Lab 6 Calibration of a Flowmeter (Partial Report)

In this lab, the objective is to calibrate two types of flowmeters. The first type includes Venturi meters and orifice-plate meters, which utilize pressure change measurements. The calibration will be done by determining the discharge coefficients as functions of the flow rate and comparing these flow coefficients to the accepted ISO values. The second type of flowmeter includes a paddlewheel flowmeter, which provides a voltage to measure the flow and will also be calibrated.

Supplies

This equipment is necessary for conducting this experiment.

Step 1: Experimental Setup

Step 1. Make sure the discharge valve is closed and the mercury levels in the differential manometer are equal. If the mercury levels are not equal, slowly open and close the two manometer drain valves until all of the trapped air is removed and the mercury levels even out.

Step 2: Calibration of the Manometer Differential Pressure Transducer

In this step, we will calibrate the Validyne differential pressure transducer, which measures the pressure difference caused by a hydraulic flowmeter, with 5 different pressures.

Step 2.1. Zero the transducer output on the VFn interface box.

Step 2.2. Open the valve to reach the maximum flow rate.

Step 2.3. Record the readings produced by the transducer in volts and the manometer levels in centimeters.

Step 2.4. Additionally, record the weight-time measurement to figure out the exact flow rate. Pick a weight and have it on standby, along with a stopwatch. Then, overbalance the scale so that the arm of the scale hits the bottom of the stop and close the drain. Once the scale arm rebalances, start the stopwatch and add the weight promptly. The scale arm will be unbalanced again. When the scale arm rebalances again, stop the stopwatch.

Step 2.5. Reduce the height of the mercury levels in the manometer. The height you reduce by will depend on your starting height. Divide the maximum/initial height by 5 and reduce the height of the mercury level by that interval. Repeat this until you reach a height of 0 cm, you should end up with 5 unique data sets.

Step 3: Collecting Data

In this step, we will collect data from both types of flowmeters.

Step 3.1. Open the discharge valve slowly until the valve is fully open or you reach the maximum allowable manometer deflection. Record this deflection as Δhmax.

Step 3.2. As you increase the flow, observe both voltage readings. As soon as the paddlewheel voltage changes to a significant nonzero value, record both readings.

Step 3.3. At the maximum allowable flow rate, record the:

manometer readings
paddlewheel flowmeter readings
weight-time measurement (to measure the flow rate)
time-averaged pressure-transducer voltages

Step 3.4. Repeat these steps for successively slower flow rates, which will be determined by manometer deflections (Δh) that are approximately 0.9^2 * Δhmax, 0.8^2 * Δhmax,..., 0.1^2 * Δhmax. For the following configurations, allow the mercury in the manometer to become steady before proceeding.

Step 4: Results (LR1)

Use the data collected to plot the flow rate Q as a function of manometer deflection and allow a smooth curve, which will act as a calibration curve, to pass through the data.

Step 5: Results (LR2)

Use the data to plot the flow rate Q as a function of manometer deflection on logarithmic scales and allow a smooth curve, which will act as an alternate calibration curve for the flowmeter, to pass through the data. The data does not appear to fall along a straight line, which means that the relationship between manometer deflection Δh and flow rate Q is not linear. However, the data points do fall along a nonlinear line, which may indicate that a power-law relation of the type Q = K(Δh)^m applies to the data.

Step 6: Results (LR5)

Using values from your calibration curve, plot the discharge coefficient Cd as a function of the Reynolds number Re on linear-log scales. The Reynolds number is calculated using the full pipe diameter D and the velocity in the pipe V1.

Re = (V1*D)/v

Step 7: Results (LR6)

Use the data to plot voltage output vs. the actual discharge rate calculated using the weight-time measurements. Allow a smooth curve, which will act as a calibration curve, to pass through the data points with linear scales. Based on the graph, since the data appears to have a solid linear relationship, there is no specific fluid velocity cutoff. However, it can be assumed that the cutoff velocity is outside the range of 0.633 m/s to 3.254 m/s because these are the minimum and maximum values for the velocities found in the experiment.

Step 8: Discussion Questions (Q2, Q4)

Question 2:

The discharge coefficient Cd does appear to be constant over the range of Reynolds numbers tested. As shown in the data, the discharge coefficient ranges from 0.59 to 0.61 across the various Reynolds numbers. The experimentally measured values for Cd are not close to the ideal value of unity derived theoretically (value of 1). This may be due to estimations made during data collection or because we did not account for the friction along the walls of the pipe. Additionally, the flow was assumed to be steady, although it may not actually have been steady due to the limitations of the equipment. In order to obtain more realistic values for Cd, the theory will have to incorporate factors such as friction.

Question 4:

The paddlewheel flowmeter is reliable. According to the graph in the previous step, Step 7: Results (LR6), the measured paddlewheel voltage has a strong linear relationship with the flow rate. The flowmeter does not appear to perform better at specific flow rates (same performance at both high and low flow rates) because the data points are equally close to the line of best fit for the data set. There is no correlation between the stray from the best-fit line and the flow rate, so it can be assumed that the flowmeter performs equally well at both high and low flow rates.