## Introduction: Calibration of Flowmeters

In this Instructable, I will explain how to calibrate orifice-plate and paddlewheel flowmeters to determine the flow rate of a fluid through a pipe and the reliability of the different flow meters.

Orifice-plate meters have a sudden convergence and divergence from a plate obstruction. This sudden constriction causes the flow downstream to swirl, leading to energy loss in the flow. To measure the pressure drop over the constriction, pressure taps are connected to the pipe just upstream and downstream from the constriction. By measuring the height difference between the mercury-water manometer columns created from the pressure drop across the control volume, the flow rate can be calculated.

The paddlewheel meter produces a voltage that is proportional to the fluid velocity. This linear relationship can be analyzed to determine the reliability of the paddlewheel meter for measuring the flow rate of a fluid.

The flow rates measured by the orifice-plate meter and the paddlewheel meter can be compared to each other and the flow rate calculated by the weight-time method to determine the reliability of the flow meters.

## Supplies

Pipes

Water/Fluid

Weighing Tank

Scale

Weight

Timer

Orifice-plate meter

Paddlewheel meter

Manometer

Pressure Transducer

LABVIEW Software

## Step 1: Calibrate Pressure Transducers

Before beginning the calibration process, check to make sure the discharge valve is closed to avoid pressure fluctuations, and that the mercury levels in the manometer are equal. If they are not, open the manometer drain valves until they are equal.

With the discharge valve closed, open the manometer valve to reduce the pressure in one of the manometer columns. Record the voltage output from the transducer and the height difference between the manometer columns in the LABVIEW software. Repeat these steps 5-8 times, opening the manometer valve more each time.

The LABVIEW software will then perform a linear least-squares analysis on the manometer–transducer data that will be used to calibrate the measurements.

## Step 2: Set Flow Rate

The flow rate is set by opening the supply valve. For the first run, the valve is opened completely to set the maximum flow rate.

## Step 3: Measure Flow Rate Using Weight-Time Method

The weight-time method is used to measure the flow rate of the water in the pipes. The procedure for the weight-time method is as follows:

- Overbalance the scale by sliding the cursor until the scale arm hits the bottom stop.
- When the scale arm rises above the balance mark, add the weight to the balance pan and start the stopwatch immediately. The scale arm should hit the bottom stop again.
- Stop the stopwatch when the scale arm regains balance and passes the balance mark.
- Record the time and the chosen weight. The weight ratio for the weigh scale is 200:1, meaning 200 lbs of water added to the weighing tank will balance 1 lb of weight on the scale.

With the weight of the water added (W), the time it took the water to be added(∆t), and the specific weight of the fluid (γ), the flow rate (Q) can be calculated by:

Q = W/(γ∆t)

## Step 4: Measure Pressures

To calculate the flow rate using the orifice-plate flowmeter, the manometer height difference is needed. Measure this height difference carefully by getting eye level with the meniscus of the liquid in each column to avoid parallex error. Record this height in the LABVIEW software with the pressure transducer output.

Record the voltage output from the paddlewheel flowmeter as well.

## Step 5: Repeat Steps 2-4

Repeat steps 2-4, closing the supply valve incrementally to achieve 90%, 80%, 70%,..., 10% of the maximum flow rate.

## Step 6: Orifice-Plate Flowmeter Results

Plotting the flow rate (Q) versus the manometer deflection (𝛥h) with linear scales for the orifiice-plate flowmeter yields the first graph. Plotting the same data using a logarithmic scale for the flow rate yields the second graph. The data in the second graph appear linear which indicates that there is a power-law relation of the type Q=K(𝛥h)^m that applies. From the data obtained, Q=0.0014(𝛥h)^0.5674.

Plotting the given values of the discharge coefficient versus the Reynolds number yields the third graph which is an unexpected graph. The expected relationship between these flow properties should resemble the curves in the fourth graph. The discharge coefficient increases as the Reynolds number increases up to a point, but this increase is very minimal as the discharge coefficient should be fairly insensitive to the flow conditions. Ranging from around 0.45 to 0.59, the discharge coefficient is not close to unity, or one, which was expected. To obtain more realistic values for the discharge coefficient, the vena contracta diameter should be used instead of the orifice diameter. The orifice diameter is typically used because it is easier to measure than the vena contracta diameter.

## Step 7: Paddlewheel Flowmeter Results

Plotting the flow rate versus the output voltage of the paddlewheel flowmeter yields the graph in the figure. The data point at the highest flow rate seems to be nearing a cutoff flow rate. At this point the velocity was found to be 2.48 m/s, by using the equation Q=AV -> V=Q/A. This is was the highest flow rate tested, so this velocity also corresponds to the maximum fluid velocity achieved in this experiment.

From this plot, the paddlewheel flowmeter seems to be reliable for the flow rates tested. The R^2 value is so close to one which means the paddlewheel voltage output can predict the flow rate very well. With the flow rates tested, there did not seem to be any readings that were noticeably inaccurate, but the reading at the highest flow rate seems to be the most inaccurate of the readings, indicating that the reliability of the paddlewheel flowmeter decreases at higher flow rates.