## Introduction: Calibration of Flowmeters - Matthew Mota

Welcome to the new position!

The new company is excited to have you on the team and looking forward to having you work on the following laboratory exercise. We hope that you can follow along with the objectives, procedures and points of discussion. Please contact me, with the previously given contact information, if you have any questions.

## Step 1: Objective

The purpose of this entire laboratory exercise is to determine the preferable calibration of a Venturi meter and an orifice-plate meter with a paddlewheel flowmeter being used too. Flow coefficients will be calculated through experimental data and compared with ISO published values. These coefficients will help us understand the needed calibration for each meter type. The picture you see are examples of the meters you will be working with.

## Step 2: Theory

Using conservation of mass and Bernoulli's equation, we can end up with the following equation to relate the pressure difference in an apparatus:

p1-p2=(ρw/2)V2^2[1-(d2/D)^4].

ρw is the density of water, V2 is the velocity at a chosen point, d2 is the throat or orifice diameter of a given flowmeter and D is entrance diameter.

As well, the difference in pressure can be measured by using the differential manometer in the apparatus. The difference can be measured using the following equation.

p1-p2=∆h(SHg-1)ρwg.

∆h is the difference in height between the right side manometer to the left side manometer. When combing the two equation, we can get V2 and get Q, flow rate, by multiplying area. The ultimate equation is:

Q=(Cd/(1-β^4))(π(d^2)/4)(2g*∆h(SHg-1))^.5

Cd is the discharge coefficient that we are calculating for with the various flowmeters. The ideal value for Cd is 1.0, unity, for perfect flow. β is d/D which are the same values from the previous equations.

The equation can be simplified to:

Q=Cd*B*(∆h)^.5

B is a derivable constant from the geometry of the flowmeter and some other parameter factors. Cd should be constant despite different flow conditions.

## Step 3: Setup

The pictures shared show the plan view setup for the exercise in the laboratory. Every test will use one hydraulic flowmeter, Venturi or orifice-plate, and the paddlewheel flowmeter. The paddlewheel flowmeter should be connected to the Signet 8511 transmitter as that will determine the voltage output, the flow rate is determined by the voltage output. As well, LabView should be connected to the transducer to determine the pressure difference of the flowing water.

## Step 4: Calibration Procedures

- Make sure discharge value is closed.
- Ensure that the experiment is done statically with no flow.
- Make sure mercury levels in manometer are equal.
- Zero the transducer output on the VFn box.
- Bleed the "CAL VALVE" of the manometer and take recordings of the transducer output and manometer height differences using the LabVIEW software. Do not exceed 10 V.

## Step 5: Data Acquisition Procedures

- Ensure the paddlewheel flowmeter is has 6.25 turns for P1 and P4 and 3.00 turns for P3. These can be found on its Gain Adjust control.
- Open the discharge valve slowly.
- Start recording values when the transducer and voltage output readings increase.
- At maximum flow rate: record manometer heights, take weight-time measurements of the flow rate and ensure LabVIEW is recording values for the transducer and paddlewheel flowmeter.
- Repeat the procedures so that the flow rate is decrease to the point where the manometer height difference is only 90% of what it was. Keep on repeating in intervals of 10% until you reach 10% of the manometer height difference.

## Step 6: Results

After the experiment, make sure your data is gathered from LabVIEW and neatly put on a spreadsheet for convenient viewing. Tables and graphs are recommended to present the data. The following steps are some key points that you note down from your data and left open for discussion.

## Step 7: Flow Rate V. Manometer Deflection (Linear Scale)

## Step 8: Flow Rate V. Manometer Deflection (Logarithmic Scale)

On both graphs, the data points follow the trend-line very well. This shows that there is a correlation between flow rate and manometer deflection, which represents pressure difference. The relationship can be defined as a power-law relation:

Q=K(∆h)^m.

Make sure your data has a more-or-less similar trend.

## Step 9: Discharge Coefficient V. Reynolds Number

Reynolds number, determined by velocity times diameter of pipe over the viscosity of the fluid, has an exponentially decreasing relationship with the fluid's discharge coefficient. The relationship implies that the slower a fluid moves, the lower the discharge coefficient would be. This makes sense, as a more viscous fluid would move overall more slowly. Make sure to keep this mind to compare Reynolds number to flow rate as well.

## Step 10: Flow Rate V. Paddlewheel Voltage

The flow rate and voltage have a positive, linear relationship. This just goes to show that when the flow rate is higher, or the fluid is passing through the pipe faster, the paddlewheel can turn more and produce more power. While this data does not show any moment of when the paddlewheel is motionless, keep an eye out if yours does. By dividing the flow rate by the area of the pipe, we get a maximum velocity of 25.3 m/s. Ensure that your maximum velocity is similar.

## Step 11: Discussion: Cd & Paddlewheel

The Cd value was not recorded to be constant throughout the trials. As well, the Cd was not close to the unity value, of 1.0, that we had expected. The simplification of the flow rate equation may have impacted the Cd values derived. The friction of the hydraulic flowmeters would also interfere with accurate flow rate and Cd values. Keep this mind while doing your calculations, we would love to hear your ideas around this issue.

The paddlewheel was not very reliable as a method of obtaining flow rate values. The Cd, being far from 1.0, shows the problems of using a paddlewheel. It is clearly better at detecting larger values since those are closer to 1.0 than the lower flow rates. Keep this mind as you may come up with any improvements for this exercise.

## Step 12: Conclusion

As can be seen by the data, the coefficients of flow/discharge from the hydraulic and paddlewheel flowmeters were not very accurate to the theoretical values. The laboratory exercise could use some more time to develop and we would really appreciate any recommendations. Again, feel free to contact me at any time for any questions or progress.