Calibration of Flowmeters Tutorial

Congratulations on your new position with XYZ Company! Unfortunately, I will not be able to train you to calibrate our lab's flowmeters in person, but hopefully this tutorial will provide you with any information that you need!

The basic setup of the procedure is shown above. It includes two different flowmeters, the hydraulic (Venturi) flowmeter and the Paddlewheel flowmeter. The first is composed of a mercury differential manometer and a Validyne pressure transducer, to monitor the change in pressure through a Venturi or orifice-plate. The second, uses a paddlewheel (Signet 3-8511-P0 "lo flo" device) and a Signet 8511 transmitter. The goal of the procedure is to calibrate the Validyne pressure transducer specifically. All data acquisition is done through the LabVIEW software.

The first step of the calibration procedure is to prepare the testing apparatus. This includes closing the discharge valve, as well as setting the left and right mercury manometer levels equal to each other. The latter can be done by adjusting the two manometer drain valves labeled "CAL VALVE", which bleeds the air out of the system. It is important that the zero-flow reading on the manometer should be zero, as there is no pressure difference through the flowmeter.

The first item that requires attention is the calibration of the Validyne transducer connected to the hydraulic flowmeter. It must be done statically - at zero-flow - or else the moving water will create measurement fluctuations. First, the transducer output on the VFn interface must be zeroed. We can then simulate a pressure difference in the manometer by partially opening the valve labeled "CAL VALVE". After doing so, we must record five or more data points, measuring the total transducer output in volts as well as the manometer height levels in centimeters. Each data point should be recorded after slightly opening the manometer drain valve more, from minimum to maximum pressure differential. Note that the voltage output should not exceed 10V due to the limitations of the A/D board. After the data points are entered into the LabVIEW software, the program will run a linear least-squares analysis on the data and store it for future use.

In order to collect data from both flowmeters, the gain adjust control of the paddlewheel must be set to 6.25 turns for pipes P1 and P4, and set to 3 turns for pipe P3. This is done to control the output voltage range of the flowmeter to 10 volts.

The maximum flow rate through the apparatus is achieved when the discharge valve is completely open, allowing the most water to cycle through. In order to calculate this maximum flow rate, open the discharge valve fully and record the voltage reading from both the Validyne transducer and the paddlewheel flowmeter. The paddlewheel voltage reading should be taken once the value reaches a significant non-zero value. At this time, the height difference of the differential manometer should be recorded as well.

The same procedure described in step 4 should now be completed and recorded in intervals such that the total manometer deflection delta h for each interval is equal to the max flow rate deflection times 0.9^2, 0.8^2, 0.7^2, 0.6^2, 0.5^2, 0.4^2, 0.3^2, 0.2^2, and 0.1^2. This should add up to ten data points overall. Again, at each of these calculated height differentials the exact heights of each side and the voltage reading displayed should be recorded. Adjusting each height interval should yield a 10% decrease in flow between each successive data point. The pressures and flow rate are adjusted using the large green pipe valve wheel. Our LabVIEW software will take your recorded data observations and compute the flow coefficient Cd as a function of Reynold's number Re. It will also record the flow rate Q using the time-weight method described in step 6.

The weight-time method relates the flow of water Q to the weight of the water discharged through the system and the time that the water was flowing through the system. It will be used as a metric to judge the flow rate at each of the data step intervals in step 5. For each data interval, the scale should be reset and the time it takes for the scale to reach a set weight should be measured. Doing so provides the weight of water passed through the system as well as the time it took for said weight to pass through the system, providing us with a flow rate Q for each interval.

The above LabVIEW excerpt shows us the results of the experiment. At this point, the software should have calculated the slope and intercept of the transducer calibration curve, as well as each flowmeter's voltage readings, the flow rate, the manometer difference reading, the flow coefficient Cd, and the Reynold's number for each trial.

The above curve plots the flow rate Q against the manometer deflection level delta h. This curve is the calibration curve for the flowmeter. Notice that at low deflections, the flow rate Q is more sensitive to an increase in delta h. The curve is evidently non-linear as expected from the equation shown above. The best fit equation defines a very close square root function, consistent with the general form of the equation shown above as well.

By turning the linear plot above into a log scale plot, we can clearly see a linear connection between the logarithm of flow rate and manometer deflection. It further shows that which was shown in the first plot, that the relationship between the two is an exponential function with the approximate equation y = 0.0019x^0.5078. This plot shows conclusive evidence of a power-law relation between flow rate and manometer deflection.

Plotting the flow coefficient against the Reynold's number indicates a questionable positive correlation. While the coefficient fluctuates, it is evident that the flow coefficient does not change significantly with a change in Reynold's number. Although it fluctuates some, the flow coefficient is relatively constant. The fluctuations are likely the result of imprecise measurements and experimental error.

The above graph plots the paddlewheel flowmeter's voltage reading against the weight-time measured flow rate Q. The plot is clearly linear, between the flow rates of .005 and point 0.020 m^3/s, before and after which the voltage sharply decreases to zero based on experimental observation. The flow velocities of the fluid through the pipe are listed in the chart for each voltage reading of the paddlewheel flowmeter. The cutoff velocities are 0.633 m/s on the lower end and 3.25 m/s on the high end. The maximum velocity through the pipe is the upper cutoff, 3.25 m/s.

It is difficult to determine whether or not the flow coefficient Cd is constant over the range of Reynold's numbers because of the spread of the values. Overall however, Cd seems relatively constant around the value of 0.61. If there were a non-constant relationship, then the slope would be nominal, so with the limited data we have it is safe to posit that the coefficient is effectively constant. The flow coefficient is also notably far from theoretical unity (Cd = 1). One of the main reasons this is the case is because our calculations idealize the flow through the system, not accounting for turbulent flow, gravity effects, internal pipe conditions, and human error. Also, the diameter d, which represents the orifice opening, is not the same diameter of the vena contracta, the point at which fluid velocity is at a maximum. This causes the contraction ratio beta to be greater than what is accurate and results in a below-realistic flow coefficient as shown in the plot above comparing Cd to beta. Adding a correction to account for this would raise the value of Cd closer to unity. Experimental errors are also a challenge with this lab considering its size, so decreasing human error and increasing experimental precision and accuracy would also provide better results.

The reliability of the paddlewheel flowmeter is good enough to draw conclusions from our data, however there was certainly a noticeable margin of error between this method and the other. However, the gap between the two methods decreases as flow rate increases. The higher the flow rate through the system, the more accurate the paddlewheel flowmeter tends to be.