ME 241, BME 270 Lab 2: Flow Measurement
In this lab you will learn about different flow measurement techniques. The experiment should take less than 45 minutes, and the lab report should take 3 to 4 hours to complete.
WHAT YOU ARE GOING TO DO: You will measure the flow rate in a pipe system using several common measurement techniques.
WHAT YOU SHOULD LEARN: You should learn 1) how to use a pressure transducer, 2) how to use common industrial flow meters (a sharp-edged orifice and a venturi meter), and 3) how to calculate the flow rate in a pipe based on a velocity profile measured using a pitot tube.
DETAILS: The experimental setup consists of a long pipe through which water is pumped from a storage tank. Weighing the total volume of water exiting the pipe in during a period of time provides a simple measurement of the volumetric flow rate. Along the length of the pipe are three flow measurement stations where you will measure the fluid volumetric flow rate in gallons per minute (gpm) using a (a) sharp-edged orifice, (b) venturi meter, and (c) a pitot tube.
Weighing Tank Measurement:
Procedure:
p1. CAREFULLY and CLEARLY sketch the flow circuit including the location of BOTH pumps, weighing tank, storage tank, all valves, and all flow measuring devices on the back of your data sheet.
p2. Set up the flow system and pressure transducers as follows:
p2a. Turn on the pump from the storage tank to the piping system using the right switch on the front of the table to establish a flow through the piping system. Leave the pump between the weighing tank and the storage tank off.
p2b. Let the piping system fill with water and allow the bubbles in the pipes to purge.
p2c. Close the valve at the end of the piping system just upstream of the weighing tank. Do not turn off the pump.
p2d. Open both set screws on each of the three pressure transducers using the special Allen wrench provided by the TA. Allow the air to bleed out of the lines to the pressure transducer and the transducer itself. All valves in the pressure transducer lines should be open (valve handle aligned with the flow through the valve).
p2e. Turn on the voltmeter. Zero the pressure transducer 1 by turning the switch on the box above the pressure transducer electronics to T1 and adjusting the trim pot labeled "ZERO" for channel 1 using a small screwdriver until zero reads on the voltmeter. Repeat for pressure transducer 2 (T2 and channel 2) and pressure transducer 3 (T3 and channel 3).
p2f. Open the valve at the end of the piping system just upstream of the weighing tank to establish a large flow into the weighing tank. DO NOT ADJUST THIS VALVE AGAIN UNTIL YOU HAVE COMPLETED THIS ENTIRE LAB.
p3. Use the weighing tank to measure the flow rate as follows:
p3a. Measure the flow rate using the weighing tank by noting the time required to increase the weight of water in the tank by 100 pounds. Record information on the data sheet.
p3b. You may want to do calculations c1, c2, and c3 to find out if the flow is laminar or turbulent.
p3c. Leave the pump between the storage tank and the piping system on. Turn on the pump between the weighing tank and the storage tank using the left switch on the front of the table so that the storage tank refills. DO NOT ADJUST THE FLOWRATE IN THE PIPING SYSTEM. Move on to the sharp-edged orifice meter procedure.
Calculations:
c1. Calculate the volume of water and the volume flow rate in gallons per minute (gpm). (1 gallon of water weighs 8.347 pounds; 1 ft3=7.481 gal.)
c2. Calculate the average velocity of water flowing through this 1.05 inch ID (inner diameter) pipe.
c3. Calculate Reynolds number (the ratio of inertial to viscous forces) for this flow. The kinematic viscosity of water at 20°C is 1.082 x 10-5 ft2/sec.
c4. Calculate the average water velocity and volumetric flow rate that would yield a Reynolds number of
2300 (the critical Reynolds number for transition from laminar to turbulent flow) for this size pipe.
Write-up: Include the following in your write-up:
1. Calculations of the volume flow rate (step c1), the average velocity (step c2), the Reynolds number (step c3), and the velocity of the water and volume flow rate at the transition from laminar to turbulent flow (step c4).
