Calibrating a Flowmeter

The ability to measure flow is something that is extremely useful when dealing with fluid mechanics. When designing pipes and other such vents/ducts, the amount of flow and all physical phenomena associated with flow are important to take into consideration. This is why the calibration and use of several methods of flow measurement will be discussed in this Instructable. We will be taking a look at the calibration of a pressure transducer, using a weight-time method to find the flow, and using the voltage outputs of both a hydraulic flowmeter and paddlewheel flowmeter. After the flow data is gathered with these different methods, there will be some discussion as to how to interpret it along with the importance of calibrating measurement systems.

• A stopwatch
• Paper/Excel spreadsheet to record data
• Signet 3-8511-P0 "lo-flo" paddlewheel flowmeter
• Validyne pressure transducer
• Orifice-plate flowmeter
• Mercury-water manometer
• Voltage measuring equipment
• NOTE: check Table 1 above for complete equipment descriptions and dimensions

After entering the lab, look for the large green pipe on the ceiling. In this vicinity, mounted to a support column of the laboratory is a mercury manometer with pressure taps coming from an orifice-plate flowmeter in a green pipe and entering a tube system with a pressure transducer and manometer system. We will be artificially reducing the pressure in the manometer tubing and then measuring the output of the transducer in volts using the equipment in the first image of this step.

The mercury manometer should have the fluid in both sides of the instrument level with each other at 0 before proceeding on with the rest of the experiment. After that is ensured, use the valve labeled in the second image of this step in the top-right corner marked "CAL VALVE" to bleed pressure out of the system. At least five data points should be recorded, all having 2 measurements: one with volts as the units and one with centimeters as the units. These will correspond to the data points reflecting the voltage given by the pressure transducer and the manometer deflection caused by the artificial drop in pressure. Make sure to use the bottom right screen of the voltage equipment when recording data for the pressure transducer instead of any other. The easiest way to make sure you take enough calibration readings for the manometer and transducer is to find the maximum measurable deflection of the manometer and then divide it by 6, thus letting the quotient indicate how much you should try to decrease the manometer reading before stopping and recording the next data. This will ensure you have more than 5 readings evenly spaced apart. Each time the manometer pressure is recorded, the corresponding voltage output given by the transducer should also be recorded with each manometer deflection per the data input file attached below. Once all the necessary data points have been measured, the calibration of the other flow measurement methods may begin.

Since a calibrated pressure transducer is now in operation, it is time to collect the flow data necessary for this experiment. A pressure transducer and a paddlewheel flowmeter will be used to obtain voltage outputs in conjunction with measuring the flow rate using a weight-time method. There will need to be 10 data point readings measured, all using a least squares system starting with (1.0) squared to (0.1) squared, decreasing by (0.1) each time, all multiplied by the maximum measurable manometer deflection. When taking these readings, it is best to calculate the least squares times maximum manometer deflection value beforehand. Once this is done and the target manometer reading is found, turn the black wheel on the valve labeled "F4" on the vertical portion of the green pipe. This will allow water to flow through the pipe. Once the water begins to flow, increase the flow until a maximum measurable manometer deflection is obtained.

Since the maximum flow rate is necessary to calculate the least squares and is necessary to measure anyway, it should be the first set of data points in the record sheet attached in the previous step. For each step where the flow rate changes, the voltage outputs of both the paddlewheel flowmeter and pressure transducer should be recorded. These voltage measurement locations are reiterated in the last picture of this step. After those two values are recorded, the weight-time method will be implemented to measure the flow rate.

First begin by checking to make sure that someone is watching the discharge tank and that someone is always on stand-by to use the drain valve. Allow the drain valve to remain open until the weight time setup is ready to be used. Let someone with a timer stand by the scale system and record the current plus another weight which they will add to the scale arm momentarily. Once the timer user with the weight, the tank spotter, and the drain valve user are all on stand by, this method is safe to start.

