according to the definition of the discharge coefficient shown in Equation (2). Make sure you show the trendline equations and R2 values on the graph. Think about your choice of the type of trendline (i.e. linear, power law, polynomial, etc.). Often the theoretical model dictates the best type of trendline. Using the Cd values determined in part 5, calculate and tabulate the corrected venturi and orifice plate meter flow rates. Evaluate the percentage difference between the variable area, venturi and orifice meter flow rates, and the volume collection volume flow rates. On a second graph, plot the flow rates determined by the three types of flow meters as a function of . Use the same scales for ordinate and abscissa and plot the results from all three methods on the same graph. Include a 45 degree line on the graph. Include error bars for the variable area flowmeter vs. volume collection flow rate data. Comment on the results. Which flow meter seems to be most accurate? How could the experimental uncertainties associated with the volume collection method be improved (hint: look at the relative uncertainty equation that you derived in part 3)? What types of applications is each type of flow meter (variable area, venturi, orifice meter) best suited for? What seem to be the pros and cons of each type of flow meter? Make sure you include and properly cite references that you consult, and discuss the validity of the sources of information (i.e. are the sources trustworthy? How do you know?)

References: 1. Armfield Limited, “Flow Meter Demonstration F1-21 Instruction Manual,” Issue 3, September 2001 10

2. http://discoverarmfield.com/en/products/view/f1-21/flow-meter-demonstration, accessed January 18, 2015 3. Pritchard , P.J., 2011, Fox and McDonald’s Introduction to Fluid Mechanics, 8th edition, John Wiley & Sons. Laboratory Report Contents: Your lab report should include the following: ● Title page with abstract ● Results and Discussion section which should include: ○ Data table(s) that include your collected and calculated data (Tables 2 and 3 below can serve as guides for the type of information that should be included in your data tables; you may include additional information if you wish) ○ Flowrate graphs: One of versus the venturi and orifice meter ideal flow rates, with best fit curves to determine the discharge coefficients and error bars for; and one of the flow meter flow rates plotted versus (Don’t forget the 45 degree line and error bars as specified). ○ Discussion of results and conclusions; Make sure you discuss any trends that you observe from the tables and graphs and answer the questions posed in the lab handout, including the information search. ● References (including sources of information on the various types of flow meters; remember to cite these references in your report) ● Theory section showing Eq. (3), and the volume collection uncertainty and relative uncertainty equation derivations. You’ll also want to include the equations for the venturi and orifice meter ideal and corrected flow rates (Equations 1 and 2), as well as the expressions that you will use to determine these flow rates in terms of the appropriate manometer heights. Make sure you include a schematic (can be taken from this document) and d...