Introduction: Calibration of a Flowmeter
This lab involves measuring the flow rate using a venturi flowmeter, an orifice-plate flowmeter, and a paddlewheel flowmeter. In our pipe system, the segment with the flowmeters should look like the figure below.
Figure 2 below shows the plan view of the laboratory. The pipe system should be set up like Figure 2. The venturi/orifice plate flowmeter should have four pressure taps that are connected to a manometer.
You need to calibrate the electronic transducer against known static pressures. To create a known static pressure, you have a mercury manometer connected to bleed valves that are connected to our supply pipe. Open a bleed valve. By opening the bleed valve, you can expose one leg of the manometer to high pressure. Record the pressure difference between the manometer legs. Then, average the voltage of the digital pressure transducer and record the data.
Partially close the bleed valve to reduce the pressure difference between manometer legs. Record the pressure difference between the manometer legs. Average the voltage of the digital transducer and record the data.
Repeat the previous step until one gets a total of between five to eight pressure differences and record data. This should give you a linear relationship between the pressure that the transducer senses and its digital output. If you have a linear relationship, your electronic pressure transducer is calibrated.
You need to establish the maximum flow rate of the system. During these next steps, you will use a computer program will average the output of the paddlewheel flowmeter and the output of the pressure transducer. The pressure transducer is connected to an orifice-plate flowmeter. The orifice-plate flowmeter will be an additional method to help determine the flow rate.
Go into the lab's basement and find the weighing tank. The weighing tank is set on a balance that uses a 200:1, such that 200 lbs in the weighing tank are balanced by one pound on the other pan of the balance upstairs in the laboratory. Connected to the weighting tank, there is a ball valve that serves as our draining valve. The ball valve is attached to a shaft that connects to a T-handle valve in the laboratory. So, the ball valve can be opened and closed in the laboratory.
Head back to the laboratory. Close the T-valve. Open the supply valve fully to set the maximum flow rate.
Measure the pressure difference using the manometer and use the computer program to average the output of the paddlewheel and of the pressure transducer.
Now, go to the lab's balance. Get a stopwatch ready. Put a 1.5 lb weight on the balance. Start the stopwatch. Once the balance is level, stop the stopwatch and record the time on it. Record the data from the computer program.
Repeat the last step at 90%, 80%, 70%, etc. of the flow rate.
Your data should look similar to the table below.
Using linear scales, plot the data points for the measured flow rate as a function of its manometer deflection for the Venturi flowmeter or orifice-plate flowmeter. It should similar to the graph below.
Transform the previous graph into a logarithmic scale. It should look like the graph below. The data should fall in a straight line.
The equation of the previous graph should have a power relation of the type of equation below.
Your equation should prove the flow rate equation below to be true. m should be close to 1/2 like the equation below. And k is Cd * B, where Cd is the dimensionless discharge coefficient and B is a derivable constant dependent on the geometry of the flowmeter and some other fixed parameters.
Data suggests that the logarithmic graph fits the flow rate equation. You can check the accuracy further by plotting the discharge coefficient Cd as a function of the Reynolds number Re on linear-log scales, using the values from the previous graph. The Reynolds number equation is below; where D is the full pipe diameter, V1 is the velocity in the pipe, and v is the viscosity of the fluid.
If your discharge coefficient Cd is constant over the range of Reynolds numbers tested, then your Venturi/orifice-plate flowmeter measures flow rate accurately. Otherwise like in the graph below, your flowmeter measures inaccurately. This graph must show the results of using the orifice-plate flowmeter because of fluid separation in the orifice plate. The experimentally measured values of the discharge coefficient of the orifice plate are off when compared to the ideal value of unity, shown in Figure 6, derived theoretically. The fluid separation causes the drag coefficient to increase, which causes the fluid's velocity to slow down and form vortices. To correct this inaccuracy, you should not only account for the conservation of mass of the fluid but also other forces like the frictional force on the fluid by the pipe.
Create a flow rate versus paddlewheel flowmeter voltage graph. It should look similar to the graph below. This graph shows that the paddlewheel flowmeter is reliable because the trendline's Coefficient of Determination (R^2) is very close to one, proving that the data is precise. Looking at the graph, the points with lower flow rates are close to the trendline. This proves that the paddlewheel flowmeter readings are more accurate at lower flow rates because the points with lower flow rates deviate less from the trendline than data points with higher flow rates.