Lab 6: Calibration of a Flowmeter Partial Report

It is important to have a good calibration of a flowmeter because then measurements can be accurate and confounding variables could be eliminated. This experiment calibrates Venturi flowmeters and orifice-plate flowmeters. Analyzing the pressure differentials of each flowmeter allows some experimentally obtained coefficients to be compared with ISO-published values. This way, it is possible to know whether the flowmeter is reliable or not. A paddlewheel flowmeter is also calibrated to provide an electrical output signal for monitoring purposes. This figure depicts the setup of the system. The flow rate is measured using the weight-time method, which measures how long it takes for the water to reach a certain weight. This is a mass flow rate, which can be converted into a volumetric flow rate by dividing by the density of water.

This setup for both the venturi and orifice-plate flowmeters requires a differential pressure transducer. Many of the measurements require reading a manometer, which you are looking at the height difference between the left and right sides of it. There is a main pipe which you have to open and close, where it will range from completely open to partially open. The paddlewheel flowmeter is further along the pipe for extra calibration and observation purposes. LabVIEW will be the software used to collect and store the lab data.

First, make sure the discharge valve is fully closed. This is for the weight-time measurement so that water doesn't leak out of the system. Then, check the mercury levels in the mercury manometer for the venturi/orifice-plate flowmeters. They should be equal but if they are not, slowly open and close the manometer supply valves to get any excess air out of the system.

Using the LabVIEW software, the output voltage needs to be calibrated from the transducer. The manometer supply valve should be opened and closed to artificially create a pressure difference and the measured manometer level. The voltage should be taken at least 5 times in 5 different spots to ensure a good calibration. This should not exceed 10 V.

Check that the Gain Adjust control of the paddlewheel flowmeter is set to 6.25 turns for P1 and P4 and set for 3 turns for P3. Open the valve fully and wait to ensure no vibration of the pipes. This determines that there is laminar flow rather than turbulent flow, allowing your measurements to be more accurate.

Once the water flow is laminar, record the manometer readings, the paddlewheel flowmeter readings, a weight-time measurement, and the pressure-transducer voltages. This is the maximum flow rate.

Manometer Readings

1. Record the difference between the heights in the manometer. This is the maximum height, hmax.

Weight-Time Method

1. Start a timer when the scale weight is balanced with the tank weight.
2. Add a weight to the scale
3. Stop recording when the scale weight is once again balanced with the tank weight.

Paddlewheel Voltage

1. Record using the LabVIEW software.

There should be 9 more measurements using Step 4 as a reference. The slower flow rates are at (0.9)^2*hmax, (0.8)^2*hmax, ..., (0.1)^2*hmax. These correspond to 90% flow, 80% flow, ..., 10% flow respectively.

This relationship shows how pressure difference through the manometer can be calculated using Bernoulli's Equation. The height difference in the manometer and the properties of water and liquid are used to determine this. The flow rate is also calculated from this relationship as well and the flow rate vs. manometer deflection is shown below.

Lab Report Q1

Lab Report Q2. Since the relationship appears linear when using logarithmic scales, there is a strong indicator that a power-law relationship applies. This makes sense as flow rate was also reduced by the percentage squared times the maximum height.

Lab Report Q5. The discharge coefficient, C_d, is calculated by LabVIEW after the 10 measurements are taken. Then, Reynolds Number is also calculated using the equation Re = (VD)/v, where V is the flow velocity (taken by dividing flow rate by area), D is the pipe diameter, and v is the water viscosity.

Lab Report Q6. The rising cutoff flow rate is 0.003 m³/s and the falling cutoff flow rate is 0.020 m³/s. The pipe diameter is 4 inches, or 0.1016 m. Using , we get that . Divide each flow rate by the area to get the corresponding fluid velocities. For the rising cutoff flow rate, For the falling cutoff flow rate, .

Lab Report Q9. The discharge coefficient is mostly constant, staying at around 0.7-0.8. They are close to the ideal value of unity. The ideal value of C_d is 1. By not being 1, there is some error to be accounted for. One potential source is from the manometer reading, especially given that it doesn't stabilize at a single point. Another source of error could be from the flow itself. While waiting until the pipe wasn't vibrating is a good way to know if the flow is laminar or not, it is not a perfect system, especially when the flow rate was reduced.

Lab Report Q11: The paddlewheel flowmeter offered mixed results. It was not as reliable as the hydraulic flowmeters because it's not designed to take many measurements at lower voltages. Thus, the paddlewheel flowmeter is more reliable at higher voltages than lower voltages.