Calibration of a Flow Meter

The following instructions should be sufficient for you to follow to successfully perform your job at this company. We are glad you're interested in fluid dynamics and look forward to your success in this position. Without any further introduction, let's get into the calibration.

Your role at this company has one overarching objective: calibrating bulk-flow measuring devices like Venturi meters, oriface-plate meters, and paddlewheel flowmeters. Venturi and oriface-plate meters measure pressure changes and paddlewheel flowmeters use an electrical outlet for measurements, monitoring, and control. They will be calibrated by determining their respective flow coefficients of their flow rates in terms on the Reynold's number, and comparing the coefficients to International Organization for Standardization (ISO) published values.

The apparatus for each flowmeter consists of a pipe with both a hydraulic flowmeter and a paddlewheel flowmeter in the ceiling, as well as a weighting tank in the basement. The general view of this apparatus can be seen in Figure 1, and the specifications for the machinery can be seen in Table 1. The actual experimental setup of the apparatus is shown in Figure 2.

First, the hydraulic flowmeter uses a Validyne pressure transducer and a manometer to measure the pressure difference. This flowmeter will either be a Venturi flowmeter that will measure the pressure difference between the entrance and the throat, as shown in Figure 3, or an oriface-plate flowmeter that will measure the pressure difference between the entrance and the vena contracta, as shown in Figure 4.

Next, the paddlewheel flowmeter measures a voltage output by being connected to a transmitter that sends an output current through a fixed resistor. This is measured by counting the number of times the paddlewheel spins (one (1) revolution) over one (1) second.

First, the starting equation is taken from Bernoulli's equation to determine the pressure difference:

p1-p2 = (RHOw / 2) * ((v2)^2) * [1-(((d2) / D)^4)] (1)

Where RHOw is the density of water, v2 is the velocity, d2 is the second diameter, and D is the first diameter (see Figures 3 and 4). Using the attached mercury-water manometer, equation (1) can be simplified:

p1-p2 = deltaH * (SGhg - 1) * RHOw (2)

Where deltaH is the height difference in the manometer and SGhg is the specific gravity of mercury. Using equations (1) and (2), the following equation can be found for Q:

Q =((Cd / (1 - ((d2 / D)^4))) * ((d2 / D) / 4) * (2g * deltaH * (SGhg - 1)^0.5) (3)

Where Cd is the discharge coefficient. Equation (3) can be simplified even further to the following equation:

Q = Cd * B * (detlaH)^0.5 (4)

Where B is a constant derived from the geometry of the flowmeter.

1. Ensure that the discharge valve is closed, and level the mercury so deltaH = 0 by opening and closing the manometer drain valves.

2. While there is no flow in the test section, calibrate the output voltage from the pressure transducer.

3. With the discharge valve closed, open the "CAL VALVE", record the transducer voltage and deltaH from the manometer (in cm), and close the "CAL VALVE"

4. Adjust the Gain Adjust control of the paddlewheel flowmeter to 6.25 turns for P1 and P4 and 3.00 turns for P3 (Figure 2).

5. Zero the paddlewheel flowmeter output

6. Open the discharge valve slowly until it is fully open (or the allowable deltaH is reached).

7. Record the differential pressure voltage from the Validyne transducer and the paddlewheel voltage reading.

8. At maximum flow, record the deltaH on the manometer, paddlemeter flowmeter readings, a weight-time measurement and the time-averaged pressure-transducer voltages.

9. Repeat this procedure (steps 6-8) for a total of 10 data sets.