## Introduction: Calibration of a Flowmeter

Welcome to the team! We are all looking forward to having you work alongside us. Please review the instructions below to begin learning about your work at your new position. Calibrating flowmeters is an extremely critical task for the analysis of fluid systems, so make sure to follow along and reach out if you have any questions.

## Step 1: Objective

The objective of this experiment and your role at the company is to calibrate bulk-flow sensors such as the Venturi meter, orifice-plate meter, and the paddlewheel flowmeter. This devices measure bulk flow by determining pressure changes, as well as the Reynold's number of the flow rate. The paddlewheel flowmeter functions similarly, but relies on voltage values to measure the flow. After calibration, the observed values must be compared to published ISO values that have been determined for this type of equipment.

## Step 2: Flowmeters and Theory

Venturi and orifice-plate flowmeters rely on observing pressure differences to determine the flow rate. Both of these can also be calibrated against the weight-time method to assist in the calibration process. It should be noted, however, that orifice-plate flowmeters are less reliable, as there is high energy loss within the system. Swirls occur on the backsides of the plates that ultimately reduce the accuracy of the flowmeter. For both hydraulic flowmeters, the pressure difference is measured by attaching pressure taps upstream and downstream of the convergence in the meter. A mercury-water manometer is attached across the system that can be easily measured to determine the pressure drop.

As previously mentioned, the paddlewheel flowmeter will instead rely on the voltage difference in the system to measure flow rates.

From Bernoulli's equation, we can generate the following equation to determine the pressure difference in the system:

p1-p2=(ρw/2)V2^2[1-(d2/D)^4],

where ρw is the density of water, V2 is the velocity at the point of observation, d2 is the diameter at the convergence of the flowmeter, and D is entrance diameter of the pipe. This equation can be simplified using the differential manometer to observe the pressure difference:

p1-p2=∆h(SHg-1)ρwg,

where ∆h is the change in the height of the mercury from the right to left side of the manometer, and SHg is the specific gravity of mercury. Combining these equations results in an expression for V2, which can be expressed as the flow rate Q when multiplying by the area:

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

where Cd is the discharge coefficient, and β is the ratio d2/D from the previous values. Cd =1 in ideal situations, but is found to be slightly less in practice. Upon further simplification, the equation can be reduced again to:

Q=Cd*B*(∆h)^.5

where B is a derivable constant that is based on the geometry of the flowmeter among other fixed parameters. This equation assumes a reasonably constant Cd, regardless of different flow conditions.

## Step 3: Flow System

The flow system and experimental setup for the lab can be seen in the above pictures. For each test, a paddlewheel flowmeter will be attached to determine the flow rate from the voltage output. It must be connected to a Signet 8511 transmitter to produce results. Additionally, either the Venturi flowmeter or the orifice-plate flowmeter will be employed the tests. Only one of these hydraulic flowmeters will be used for each test, while the paddlewheel flowmeter will appear at every test location.

## Step 4: Calibrating the Flowmeter

- Begin by ensuring the discharge valve is sealed. This procedure must be completed statically with no flow in the system.
- Make certain the two columns of mercury in the manometer are equal.
- Zero the transducer output VFn interface box.
- Open the manometer bleed valve. It is labeled 'CAL VALVE.' Record the readings of the transducer output and manometer levels in the LabVIEW software. Make sure not to let the maximum output voltage exceed 10V as the values will become inaccurate.

## Step 5: Collecting Data

- Use the Gain Adjust control to make sure the paddlewheel flowmeter has 6.25 turns for both P1 and P4 and 3.00 turns for P3.
- Begin opening the discharge valve. Do this carefully and slowly.
- Observe and record values of the voltage as soon as a significant nonzero value appears.
- Once the maximum flow rate is reached, record the manometer and paddlewheel flowmeter readings, take a weight-time measurement, and use the LabVIEW software to record the time-average pressure-transducer voltages.
- Repeat this procedure at 90% of the maximum flow rate. Continue to decrease the flow rate by 10% until it is only 10% of its original rate. Take the same data until the set of all ten points is completed.

## Step 6: Analysis

Congratulations! This concludes the experimental procedure for the calibration of flowmeters. The data must be recorded using LabView, and it can be tabulated and plotted to allow better visualization of the results. The following images and steps are highlights of the relationships observed in the experiment.

## Step 7: Plot of Flow Rate Vs Manometer Deflection on a Linear Scale

## Step 8: Plot of Flow Rate Vs Manometer Deflection on a Logarithmic Scale

Both the linear scale and logarithmic scale plots show the data adheres to the trend-line with good accuracy. This relationship indicates a correlation between flow rate and manometer deflection. The linking factor here is the pressure difference. A power law relates flow rate and manometer deflection very well, and any data gathered by this method should be modeled accurately by:

Q=K(∆h)^m.

## Step 9: Plot of Discharge Coefficient Vs Reynolds Number

Reynold's number can be determined by the equation:

ReD = V1D/v

where V1 is the velocity, D is the diameter of the pipe, and v is the viscosity. The plot indicates that the discharge coefficient decreases exponentially as Reynold's number increases. This relationship indicates that the discharge coefficient is lower for slower moving fluids. This should hold, as fluids with higher viscosities should move slower overall.

## Step 10: Plot of Flow Rate Vs Paddlewheel Voltage

From the plot, it is clear that there is a linear relationship between the flow rate and the paddlewheel voltage. As the flow increases, the paddlewheel turns more rapidly and produces a higher voltage. There are no data points on the plot that demonstrate a moment when the paddlewheel is motionless. The maximum velocity observed at the paddlewheel can be measured by using the maximum flow rate and dividing it by the area of the pipe it was passing through. That procedure generates a maximum velocity of about 25 m/s.

## Step 11: Discussion of the Discharge Coefficient and Accuracy of the Paddlewheel

From the plot, it is clear that Cd was not constant throughout the trials. the discharge coefficient did not even approach the assumption of unity of Cd = 1. This error might have occurred because of the physical presence of the flowmeters in the flow. The friction caused by hydraulic flowmeters, as well as the swirls that occur in the orifice-plate flowmeters would interrupt the flow as well as the Cd values. The ideal conditions for the unity assumption to occur do not take into account what happens in real practice.

It also seems that the paddlewheel was mildly inaccurate. As mentioned, all values of Cd were not constant and were not close to unity. It seems that the higher flow rates produced more constant results, as well as higher overall Cd values. This makes sense as the motion of the paddlewheel is more inconsistent at lower flow rates.

## Step 12: Conclusion

From the results, it appears that the hydraulic flowmeters did not do an extraordinary job of determining flow rates. The inconsistency of the Cd values as well as there overall low measurements verifies this performance. The paddlewheel flowmeter generated decent data, but became unreliable at lower flow rates as well.

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