The objective of the calibration of flowmeters is to determine flow coefficients as functions of flow rate. This flow rate can be measured in terms of the Reynold's number for a given fluid. The flow coefficients, known as the discharge coefficient, will be used to calibrate the orifice plate flowmeter via pressure change. The experimentally determined discharge coefficients are compared to published values. A paddlewheel flowmeter will also be calibrated using its electrical output voltage. The flow rate measured using the orifice plate will be compared to the value measured by the paddlewheel calibration and by the weight-time method.

Supplies

The apparatus of this experiment consists of two types.

The first apparatus contains the:

Orifice plate flowmeter
Differential pressure transducer
Manometer
Pipe
VFn interface box
Paddlewheel flowmeter and digital readout device (Signet 8511)
CAL VALVE
Discharge valve
LabVIEW software

This first apparatus is set up in the figure where the water flows in and is first measured by the orifice plate flowmeter then by the paddlewheel flowmeter. The paddlewheel flowmeter is a device that operates from a range of 0.3 ft/s to 20 ft/s and it is hooked up to a device called the Signet 8511 which provides a 4-20 mA output. The device reads the number of revolutions over a period of 1 second and does so continuously meaning the value should be read when the reading is steady or the values should be determined over an average.

The second apparatus consists of:

Weighing tanks
Pipe
3-4 stopwatches
Torque balancing apparatus
Valve
Counterweight
Manometer

This apparatus is a simple design and it utilizes the weight of the water and manometric heights to measure the flow rate.

Step 1: Preparations

To begin make sure that the discharge valve is closed. The levels of mercury in the manometer for the hydraulic flowmeter must be equal for this laboratory to be successful. If the levels happen to be different, slowly open and close the two manometer drain valves (one of which is labeled “CAL VALVE”). This is to get rid of any trapped air. If it is necessary, adjust the measurement device so that the height is zero when there is no flow.

Step 2: Calibrate Output Voltage

This step is necessary to calibrating the pressure transducer used for the orifice plate flow meter.

First, zero the voltage reading on the VFn interface box. Then, with the discharge valve closed, open the manometer valve labeled "CAL VALVE" to reduce the pressure. Take the readings of the the pressure transducer in volts (V) and the manometer in centimeters (cm). This process generally should be done five times total with the manometer valve opened more and more each time. The voltage output should NOT exceed 10 V as voltages read above this value are incorrect.

The LabVIEW software conveniently produces a linear least-squares analysis on the manometer-transducer data as it is collected and put into the software. It will calculate the slope which is crucial to a later step in data analysis.

Step 3: Data Acquisition

The first part of this step is to check the Gain Adjust control for the paddlewheel flowmeter is set to 6.25 turns (10 turns represents one thousand Ohms). Then use the Zero Adjust control to set the paddlewheel at zero.

After this preparation, open the discharge valve slowly until the allowable manometric deflection is reached or until it is entirely open. Observe the hydraulic orifice-plate flowmeter reading and the paddlewheel reading and record the values as soon as the paddlewheel reading has a significant nonzero value.

At the maximum flowrate, record the manometric deflection, the voltages provided by the paddlewheel, and the voltages provided by the pressure transducers from the oricifce-plate flowmeter. Keep in mind the maximum deflection value obtained from the manometer this value will be the h max value used later.

Step 4: Experimentation

When h max has been determined, you will be able to determine 90, 80, 70, (etc.) percent flow rates by using the proportionality of flow rate (Q) and manometric deflections (h): Q ∝ (h max)^0.5

This means when 90% flowrate is measured, you must find 81% of the maximum deflection or the decimal 0.81 multiplied by the maximum deflection. Record the voltage reading from the orifice-plate flow meter and the paddlewheel flow meter incrementally by reducing the flow rate by 10% each trial.

At each flow rate measurement a weight-time method must be used to measure Q in this way. This process may require multiple people as there must be someone to open the drain valve and close the drain valve, a person to place the counterweight on the scale, and a few people to measure the time it takes for the container to fill the weight. This process is simple, begin by closing the drain valve and let the containment tank fill. Once the tank fills enough so the scale is tipped by the tank the person holding the weight should place the weight on the scale and the timers should start recording. Once the container has added the specified amount of weight it will tip the scale and the time should be recorded for calculations. This time will be used to find the flow rate Q.