2. Discuss briefly (a few sentences per topic)
• Is the flow in this pipe laminar or turbulent?
• Do you expect a parabolic velocity profile or one that is blunt?
Sharp-Edged Orifice Measurement:
The pressure transducers for the sharp-edged orifice, the venturi meter, and the pitot tube are arranged as shown in the following figure. The valves are necessary to prevent damage to the diaphragm in the pressure transducer that can result from prolonged exposure to high pressures. All valves should remain open (valve handle aligned with flow) except when measuring the pressure with the pressure transducer. Valves 1 and 2 are not present on one of the two set-ups in the lab. To measure a pressure use the following procedure:
Pres1: Adjust the switch on the box above the pressure transducer electronics to the appropriate setting (T1 for orifice meter, T2 for the venturi meter, T3 for the pitot tube).
Pres2: Close valve 3 for the appropriate pressure transducer.
Pres3: Record the voltage on the voltmeter.
Pres4: Immediately, re-open valve 3.
It is not necessary to reproduce the above schematic on your datasheet.
Procedure:
p4. Record the calibration of the pressure transducer 1 (volts per psi) listed on the pressure transducer electronics.
p5. Record the voltage difference of the pressure transducer for the sharp-edged orifice meter following the procedure Pres1 to Pres4.
p6. Record the orifice diameter d2 (see following figure). This diameter should be displayed on the sharp-edge orifice.
Calculations:
c5. Convert the voltage difference to a pressure difference P using the calibration.
c6. Assuming that the discharge coefficient is CD=0.6, compute the volumetric flow rate in gpm (gallons per minute) according to the following relationship:
in which p=p1-p2 , A2=(/4)d22 with d1 = 1.05 inch and d2 from step p6.
c7. Use the value for Q found in step c1 to compute the exact discharge coefficient, CD, according to the relationship given in step c6.
Write-up: Include the following in your write-up:
3. Calculations of the volume flow rate for the sharp-edged orifice (step c6).
4. Calculations of the exact discharge coefficient, CD (step c7).
5. Discuss briefly (a few sentences per topic):
• Find the discussion of orifice plate meters in your textbook and describe the origin of the equation in step c6 above. You need not derive the equation. What equations is it derived from? What is the range of CD given in your textbook?
• How does the discharge coefficient, CD, found in step c7 compare to those in the book and the assumed value of 0.6 in step c6? Comment.
Venturi Meter Measurement:
Procedure:
p7. Record the calibration of the pressure transducer 2 (volts per psi) listed on the pressure transducer electronics. Convert this calibration to volts per inch of water and record. (27.68 inches water = 1 psi)
p8. Record the voltage difference of the pressure transducer for the venturi meter following the procedure Pres1 to Pres4. Convert the voltage difference to a pressure difference P and record this on the data sheet.
p9. Use the chart attached to the venturi meter to determine the volumetric flow rate according to the venturi meter manufacturer’s specifications. The appropriate capacity curve is the one labeled 1”–567. To use this chart, determine the pressure drop across the venturi in inches of water. Move horizontally from the corresponding value located on the ordinate to the correct capacity curve. When you intersect the capacity curve, move vertically to the abscissa. The value indicated on the abscissa is the volumetric flow rate in gpm. Record on your data sheet.
Calculations:
c8. Convert the voltage difference to a pressure difference P.
c9. Use Bernoulli’s equation to compute the volumetric flow rate in gallons per minute (gpm). The venturi used in this experiment has an inlet diameter of 1.000 inch and contracts to a diameter of 0.567 inches.
Write-up: Include the following in your write-up:
6. Calculations of the volume flow rate for the venturi meter (step c9).
7. Discuss briefly (a few sentences per topic):
• Compare the manufacturer's value for the flow rate (step p9) with what you calculated (step c9) and explain any differences.
