Operating the Lab 6 Apparatus

Here is the schematic design for the flow that you will be working with.

Important parts of the apparatus include:

1. Discharge valve - Controls the flow of water (counterclockwise to open) (Image 1)
2. Voltage display - Given user input on voltage change in pressure transducer (Image 2)
3. Manometer - Used to measure the same pressure change as the transducer (Image 3)
4. Discharge weight scale - Used to measure the weight of output flow (1:200 weight ratio) (Image 4)
5. Weight-tank output control - Used to stop water from exiting the tank (Image 5) for weight-time measurements

The first step in operating the apparatus will be to calibrate the differential pressure transducer. To begin, ensure that the manometer's columns align, and if they are not use the bleed valves to remove air from the system and balance them. Also, note down the temperature I the lab. Now, without starting any flow, use LabVIEW to take a reading of the voltage output along with the difference in the heights of the manometer (This should be 0 for the first point). Next, use the bleed valve labeled "CAL VALVE" (with the green handle in the image) to artificially alter the pressure. Take voltage readings at each of the different pressures as you continue altering the pressure with the bleed valve until at least five data points have been recorded. The LabVIEW program with do a least squares regression to calibrate the instrument for the rest of the lab. Make sure that water refills the system, and CLOSE the CAL VALVE for the rest of the tests.

Next, slowly but completely open the discharge valve. Then, slowly close it until the voltage display reads ten or slightly less. We will treat this as the maximum pressure difference for the rest of the tests. Mark down the difference in height read on the manometer. Next, use the weigh station to measure the mass rate of flow. For early trials, with higher flow, it is best to use a larger mass on the scale so that it does not flip too quickly. Remember, 1 pound on the scale measures 200 pounds in the tank. Now, we will aim to reduce the flow rate by 10%. Using what we know about flow rate, we will want to close the discharge valve until the difference on the manometer reads 81% of its original value. This is because of the presumed square relationship between flow rate and pressure difference. The first image in this section shows a table with the relationship to follow to get proper 10% drops in flow rate. Continue taking data points reducing the flow by 10% each time until all ten points have been collected.

First, by graphing the flow rate against the deflection in the manometer (Image 1), we can start to see the curved trend line that we expect, but we want to be sure that it follows a power relationship along the lines of Q = K(dh)^m. To do this, change to using log scales for the axis of the graph. In image 2, we can see that by doing this the data seems to fall linearly. This supports the assertion of the power relationship linking flow rate and the height of the manometer.

Next, we will graph with discharge coefficient vs the Reynolds number on a linear log scale. The Reynolds number is calculated for us by LabFLOW using the entire pipe diameter and the viscosity that correlates to lab temperature. We would expect the result of each point to be constant across all trials, so identifying outliers from this value will aid you in your work. In the example provided, the value at 1.23 is extremely concerning, because any value over 1 is physically impossible. Also, the values approaching 0.7 are also somewhat cause for concern. Further discussion on what to do about outliers can be found section Understanding the Discharge Coefficient.

Next, you will look into the paddlewheel's calibration using the data already collected. The paddlewheel is only rated to have a voltage range of 10 V, but because the data in the test trial only goes up to 5.5 V we do not see the cutoff that would typically occur as readings get too high and results get inaccurate. When you are conducting your own measurements, always be cautious when approaching high or low values of voltage. At low speeds, the wheel's own inertia becomes a considerable factor, and at high speeds it may reach a critical velocity. We can see where the low voltage measurements start to break down on the graph, as the paddlewheel measures the same voltage drop for the last two trials, even though their flow rates are substantially different. The paddlewheel's inaccuracy at low flow rates can also be seen in the y intercept of the calibration curve. This point being at 0.56 means that from our calibration, we would expect the voltage drop to be zero while there is still flow moving through the pipe which is not favorable. Using the paddlewheel's measurements is also a great way to measure the velocity of the water. If we take the max flow rate divided by the circular area of the pipe, we can find that at our highest flow state, the water was traveling about 2.41 m/s.

Throughout these trials, our discharge coefficient was typically about 0.6. This makes sense, because using the chart in Image 2, we can see that with a beta value of 0.5 (The diameter halves through the orifice), which is what we used for these test, we expect a value of just over 0.6. The biggest outlier which was already mentioned in step 4 is the value at 1.23. If you were to acquire a value like this in your work, I urge you to attempt to find the source of its error, since the value is not physically possible. Other possible experimental outliers may be encountered around 0.7. These errors cannot be omitted from the data so easily as the first one, since they are much closer to the expected values, and also theoretically possible. If you plan to omit these measurements in your work, justification must be provided. The theoretically ideal value of unity is 1, however, this is never found to be the case experimentally. Using the orifice plate meter, a lot of turbulence is encountered, and the loss of energy due to friction cause the output flow to be slower than expected with theoretical laminar flow.

To ascertain the reliability and accuracy of the paddlewheel, you will want to look at how closely the voltage drops fit with the flow rate through a linear relationship. In this case, the R squared value is 0.9924 (Image 1) which means that the data is fitting to the line quite well. Another way to test for certain points' accuracy would be to remove them from the data used to create the best fit line, and then compare them to the line created from the other point. This could be a way to search for outliers, since if you take out a point and the R squared value of the line greatly improves, that point had severe influence away from the rest of the points. You can also assess accuracy for high vs low values by looking at how closely the data in that region follows the line. From the sample data taken, we can see that the paddlewheel loses accuracy at low flow rates, since those points are much further from the line than at higher values. This helps us in establishing a lower limit for the paddlewheel's reliability. You can use higher flow rates in your studies to try to assess the point where the paddlewheel loses accuracy on the other end.