Step 5: Discussion (LR1)

After obtaining the data, you must prepare a graph of the flowrate Q measured by the weight time method to the manometric height deflection h of the orifice-plate flow meter. This graph should look like the following.

Step 6: Discussion (LR2)

The next step is to create a log-log graph of the previous graph. This should look like the following.

As seen in the graph, the data should look like it is on a linear fit. This linear fit should be strong which is shown by an R^2 value of 0.9666. Because the data appears to fall on a stright line after applying it to a log-log graph, the previous assertion (in Step 4) is confirmed that Q is proportional to the square root of the maximum value of the manometric deflection. This is equivalent to saying that Q = K(h)^m where K is some proportionality constant and m in this case is 1/2.

Step 7: Discussion (LR 5)

Next you must plot the calculated discharge constants (Cd) with the calculated Reynold's number (Re) on a linear log plot. Note that Re = ((V1)*D) / v, where V1 is the velocity in the pipe, D is the diameter of the pipe, and v is the viscosity calculated by LabVIEW as a function of the room temperature during the laboratory experiment. This plot should look like the first plot. The second plot was obtained in an experiment recently conducted on Februrary 26, 2024.

Step 8: Discussion (LR 6)

The next graph will be a graph using linear scales of both the volumetric flowrate Q and the voltage output from the paddlewheel flowmeter. Graph the flow rate Q as a function of the voltage obtained from the paddlewheel flow meter. The example shown had no cutoff values as all of the voltage values were in the acceptable range given by the apparatus information. These cutoff values for voltage were defined as values outside of the range of 0-10 V. The velocities must be calculated and determined. For the example, the velocities from high voltage to low voltage on the graph were 3.254 m/s, 2.567 m/s, 1.940 m/s, 1.295 m/s, and 0.633 m/s. This shows the maximum velocity of the fluid was 3.254 meters per second.

Step 9: Discussion (Q2)

Compare the discharge coefficient (Cd) with the Reynolds number (Re) and determine if Cd is essentially constant over the range of Re used.

From the experiment that was conducted and after observing the second graph used in step 7, Cd does have some relationship to Re. This relationship is not strong likely due to many errors causing this. These errors can be small things such as possibly trapped air, or errors in the temperature measurement. The temperature measurement is made with a simple mercury thermometer so the estimation for the viscosity constant by the LabVIEW software, v, may be wrong. Although the graph obtained by the experiment should look more like the graph determined professionally it has a similar net shape; as the Reynolds number increases the discharge coefficient will decrease.

Something that could mitigate this error would be to use more values of voltages. This would result in a great dataset which means more data could be extrapolated upon. This also would help when looking at the discharge coefficient in laminar versus turbulent flow and the difference would be more obvious. Something that could also get these values closer to the unity value would be to increase the diameter of the orifice-plate flow meter. This would result in less flow separation and a Cd value, closer to 1. The discharge coefficient values are also generally far from the unity value of 1. The relative error from the unity value of 1 and the average discharge coefficient value of 0.61 is 39% which is very far off.

Step 10: Discussion (Q4)

Determine the accuracy of the paddlewheel flow rate measurement method.

The paddlewheel flowmeter is less accurate at high flow rates because it can only spin so fast before it is letting water through without actually capturing it. Fluid moving too quickly would also result in the rate of measurement not being entirely accurate as it can only measure over periods of one second.

Overall, as with other technological devices to measure a property of a system, they are very convenient to use as they give relatively well establish values. This does not combat the fact that they will always be less reliable than a method that empirically measures how much weight or volume of fluid is flowing over a measured period of time. This weight-time method, as "archaic" as it is, has been used and will continue to be used as a more accurate method than the paddlewheel flow meter.

Step 11: Conclusion

Congratulations!

You are now ready to complete this laboratory and you are ready to calibrate bulk flow measurement devices such as orifice-plate flowmeters, paddlewheel flowmeters, and the classic weight-time method. You are able to observe the data and create the following graphs to provide a visualization for the data you will obtain. These graphs are important as they give many insights on if the data obtained can be utilized as accurate data or if it must be taken again with the same or possibly new methods. Thank you for your time and good luck on the new job.