Mass Conservation and Flow Rate Measurements

1. Setting the facility

1. Make sure that there is no flow in the facility.
2. Verify that the data acquisition system follows the schematic in Figure 1B.
3. Connect the positive port of pressure transducer #1 (see Figure 1B for reference) to the traversing Pitot tube ().
4. Connect the negative port of this same pressure transducer to the static probe of the intake passage (). Hence, the reading of this pressure transducer will be directly ().
5. Record this transducer's conversion factor from Volts to Pascals (). Enter this value in Table 1.
6. Connect the positive port of pressure transducer #2 (see Figure 1B for reference) to the static probe of the intake passage () using a tee.
7. Leave the negative port of pressure transducer #2 open to the atmosphere (). Hence, the reading of this transducer will be directly ().
8. Record this transducer's conversion factor from Volts to Pascals (). Enter this value in Table 1.
9. Set the data acquisition system to sample at a rate of 100 Hz for a total of 500 samples (i.e. 5s of data).
10. Make sure that channel 1 in the data acquisition system corresponds to pressure transducer #1 ().
11. Enter the conversion factor in the data acquisition system to make sure that the pressure measurement () is directly converted to Pascal.
12. Set the Pitot probe at the end of its travel, where it touches the pipe's wall. Since the probe is 2 mm in diameter, the first velocity point is at a radial coordinate 1 mm away from the wall. That is, at a radial position of mm (here, mm).

Figure 2. Experimental setting. (A): Flow passage under study. (B): manual traversing system for the Pitot tube. Please click here to view a larger version of this figure.

Table 1. Basic parameters for experimental study. Par ameter Value

Parameter	Value
Flow passage radius (Ro)	82.25 mm
Transducer #1 calibration constant (m_p1)	136.015944 Pa/V
Transducer #2 calibration constant (m_p2)	141.241584 N/V
Local atmospheric pressure	100,474.15 Pa
Local temperature	297.15 K
P_atm-P_2	311.01 Pa

2. Measurements

1. Turn the flow facility on.
2. Record the reading of pressure transducer #2 in Volts from the digital multimeter.
3. Enter this value in Table 1 as and convert the reading from Volts to Pascals using the factor .
4. Use the data acquisition system to record the reading of ().
5. Enter the value of in Table 2.
6. Use the traversing knob to change the radial position of the Pitot tube according to the value suggested in Table 2.
7. Repeat steps 2.4 and 2.6 until Table 2 is fully populated.
8. Change the flow rate by varying the system's discharge.
9. Repeat steps 2.4 to 2.8 for at least ten different flow rates.
10. Turn the flow facility off.

Figure 5. Experimental setting. Perforated plates to restrict flow at the discharge of the flow system. Please click here to view a larger version of this figure.

Table 2. Representative results. Velocity measurements. r (mm) P_T - P₂ (Pa) u (r) (m/s

r (mm)	PT - P2 (Pa)	u(r) (m/s)
2.25	300.35	22.34
12.25	302.84	22.43
22.25	305.82	22.54
32.25	302.34	22.41
42.25	294.88	22.13
52.25	295.37	22.15
62.25	292.88	22.06
68.25	293.63	22.09
72.25	294.13	22.10
75.25	299.60	22.31
77.25	293.13	22.07
79.25	284.67	21.75
80.25	256.31	20.63
81.25	198.33	18.15

3. Data Analysis.

1. Determine the velocity profile using the pressure difference values, P_T - P_2, from Table 2. Enter the results in Table 2.
2. Plot both the pressure and velocity values from Table 2 using the radius,, as the abscissas (Figure 3).
3. Calculate the integral in equation (8) based on the velocity and radius values from Table 2.
4. Calculate the discharge coefficient for each flow rate using equation (8).
5. Plot the discharge coefficient using as the abscissas.
6. Fit a function to the discharge coefficient, a power law is a good choice.

Figure 3. Representative results. (A): Example of measurement of static pressure along the radial coordinate of the flow passage. (B): Velocity distribution determined from the measurements of static pressure. Please click here to view a larger version of this figure.