TAM 335 AB2 Lab 6: Water Engineer-in-training Guide to Calibrating Flowmeters

This is a general guide that will instruct you how to calibrate some common flowmeters to accurately measure flow rate in water systems. These flowmeters are used by cities and municipalities, companies, and homes, mainly to measure water usage, but for other things as well. By the end of this tutorial, you should have a good idea of how to calibrate a newly developed flowmeter so that it can take accurate measurements. Good luck, and remember: if you get stuck, it’s better to ask a dumb question than to pretend you know what you’re doing!

Supplies

Our laboratory setup is shown in the schematic above. The rest of the instructions will refer to items on it.

The hydraulic flowmeter will be either an orifice-plate or Venturi design, and should be attached to a manometer and Validyne pressure transducer system to measure the pressure drop across the plate/throat. The paddlewheel flowmeter is the Signet 3-8511-P0 with Signet 8511 transmitter.

For the purposes of instruction, I will provide sample plots and findings for an orifice-plate and paddlewheel flowmeter throughout the process.

Step 1: Pre-calibration Checks

To start, make sure that discharge valve Fn for the system you're using shown in is closed. Again, refer back to the schematic to locate the discharge valve. Next, check that the mercury levels in the manometer attached to the pipe you're using are at the same heights. If they aren’t, slowly open and close the two manometer drain valves (one is labeled “CAL VALVE”) to bleed any trapped air in the supply lines. Adjust the scale origin until the mercury level is at 0 cm if needed.

Step 2: Calibrate the Pressure Transducer

Zero the transducer output on the VFn interface box attached to the computer you're using. Next, record five voltage and manometer height measurements in the LabVIEW software as you incrementally adjust the "CAL VALVE" from closed to open. The first measurement should be taken when the valve is completely shut, and the fifth measurement when the valve is completely open. If the voltage exceeds 10V ask another engineer for assistance - above 10V will not be measured correctly.

Click 'Finish' on the LabVIEW software when you're done and move on to the next step.

Step 3: Acquire Data

First adjust the Gain Adjust control for the paddlewheel flowmeter to the corresponding value:

1. P1 (pipe 1) & P4 - 6.25 turns
2. P3 - 3.00 turns

Then use the Zero Adjust control to set the paddlewheel output to zero.

Next, slowly open the discharge valve until the mercury levels surpass the scale length, or until maximum flow, whichever occurs first. DO NOT ALLOW THE MERCURY TO ESCAPE THE MANOMETER. Err on the side of caution. Record the water temperature in LabVIEW after letting the water flow a short while.

For each flow rate, wait until the mercury in the manometer has become reasonably steady before acquiring data.

At the maximum flow rate, record the manometer readings, record the paddlewheel flowmeter readings, take a weight–time measurement, and, using the LabVIEW software, record the time-averaged pressure-transducer voltages. Make a note of the maximum manometer deflection ∆hmax . For F1 and F3, acquire data only as the flow is going into the weigh tank.

Repeat the procedure at successively slower flow rates set so that the total manometer deflections ∆h are approximately (0.9)^2 ∆hmax, (0.8)^2 ∆hmax, (0.7)^2 ∆hmax, ... , (0.1)^2 ∆hmax. This will correspond to 90%, 80%, 70%, ⋅ ⋅ ⋅, 10%, of the maximum flow rate, respectively. Observe carefully both the Validyne differential pressure voltage reading and the Signet paddlewheel voltage reading as the flow is decreased, and record both readings at the instant when the Signet paddlewheel voltage drops suddenly to zero.

After the 10 data sets have been acquired, the flow coefficient Cd is displayed in the LabVIEW software as a function of the flow rate expressed in terms of the Reynolds number Re, and the paddlewheel flowmeter readings are recorded in a spreadsheet with the flow rate Q measured by the weight–time method.

Step 4: Data Analysis - Hydraulic Flowmeters

For the hydraulic flowmeters, the flow rate theoretically can be represented as

Q = (C_d)*B*(∆h)^.5

C_d is the dimensionless discharge coefficient, and B is a derivable constant based on flowmeter geometry and an other fixed parameters. C_d should be relatively constant over small flow rate changes. The full equation for flow rate attached above allows us to solve for B.

