Calibration of a Flowmeter

Measuring devices need to be calibrated regularly in order to make sure they are producing accurate measurements. For a bulk-flow measuring device such as a Venturi flowmeter, an orifice-plate flowmeter, or a paddlewheel flowmeter, this calibration is done by way of measuring flow coefficients using Reynolds numbers and then comparing these values with published standard values.

• A pipe mounted with two different flowmeters:
• A hydraulic flowmeter (such as a Venturi or orifice-plate flowmeter) that uses a pressure transducer and a mercury-water manometer to measure pressure differences
• A paddlewheel flowmeter that uses the voltage output of a paddlewheel to measure flow
• A weighing tank connected to the pipe/flowmeter system
• A timer
• Data collection software

Before calibration can be done, the setup of the system needs to be checked. The valve allowing discharge needs to be closed. The mercury levels on the two sides of the manometer need to be equal, and if they are not the manometer drain valves should be adjusted to let out air trapped in the supply lines. The manometer should also be adjusted so that a lack of flow reads as zero pressure change.

Begin by zeroing the transducer output. While the discharge valve is closed, open the manometer bleed valve (which has a "CAL VALVE" label) slightly, reducing the pressure in one manometer line. Record the transducer output and manometer levels at this position.

Repeat the pressure reduction and recording process for five data points corresponding to five different valve configurations. The maximum voltage output on the transducer should not exceed 10 V. Once the data is recorded, the "CAL VALVE" can be closed. The data can then be fit to a curve for comparison.

Begin by setting the Gain Adjust setting on the paddlewheel flowmeter is set to 6.25 turns for P1 and P4 and 3.00 turns for P3. Then the paddlewheel flowmeter output must be zeroed using the Zero Adjust control.

Slowly open the discharge valve. Stop opening it when the allowable manometer deflection is reached or the valve is fully open. Observe the changes in the pressure voltage readings. When the Signet paddlewheel voltage reaches a significant nonzero value, record the voltage readings from the Validyne transducer and the Signet paddlewheel.

Record the readings off the manometer and paddlewheel flowmeter as well as a weight-time measurement at the maximum flow rate. Also record time-averaged pressure-transducer voltages. Finally, record the maximum manometer deflection Deltahmax.

Repeat step 3 at lower and lower flow rates corresponding to manometer deflections around (.9)^2*Deltahmax, (.8)^2*Deltahmax, (.7)^2*Deltahmax,...(.1)^2*Deltahmax. Observe both of the voltage readings as the flow decreases. When the Signet paddlewheel voltage drops to zero, record voltage values from both the Validyne transducer and the Signet Paddlewheel.

Once 10 data sets have been found, the flow coefficient C_d can be found.

By plotting the measured flow Q as a function of the manometer deflection, the calibration curve for the Venturi or orifice-plate flowmeter can be found. Graphs with data from a calibration are shown - one with deflection on a linear scale and one with deflection on a logarithmic scale. As shown, the curve on the logarithmic scale is fairly linear, implying that a power-law type relation similar to Q = K(Deltah)^m applies.

This curve can be compared to the theoretical relationship Q = C_d*B*sqrt(Deltah), where B is a constant that depends on the flowmeter's geometry. This comparison allows us to ensure the flowmeter is accurate or to correct if it is inaccurate.

Using the same flow and deflection data from step 5, the discharge coefficient C_d can be found.

The graph shows the discharge coefficient as a function of the Reynolds number Re_D of the data points from step 5. The Reynolds number is calculated as Re_D = (V_1*D)/v, where V_1 is velocity, D is the pipe diameter, and v is the viscosity of the fluid.

The discharge coefficient is essentially constant over this range of Reynolds numbers. Using the dimensions shown in the supplies step, we can find the diameter ratio beta. This data was collected at station F4, so beta is 0.311. The theoretical graph shown tells us that C_d should be around 0.6, which is significantly different from our measured value, which is around 0.13. These measurements could be made more accurate if the theoretical calculations better accounted for forces like viscosity.

The calibration curve for the paddlewheel flowmeter can be found by plotting the discharge rate against the voltage produced. This curve for the data used is shown.

In our data, the paddlewheel appears to be motionless below Q= .0005 m^3/s. This flow corresponds to a velocity of about 0.08 m/s.

The data from the paddlewheel appears to be more reliable than the data from the hydraulic flowmeter. The reading is especially accurate at higher flow rates.