## Introduction: Lab 5: Calibration of a Flowmeter

During this lab you will be learning how to calibrate bulk-flow measuring devices by determining the flow coefficient as a function of the Reynolds number. Bulk-flow measuring devices, such as Venturi meters and orifice-plate meters, rely on change in pressure measurements. Once the flow rate for the bulk-flow devices is obtained experimentally it with be compared with ISO published values for similar devices. In addition to the Venturi and orifice-plate meters a paddlewheel flow meter will also be calibrated.

## Step 1: Apparatus

The system we are working with today may look complicated, but in reality it is rather simple. Each apparatus consists of pipe mounted to the ceiling that is fed by a weighing tank. In the pipe there are two different flowmeters, one hydraulic and one paddlewheel. The hydraulic flow meter is read using a differential pressure transducer and a manometer, and the paddlewheel flow meter is connected to digital readout that displays the current. All of these flow meters will be calibrated compared to a weight-time method.

## Step 2: Step 1: Set Up

Verifiy that the discharge valve is closed before proceding to check the levels of mercury in the manometer for the hydraulic flowmeter. If the levels in the manometer are not the same then bleed the trapped air in the supply lines by opening and closing the drain valve. If necessary adjust the central scale on the manometer to ensure that the manometer gives a zero reading for no flow

## Step 3: Step 2: Calibration of the Differential Pressure Transducer

Start by zeroing the transducer output using the VFn interface box. Then using the manometer bleed valve labeled "CAL VALVE" reduce the pressure in one of the manometer lines. Record 5 data points of the transducer output and the corresponding manometer level. The pressure difference points should have a minimum of 0 with the valve closed, and a maximum with the bleed valve all the way open. Note, the voltage should be less than 10V at the maximum point.

## Step 4: Step 3: Plotting the Calibration Data

Plot these 5 points that were obtained using the methods in the previous step in the LabVIEW program to generate a model that represents pressure the relation between pressure and voltage. Plotting the data on a linear scale will give you a graph similar to the first one, where the line of best fit is the calibration curve. It should be a power series, in this case the equation for our calibration curve is Q = 0.00145 * Δh^0.567. To verify this plot the data on a logarithmic scale as seen in the second plot. This plot is also our alternative calibration curve, on this curve the data should fall on a straight line, and this indicates that the data does follow a power series trend of Q = K(Δh)^m. The final thing that you should plot using this data is going to be the discharge coefficient as a function of the Reynolds number on a linear-log scale. This will produce the graph as seen in the third figure.

Looking at the discharge coefficient Cd compared to the Reynolds number we can see that although the Cd values are not perfectly constant, and the values of Cd tend to increase as the values of Reynold's number increases. The values for Cd range from 0.45 to 0.59, compared to a theoretical values of Cd = 1 these values are off by between roughly 40% to 55%. That is a significant error, but that is likely due to the theory that is used to find Cd, and there are possible corrections for this theory that can make the theoretical Cd more accurate. A value of Cd = 1 is not possible in the real world, as it assumes the actual discharge will be equal to the theoretical discharge. We need to account for energy lost from frictional and pressure drag. As we saw in the graph the Reynold's number will also affect the Cd value, as it affects how easily the fluid flows.

## Step 5: Step 4: Data Acquisition

First check the Gain Adjust control of the paddle wheel is set to 6.25 turns for P1 and P4, and 3.00 turns for P3. Then zero the paddlewheel flowmeter output using the zero adjust control. Then slowly open the discharge valve until the valve is either open all the way or until the allowable manometer deflection is reached. Pay close attention to both the signet paddlewheel voltage and the pressure voltage readings. As soon as the paddlewheel produces a significant voltage record both values. Once the maximum flow rate is reached record the flow rate using the manometer, paddlewheel, and the weight time method. Graph all of these in the LabVIEW software to get a time-averaged pressure-transducer voltage. Also note the maximum manometer deflection.

## Step 6: Step 5: More Data Acquisition

Repeat step 3 with slower flow rates so the manometer deflections are approximately (x)^2 max deflection. Repeat the test with x = 0.9, 0.8, 0.7,..., 0.1. Make sure that the mercury in the manometer is settled before taking any measurements. Always watch carefully for the Validyne differential pressure's and the Signet paddle wheel's voltage output to drop as the flow drops, and record both readings when the Signet paddlewheel's voltage drops to zero. Once all 10 data sets have been acquired, the data is displayed in the LabVIEW software.

## Step 7: Step 6: Plotting the Paddlewheel Data

Now, using the LabVIEW software and the data that was collected for the paddlewheel output voltage, plot the collected data and create a calibration curve. Be very careful to ensure that there is no data above or below the cutoff flow rates, where the paddlewheel will appear motionless. Then calculate the cut off velocities. These are at when the paddlewheel reads 2.5 volts at the minimum, or when the paddlewheel produces more than 10 volts. The cut off flow rates are a max of 0.0242 m^3/s and a min of 0.0063 m^3/s. Convert this to the velocity of the water, and it gives you a minimum velocity of 0.037 m/s and a maximum velocity of 2.997 m/s. The maximum we achieved in this experiment was 2.980 m/s at a voltage of 9.94 volts.

When looking at the data from the paddlewheel flow meter we must consider how accurate it is, and if it is reliable. By looking at the plot it is possible to see that all of the data points that were collected during the experiment line up very well with the line of best fit, and there are no clear outliers on the low end or high end of the data. There is a very slight deviation from the line for the highest 3 points, and this may indicate that the flow meter is more accurate at lower flow rates than higher flow rates, but those 3 points are still very close to the line and would be more than acceptable data. For the values we tested the paddle wheel flow meter can be considered to be reliable.

## Step 8: Completion

Thank you for viewing this training video regarding calibration of fluid flow meters. Hopefully you found this informative and you will now apply the knowledge you have acquired here in the lab for years to come. Good luck!