First, solve for flow rate using the weight-time data. Then, using linear scales, plot the data points for measured flow rate Q as a function of the manometer deflection ∆h for either the Venturi meter or the orifice-plate meter, whichever was used. Pass a smooth curve (may or may not be a straight line) through the data. This curve is the calibration curve for the flowmeter under analysis.

See the sample Q vs ∆h plot above.

Repeat the above step, this time using logarithmic scales. This is an alternate calibration curve for the flowmeter. The data will appear to fall along a straight line (see sample log-scale Q vs ∆h plot attached), indicating a power-law relation of the type Q = K(∆h)^m.

The sample plot shows that m is approximately .5, which allows us to calculate C_D, since K = (C_D)*B, and as mentioned previously, the full equation linked above allows us to calculate B. Calculate the C_D values for each flow rate measurement set.

Using values from the calibration curve, plot the calculated discharge coefficient C_D as a function of the Reynold's number Re_D on linear-log scales. Remember that Re_D = V*D/nu, where V is the fluid velocity (can be calculated from the flow rate), D is the pipe's inner diameter, and nu is the dynamic viscosity of the water. LabVIEW will calculate nu for you when you input the water temperature.

See the sample plot attached. Compare it with the reference plot also shown (White, 1994). In the case of my sample, I used pipe P4, which has β = d/D (see Table 1 above) approximately equal to 0.5 . Though my data points show some variation from the reference plot, they are still reasonably close to the 0.5 isobar.

Step 5: Data Analysis - Paddlewheel Flowmeter

The voltage produced by the paddlewheel flowmeter should be linearly proportional to the fluid velocity in the pipe.

Plot a calibration curve using linear scales for the paddlewheel data, using voltage output versus discharge rate Q (calculated previously using the weight-time method). Indicate if there are any rising and falling cutoff flow rates below which the paddlewheel appears motionless. Calculate the corresponding cutoff fluid velocities, and the maximum fluid velocity reached.

See my plot above for an example. In my case, the paddlewheel continued to output voltage even at flows well below its specified range, with no clear indication of a cutoff point. The paddlewheel seems to show slightly rising voltages (and thus measured flow rates) at flow rates between 0.0075-0.01500 m^3/s, and falling voltages at flow rates outside of that range. Overall the paddlewheel data confirms a linear dependence of voltage versus flow rate for its measurements.

For reference, the transducer voltage vs flow rate series is also shown, where Voltage = Q^2 due to a difference in measurement techniques.

The lowest and greatest fluid velocities are calculated using V = Q/A, where A is the cross-sectional area of the pipe. My V_min and V_max were 0.313 m/s and 2.42 m/s, respectively.

**TA please note there is an error in the Excel formula, you have (pi*1/4*D)^2 instead of pi*1/4*d^2.

Step 6: Discuss Your Results

Here is a good place to test the validity of your assumptions and make corrections to your theories.

One of the assumptions I made was that the discharge coefficient C_D is essentially constant for my dataset. However, this was shown not to be true in the C_D vs. log(Re) plot, with C_D values varying up to half a unit. In addition, these C_D values are well below their theoretical value of unity. The theory used to derive C_D did not take into account head loss due to flow separation, viscous effects, and turbulence. This can be improved by using a material derivative for finite control volume analysis rather than the Bernoulli equation, which can account for head loss instead of assuming steady, inviscid flow along a streamline.

These corrections are likely included in the ISO reference charts, which is why my C_D values were closer to reasonable values in comparison to them.

Though paddlewheel flowmeters are known to be inaccurate at very low and very high flow rates, the Signet performs relatively well. It has a reported functional range of 0.3-20 ft^3/s, but it was still outputting voltage at 0.09 ft^3/s. The readings it took were more accurate at low flow rates. At high flow rates, the linear curve of the paddlewheel data falls further and further away from the true curve, which looks more like V = Q^2.

Step 7: Repeat

Keep developing your theories until they can almost entirely predict the empirical data! We'll also be sending some new flowmeters your way regularly for testing, and you may have to develop new theories for calibrating them. I've attached a video about electromagnetic flowmeters that I hope you'll find interesting. Good luck and have fun!