The objective of this project is to calibrate flowmeters that depend on pressure changes (Venturi meters and orifice-plate meters) by calculating flow coefficients as a function of flow rate in terms of Reynolds number. The integrity of these calculated values will be determined by comparing them to published values.

The apparatus will be set up as shown in Figure 1. It will contain either a venturi meter or orifice-plate flowmeter and a paddlewheel flowmeter. The venturi/orifice-plate flowmeter will have a differential pressure transducer and mercury-water manometer to measure the pressure differences between the entrance of the flow and the initial contraction point of the flowmeters.

Be sure to read through the documentation for each station and understand what type of flowmeter you are working with.

The paddlewheel flowmeter will be a Signet 3-8511 "lo-flo" device with an operating range of 0.3 - 20 ft/s. This will be connected to a Signet 8511 transmitter that outputs 3-20 mA that will be sent through a resistor R to produce a variable output voltage.

For this experiment, the standard for calibration will be the flow rate measured using the weight-time technique with weighing tanks. There will be three weighing stations. Station F-1 and F-4 as shown in Figure 2 will have a weight ratio of 200:1. Station F-3 will have a weight ratio of 10,000:1.

The software that is will be used in this experiment is LabVIEW. This software will handle data collection, but first, the pressure transducer as shown in Figure 1 must be calibrated. LabVIEW will be collecting data on the flowmeters and from this will calculate flow coefficients, an output spreadsheet, and manage output files.

Supplies

Apparatus (as shown in Figure 1).

Weighing tank.

Weights.

Step 1: Step 1: Setup

To start, ensure the discharge valve is closed. The locations of each discharge valve are shown in Figure 2. Next, check the mercury-water manometer and make sure the level of mercury on both sides is level. If the mercury is not level with each other, open the manometer drain valve (one should be labeled "CAL VALVE") and bleed any trapped air in the supply lines.

Step 2: Step 2: Calibrating the Pressure Transducer

As previously stated, in order for LabVIEW to start collecting data, the pressure transducer must be calibrated.

First, zero the transducer output interface box (labeled by VF#on Figure 2). Make sure the discharge valve is still closed from step 1, then open the manometer bleed valve (labeled "CAL VALVE"). This will now allow the pressure to release in one of the manometer lines which then will let LabVIEW take measurements of the transducer output and manometer levels. Record this data in the LabVIEW software.

Five data points will be taken in this process and the voltage should not exceed 10V since the A/D board cannot read voltages higher than 10V.

LabVIEW will then use a linear least-squares analysis on the transducer data collected to generate the slope and intercept of the least-square line. This information will be used in the next step. To finish this step, close the "CAL VALVE".

Step 3: Step 3: Data Acquisition From Flowmeters

In this step, LabVIEW will be used to collect data from both flowmeters and this will be used to calculate the flow coefficient as a function of the flowrate expressed in terms of Reynolds number.

First, make sure the Gain Adjust control of the paddlewheel flowmeter (labeled P# on Figure 2) is set at 6.25 turns for P1 and P4, and is set at 3.00 turns for P3. Afterward, using the Zero Adjust control, zero the paddlewheel flowmeter output.

Now, open the discharge valve slowly until either the valve is completely open or the maximum deflection is reached for the manometer. Be extremely careful at this step at station F-1 as the mercury can be forced out even if the discharge valve is slowly opened.

To record voltage readings, pay attention to differential pressure voltage reading and paddlewheel voltage reading as the flow rate increases. When both voltage readings have a significant nonzero value, record both voltage readings.

When either the flowrate is max or max deflection is reached, record the manometer readings, record paddlewheel readings, take a weight-time measurement, and, using LabVIEW, record the time-averaged pressure transducer voltage. Take note of the maximum manometer deflection. The maximum manometer deflection will be used to determine the successive flowrates. Also, for F1 and F3, only record data when the flow is going into the weighing tank.

Nine more data sets will be taken from here. Take the next nine data sets at (0.9)2Δhmax,(0.8)2Δhmax,...,(0.1)2Δhmax. In terms of flowrate, this means measurements will be taken at 90% of max flowrate until 10% of max flowrate.

Unlike the first measurement, voltage readings will be taken at a different requirement. As the flow rate is decreased for the next data sets, measure both voltage readings only when the paddlewheel voltage drops suddenly to zero.

The measurements of the other data information will be the same as the first iteration.

Once data collection is finished, the flow coefficient will be displayed in LabVIEW as a function of flowrate in terms of Reynolds number and the flowmeter readings will be in a spreadsheet at each flowrate as calculated using the weight-time technique.

Step 4: Analysis and Discussion

Note the data collected here was at the F-4 station. The information corresponding to the F-4 station can be found in the Introduction.

A power-law relation, Q = K(Δh)m can be shown between flowrate and manometer deflection. To start showing this relation, plot the flow rate vs manometer deflection on a linear scale and plot it against a smooth curve. From the plot Flow Rate vs Manometer Deflection (Linear Scale), it is easy to see that these points and the curve don't look linear, but in order to show a power-law relation, there must be a linear relationship in the logarithmic scale, not the linear scaling. After calibrating the curve to a log scale, the plot changes and appears to have a linear relationship as shown in the Flow Rate vs Manometer Deflection plot. Therefore there exists a power-law relation between flow rate and manometer deflection. With the data recorded, the relation can be approximated by Q = 0.0014(Δh)^0.5674.

This power-law relation can also be seen between Discharge Coefficient and Reynolds Number. As shown in the plots Discharge Coefficient vs Reynolds Number (Log/Linear Scale), the same pattern follows as with the flowrate vs manometer deflection. On the linear scale, there is a curve and on the log scale, there is a linear line. Once again, a linear line on a log scale indicates there exists a power-law relation. This relation can be approximately defined as Cd = 0.1324(Re)^0.1221. There is more that can be investigated here. From the plot, it is shown that the discharge coefficient appears to have a linear relation just from looking at the linear scale plot and appears to be constant despite the Reynolds number changing but magnitudes of 10. While this may seem to be confusing, this is actually a relatively accurate representation. Looking at the ISO data provided, the sensitivity of the discharge coefficient is inversely proportional to the Reynolds number. Since the magnitude of the Reynolds number in the experiment is larger than 10^5, the effect of the Reynolds number is very low, which explains why the discharge coefficient stayed relatively constant.

There also exists a relation between paddlewheel voltage and velocity. From the plot Flow Rate vs Paddlewheel Voltage, a linear relationship is shown between the voltage and flowrate. This plot also shows there are cutoffs for the velocity of the fluids in this dataset collected. Knowing Q = VA, and A = 12.57in^2 the cutoff velocities can be calculated. The resulting upper and lower cutoffs are 2.48m/s and 0.390m/s.

Another question to be answered is the accuracy of the paddlewheel flowmeter. Using the ISO curve as a guideline, as flowrates increased, the accuracy of the discharge coefficient was much higher than at lower flowrates. From the data recorded, the relationship between discharge coefficient and flowrate has an incorrect relationship at lower flowrates leading the accuracy to be worse at those rates. This may be due sensitivity of Reynolds number at lower discharge coefficients. Despite being worse at lower flowrates, the use of a paddlewheel flowmeter is still good. The discrepancies only occurred after the flowrate got less than 0.1029m^3/s but it is also true that the values calculated in this experiment were very close to the actual values.