TAM 335 Lab F: Calibration of Flowmeters

The setup for this lab is displayed through the three figures above. Figure 1 illustrates how we use a steady flow through a pipe connected to both the paddlewheel flowmeter and a Venturi or orifice-plate flowmeter to relate the pressure differences measured from the mercury manometer attached to the Venturi/orifice-plate flowmeter to the voltage output given by the paddlewheel flowmeter. Figure 2 shows the three sections that this lab is divided into with Figure 3 being the key describing the equipment used at certain spots among Figure 2.

Step 1: Introduction

The purpose of this lab was to use the pressure differences measured by either Venturi meter and an orifice-plate meter to calibrate a bulk-flow measuring device, in our case a paddlewheel flowmeter, to determine wether a simple monotonic relationship exists between the measured flow magnitudes and the paddlewheel flowmeters output. It is important to understand the concept of conservation of energy for this lab, when calculating the flow rate for both the Venturi meter and the orifice-plate meter it is assumed that the energy in the system stays the same so we can equate the pressures and velocities at two different points through the Bernoulli equation. Finally we must also understand the importance of the discharge coefficient in relation to the flow rate equation. One of the assumptions that we also must test when calculating the flow rate through the Venturi and orifice-plate meters is that the discharge coefficient for both is equivalent to one. This lab has us evaluate how the discharge coefficient varies with higher magnitude flow rates which we can then compare to the ISO discharge coefficient curves for both meters.

Step 2: Procedure

Prior to beginning data collection for this lab it is important to check for certain prerequisites including: the discharge valve being closed and that the mercury levels are even indicating no difference in initial pressure. We start by calibrating the output voltage of the Validyne differential pressure inducer. This is accomplished with no flow through opening the Manometer bleed valve and taking simultaneous measurements of the voltage output and the manometer heights. With five different measurements taken for both and the resulting data input into the LabVIEW software we can move onto data collection for actual flows.

Data collection can be taken by slowly opening the discharge valve, releasing a steady flow, until maximum deflection in the mercury manometer is reached. Once the maximum flow rate is reached data can be taken for the time-averaged pressure-transducer voltages along with the manometer reading, paddlewheel flowmeter reading, and a weight-time measurement taken from the weighing tank. This procedure is then repeated for slower flow rates which are based on by lower multiples of the earlier recorded maximum height. Once ten measurements are taken we can then find the flow coefficient through the LabVIEW software. The completed procedure should also yield a comparison between the paddlewheel flowmeter outputs and our weight-time measured flow rates for each height deflection used.

Step 3: Flow Rate Vs. Manometer Deflection Using a Linear Scale

The graph above shows the relationship between the measured weight-time flow rate we measured and the observed manometer deflection accompanying it. It can be concluded from the graph above that while we know a relationship must exist it is clearly not a linear one.

Step 4: Flow Rate Vs. Manometer Deflection Using a Logarithmic Scale

Unlike the Flow Rate vs. Manometer Deflection with a linear scale for the axis, a linear observation can now be seen in the graph. The linear relationship caused by a logarithmic scale on both axis indicates that a power-law relation applies of the type Q = K(deltah)^(m).

Step 5: Discharge Coefficient Vs. Reynolds Number

This graph shows the relation between the Discharge Coefficient and the Reynolds Number, Which can be calculated using the full diameter of the pipe (D) and the velocity found in the pipe (V1).

Step 6: Flow Rate Vs. Paddlewheel Voltage

The graph above shows a calibration curve for the Flow Rate measured through the weight-time method vs. the corresponding paddlewheel voltage provided for the given voltage. Since a linear relation can be observed it can be assumed that the two quantities are proportional. We can also assume that the velocity of the flow in the pipe is also relatable to the Paddlewheel Voltage found since the pipe has a constant area throughout. We can thus use the equation, V = (Q/A), to find the velocity using either the flow rate or the relation between the voltage and the flow rate.

Step 7: Discussion

Question #2: We can see from the data provided that while we did have a relatively constant discharge coefficient, as is wanted, the value of this number was not close to the ideal discharge coefficient which is one. This is not necessarily cause for alarm however, one of the major assumptions that we made is that conservation of energy would apply perfectly and that the flow rate was perfectly constant. In the case of our experiment however, some flows may not be entirely uniform and possible compression of fluids accompanied with stalls occurring. To have this theory better applied to our experiment, some of the assumptions about the flow may have to be relaxed taking into account energy losses or stalls that may occur around the flowmeters.

Question #4: The paddle wheel flowmeter can be seen as accurate through the linear relationship it had with the flow rates we measured through the weight-time method. The reading appeared to be more accurate at the lower flow rates that it could measure with most deviations occurring with the higher measured flow rates.

Step 8: Conclusion

This lab showed the method used to calibrate certain flowmeters and how to use a paddlewheel flowmeter to measure flow rates of given systems. We were also able to learn about the discharge coefficient in ideal conditions and evaluate potential causes for deviations from this ideal number. Overall, we were able to assess the reliability of different flow rate measurements by comparing their results to our baseline method of measurement, the weight-time method. While we were able to see that our most reliable method is still the weight-time method, we learned that an acceptable alternative for most situations would be the paddlewheel flowmeter especially at some of the lower flow rates.