Pitot Tube Measurement:
Procedure:
p10. Record the calibration of the pressure transducer 3 (volts per psi) listed on the pressure transducer electronics.
p11. Adjust the pitot tube so that its sensing pressure port is at the center of the pipe (the center of the pipe corresponds to a reading of 0.525 in. on the micrometer) and record the voltage difference of the pressure transducer for the pitot tube following the procedure Pres1 to Pres4.
p12. Continue to record the voltage of the pressure transducer at each radial position indicated in the table on the data sheet. This is only a suggestion, however. You are free to decide just how many points you need. Keep in mind that it is desirable to obtain many points where large gradients occur and fewer points elsewhere.
p13. Do not turn the micrometer lower than 0.025. This will bend or break the pitot tube, since the wall is at a micrometer reading of 0.0.
p14. Be sure to reopen valve 3 for all pressure transducers. Turn off the pumps.
Calculations:
c10. Convert each voltage in steps p11 and p12 to a P. (You may want to use a spreadsheet.)
c11. Use Bernoulli’s equation and the P values (step c10) to compute the axial velocity as a function of radial position, rn. That is, for each (rn, Pn) pair (in which n = 0, 50, 100, . . ., 525) compute vn at rn.
c12. Plot v as a function of r. Make sure that the greatest value of the velocity is plotted at r=0 and that v=0 (no-slip) occurs at r=R=0.525 inches. Connect data points with straight line segments.
c13. The volumetric flow rate is obtained by integrating that profile over the tube cross-sectional area as:
provided v is a continuous function of r. If, however, v is known only at discrete values of r, then this expression may be approximated by counting squares under the curve v(r)r. Tabulate v(r)r and plot v(r)r versus r using graph paper with gridlines.
c14. Estimate the area under the curve in step c13 by counting squares under the curve. You may write a computer program to do this if you wish (in this case you need not use graph paper with gridlines). Note that this product will be identically zero at both the centerline (r=0) and the wall (r=0.525 inches). Multiply your result by 2 to get the flow rate and convert to gpm.
Write-up: Include the following in your write-up:
8. Sample calculation of v from P (step c11).
9. Table of r, voltage, P, v(r), and v(r)r (steps p11, p12, c10, c11, c13).
10. Plot of the velocity profile v(r) vs. r (step c12).
11. Plot of v(r)r vs. r on graph paper with gridlines (step c13).
12. Calculation of volume flow rate in gpm from the plot of v(r)r vs. r (step c13, c14).
13. Discuss briefly (a few sentences per topic)
• Did you have enough data points to get a smooth curve for the velocity profile? Is there a location where you should have obtained more data points?
• Does the velocity profile look as expected? (laminar vs. turbulent, no-slip, center-line velocity, etc.)
• Which method of determining the flow rate yields the most accurate result compared to the result of volume flow rate measured using the weighing tank? the least accurate result? Why?
• Discuss any sources of error.
14. Include the DATA SHEET.
DATA SHEET
Weighing Tank Measurement:
Time start:______Time end:______
Weight:______
Sharp-Edged Orifice
Calibration ______volts/psi(pressure transducer 1)
Pressure transducer 1 voltage difference ______volts
Orifice diameter d2=______in
Venturi Meter
Calibration ______volts/psi (pressure transducer 2)
Calibration ______volts/inch water
Pressure transducer 2 voltage difference ______volts
Pressure difference for venturi meter based on voltage difference ______inch H2O
Qventurimanufacturer=______gpm
Pitot Tube Measurement
Calibration ______volts/psi (pressure transducer 3)
Micrometer rn = radius
reading(x 1/1000 in)volts
0.525 inches0 (center)______volts
0.47550______volts
0.425100______volts
0.375150______volts
0.325200______volts
0.275250______volts
0.225300______volts
0.175350______volts
0.125400______volts
0.100425______volts
0.075450______volts
0.050475______volts
0.025500______volts
0.000525 (wall) 0.00 volts
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