Begin by having the timer user tell the drain user to stop draining the flow. Once the top arm of the scale hits the overhanging piece of metal, the timer user must add the weight to the scale arm and then begin timing. When the weight is added to the scale arm, it will droop back down again. Once the arm hits the overhanging part of the scale again, the timer user must stop timing and record how long it took the flow to reach the total amount of weight on the scale arm. The weight on the scale arm must be recorded for each reading as well. It is at this point when it would be best to take the paddlewheel flowmeter and pressure transducer voltage output measurements and record them in the data sheet.

By the end of each step, there should be 4 measurements taken: the total weight on the hanging scale arm, the time it took for the water to push the scale arm to the top a second time, the paddlewheel voltage output, and the transducer voltage output. Once all these data points are recorded, the valve can be closed more such that the manometer deflections reflect the least squares value decreased from before. For example, if the manometer deflection is (1.0) squared times the maximum deflection for the first reading, the second manometer deflection should read (0.9) squared times the maximum deflection and so on for each step until your last step has a least squares value of (0.1) squared.

By this point in the experiment, the entire datasheet should be filled out with the proper data. Go to this link here for the Excel spreadsheet into which you will input your data: Calibration of flowmeters spreadsheet for plotting(Copy).xlsx. After the data is input into the Excel spreadsheet, it will automatically create 3 out of the 4 necessary graphs needed for full analysis. The graphs that will need to created are the plot of the plot of flow rate as a function of manometer deflection over a logarithmic scale and the plot of the discharge coefficient as a function of the Reynolds number. If it is desired, review what equations are used in the calculations of all the data in the Excel spreadsheet, please see the file attached labeled "Lab 6- Calibration of a Flowmeter Manual.pdf." Pages F-6 through F-11 would include the information sought after.

#1: The first image of this step is the data plot for flow rate Q as a function of the manometer deflection Δh for the orifice-plate meter using linear scales. This will be the calibration curve for the flowmeter.

#2: The second image of this step is the data plot for flow rate Q as a function of the manometer deflection Δh for the orifice-plate meter using logarithmic scales. This curve will be the alternate calibration curve for the flowmeter. The data has a trendline that is straight. This is an indicator that there is most likely a power-law relation Q=K(Δ)^m, with m being the slope of the line.

#5: The third image of this step is the data plot for the discharge coefficient as a function of the Reynolds number using linear-log scales. The Reynolds number equation used for the Excel calculation is in the file "Lab 6- Calibration of a Flowmeter Manual.pdf." The first value is not entirely accurate to the dataset as it has an extremely high discharge coefficient for a relatively low flow rate. This is being attributed to the fact that the coefficient of discharge for the flow was not measured directly. It heavily relies on a measurement from the pressure transducer which was calibrated earlier. However, the fact that the low flow caused the error is unsurprising since low flow rates are difficult to be measured accurately indirectly. The flow is sometimes too low to stimulate a voltage output that is accurate of what it really is.

#6: The fourth image of this step is the data plot of the discharge of the flow of the pipe given as a function of the voltage measured by the paddlewheel flowmeter. The discharge rate is what was measured using the weight-time method.

#2: The discharge coefficient was not constant over the range of Reynolds numbers tested in the experiment. The experimentally measured values for the discharge coefficient were significantly less than the ideal value of unity. The theory should be changed to account for the vorticities found behind the walls in reference to the direction of flow. The equation was stated to apply approximately anyway for the orifice-plate flowmeter, which is what we used. The fact that the theory only accounts for the one-dimensional flow (which does not include the vorticity created by the orifice plate) and is an approximation combined to yield a wide range of Reynolds numbers.

#4: The paddlewheel flowmeter was more reliable for the higher flow rates compared to the lower flow rates. This is because the flow must create enough inertia in order to push the paddlewheel in order to get it to spin, thus allowing us to get a voltage output. If the flow is too weak, then it might not turn the paddlewheel enough to receive accurate measurements of the flow. Having a higher flow rate helps create more inertia to initially make the paddlewheel start spinning and keep it spinning for accurate readings.