Calibration of a Flowmeter

The objective of this instructable is to show how to calibrate flowmeters, such as a Venturi meter, orifice-plate meter, and paddlewheel flowmeter.

The supplies for this assignment are three flowmeters, a Venturi meter, an orifice-plate meter, and a paddlewheel flowmeter.

Each set of apparatus has two separate flowmeters attached to them a hydraulic one and a paddlewheel one. A detailed description of the apparatus is shown in Figure 1. Each of the two different types of flowmeters measures the same flow rate Q. Figure 2 shows a plan view of the lab setup, including the computers where the data will be kept and the flowmeters.

All data acquisition for this experiment is done by LabVIEW software. This software requires the pressure transducers to be calibrated before use. The LabVIEW controls flow coefficients, produces valuable spreadsheets, and manages all the files.

First, check to make sure the discharge valve is closed. Then check the level of mercury in the mercury-water manometer for the hydraulic flowmeter, and make sure these levels are equal. If not equal open and close the drain valves to release all trapped air.

Now you need to calibrate the voltage of the Validyne differential pressure transducer. This is used to measure the pressure difference in the hydraulic flowmeter. First, set the Vfn output on the transducer to zero. Next with the discharge valve being closed, open the manometer value, CAL VALVE to reduce the pressure in the manometer lines. Take voltage readings off the transducer five times taking the fifth reading when the valve is fully open. Maximum voltage should not exceed 10V. Figure 3 depicts the Venturi meter.

Now acquire data for both the hydraulic flowmeter and the paddlewheel. Completely open the discharge valve, or until maximum manometer deflection occurs. Observe the voltage in both the paddlewheel and the Validyne system. Record both readings when the paddlewheel voltage has a significant nonzero value. At the maximum flow rate use the LabVIEW software to note voltages and maximum manometer deflection. Repeat this procedure at slower flow rates so that deflections are 0.9^2 * maximum deflection, 0.8^2 * maximum deflection, and so on until 0.1^2* maximum deflection. Record both readings one last time when the paddlewheel voltage drops to 0.

The table displays the laboratory results the LabVIEW system obtained. The LabVIEW software also calculated the discharge coefficient Cd, Reynolds number Re, and the velocity of the flow.

Five graphs show the most important relationships between the discharge coefficient Cd v. Reynolds number, and manometer deflection and flow rate. The second graph shows the flow rate vs. manometer deflection in the logarithmic scale and proves there is a power scale. The data point in the graph above does not follow a straight linear line. This shows that the data set is a power-law relation. The equation Q = K(Δh)^m does apply. As the manometer deflection decreased the flow also decreased in a power-law relation. The paddlewheel was moving throughout the whole experiment so there are no falling cutoff flow rates indicated in the last graph. With no cutoff rates, there was also no cutoff fluid velocity. Since the paddlewheel never was constantly moving there are no cutoffs and with no cutoffs, there is no maximum velocity.

Question 2:

The discharge coefficient C_d is not constant over the range of Reynolds Values tested. The ideal value of C_d is 1 and the experimentally measured values for C_d were all below 1. It says in the lab manual that usually in practice C_d is found to be slightly less. The experimental value of C_d also decreased as the flow rate decreased. In practice, the value of C_d for the Venturi flowmeter is less than unity but for the orifice-plate meter, it is significantly less than unity. The main correction that should be made to the theory is that the unity value for C_d should not be 1. This unity value assumes the absolute best conditions, which is not realistic in a lab setting. If the theory lowered the unity C_d value then we could experimentally determine more realistic values of C_d.

Question 4:

The paddlewheel flowmeter is seen to be pretty reliable because the R^2 value is 0.974 which is very close to 1. The readings were also more accurate at higher flow rates. At high flow rates, the paddlewheel is pretty accurate every data point falls in almost a perfect linear relationship, but when low flow rates occur the data points are not exactly on the linear trendline.