Calibration of Flowmeters

The act of measurement is integral to any experiment. Anything that is recorded can get studied. In order to get proper measurements, measurement tools need to be calibrated correctly. In studying fluids and flows, many measurement instruments can be used. Examples of such are orifice-plate flowmeters connected to a differential pressure transducer and a paddlewheel flowmeter. Orifice-plate meters use pressure difference measurements to determine flow coefficients as functions of flow rate in terms of the Reynolds number. Paddlewheel flowmeters outputs electrical signals depending on the flow.

• Hydraulic flowmeter(either Venturi or orifice-plate)
• Validyne pressure transducer
• Mercury-water differential manometer equipped with drain valves
• Paddlewheel
• Piping system that has a discharge valve to stop flow

Ensure that manometer levels are equal when the discharge valve is closed, and open and close the manometer drain valves to remove trapped air. Then, zero the transducer output on the interface box next to the computer. Open one manometer drain valve labeled “CAL VALVE” by an arbitrary amount that results in a transducer output less than 10 V and record the transducer output and manometer levels. Repeat the opening of the drain valve at an arbitrary amount four more times before stopping the calibration flow by closing the “CAL VALVE”

Fully open the discharge valve and record the manometer and paddlewheel flowmeter readings at the set flowrate. Take a weight-time measurement also at the same flowrate. Record the time-averaged pressure-transducer voltages. Repeat all recordings at flowrates that are approximately 90%, 80%, 70%, …, 10% of the max flowrate by setting manometer deflections Δh at approximately (0.9)2Δhmax, (0.8)2Δhmax, (0.7)2Δhmax, …, (0.1)2Δhmax

Use linear scales when plotting data points of measured flowrate Q as a function of manometer deflection and pass a smooth curve through the data. This is a calibration curve for the flowmeter being analyzed. An alternative calibration curve can be created by plotting the same data but using logarithmic scales. Using the logarithmic scale, it is seen that the data follows a straight line. Having data that appears linear when using non-linear scales means that the data itself follows non-linearity. Therefore, it can be concluded that the data follow a power-law relation in the form Q = K(Δh)^m applies.

Using the values from the calibration curves, plot Discharge coefficient vs Reynolds number on linear-log scales. Reynolds number Re can be calculated using Re= V1*D/v where V1 is the velocity in the pipe, D is the pipe diameter, and v is viscosity. The discharge coefficient is not constant across all the different Reynolds number values. The theoretical discharge coefficient is 1. The experiment discharge coefficient values are around 5.8-6.8 which is not close to the theoretical value. The values in this experiment more closely matches the ISO discharge coefficient curves. Some changes that can be made to be closer to the theoretical value is regarding the geometry of the flowmeter.

Using linear scales, plot a calibration curve of the paddlewheel flowmeter voltage as a function of the actual discharge rate Q calculated using the weight-time method. If any of the values appear to be zero, these values are cutoff flowrates. There were no cutoffs in the data since no velocity values of zero emerged. The maximum velocity value achieved was 3.067 m/s. In this experiment, the paddlewheel is reliable since that data is precise as seen by the R^2 value. It is also because there were also no cutoff values. Usually, the paddlewheel flowmeter would be less accurate at low flowrates because the wheel is not fully submerged. In this case, the paddlewheel flowmeter remains accurate