## Introduction: Calibration of a Flowmeter

Hi I am Yudu Chen, the former hydro-device engineer in this company. Because of the recent change on human resource, I will be leaving my position very soon, and we are expecting a new engineer to take my position, which primarily involves calibrating flowmeter, a device with which we measure volumetric flow rate of liquid through pipes. I expect the yet-to-hired engineer would be overwhelmed as I did when being asked to calibrate those devices. so I would write an instruction on how to d so, and I hope whoever is going to read this find this helpful.

## Step 1: Knowing the Pipes We Work With.

During our work, we mainly measure liquid volumetric low rate through two kinds of pipes, both of which involves change on cross-sectional area of flow and velocities of flow. The first kind we have is called venture pipe, a pipe whose change on cross-sectional area is gradual and relatively smooth. It is the pink pipe that you see when you enter our lab. The second kind we have is called Orifice plate. In this pipe, the pipe it self does not have change on cross-sectional area, but we have a plate that interrupts the flow and introduce sudden change in cross-sectional area. It is the green pipe you see in our lab. You can get their view on the above picture. The caplitalized D is the diameter of larger area in the pipe, and d is the diameter of smaller area in the pipe.

## Step 2: Knowing Three Measurement Devices We Work With

Before we dive into the lab procedure, I will first talk about three devices you would use to measure pressure difference between two points along the pipe. The reason why we need to measure the pressure difference is that it will be used in the Bernoulli's equation to calculate speed of fluid at the two points, and we can use continuity equation to find volumetric flow rate at those two points. Also, the pressure reading on the manometer is what we use to calibrate electronic pressure transducer as well as peddle wheel flowmeter.

The orange wheel is called paddlewheel flowmeter. As fluid flow through it, it would rotate, generating voltage proportional to flow rate.

The tubes connected to both Venturi pipe and Orifice plate are electronic pressure transducers, and they measure the pressure directly, whose reading you can find on lab computers through Labview software interface.

The last one is the differential manometer. As pressure on both sides of the manometer along the pipe changes, both sides would have manometer deflection due to pressure difference.

We would first work with the manometer to get actual pressure reading, and use them to calibrate the transducer for at different pressure drop between the two points. After calibrating the pressure transducers, we will use them to measure the flow rate of the liquid. We will also use those information on flowrate to model the discharge coefficient, cd, as a variation of area ratio between the two points. This information would be used to model energy loss associated with those two kinds of pipes. Although theoretically we would have different flow rate equation associated with cd for the two pipes, in practice, the equation for venturi pipe works fairly well to model the orifice-plate pipe. We will use this to analyze energy efficiency of those two pipe systems.

## Step 3: Calibrating the Pressure Transducer

We will now calibrate pressure transducers using pressure difference obtained from using differential manometers. Before we open the supply valve, make sure the manometer is equally heighted so we know it would have correct manometer deflection under a given pressure difference.

We first open the water supply valve. You can see a T shape handle in the laboratory near the scale we will use later to measure the mass flow rate.(which we can convert to volumetric flow rate by dividing by density of the liquid).

## Step 4: Adjust the Flow Rate Using Round Handle Valve

We will then adjust the flow rate using the round handle valve. We will first adjust it to the maximal flow rate by turning it counterclockwise until we can no longer move it. We will also reduce the flow rate in other trails. We will talk about how to adjust flow rate to a specific ratio of the maximum flow rate later after discussing the procedure for this specific trail.

## Step 5: Record Pressure Difference by Taking Manometer Deflection

Now we will measure the height difference between two side of manometer. You want to do so when the flow reaches the steady state when it is not changing with time. Obtaining the height difference, you can then calculate the pressure difference using the manometer law, which I believe an engineer should be familiar with. As you record manometer deflection and calculate pressure difference, your colleague would use the pressure difference you get to average the output of the peddle wheel and of the pressure transducer. Record the voltage on both devices for later analysis.

## Step 6: Measure the Mass Flow Rate As an Add on of Info on Pressure Difference

Although theoretically, we can measure the flow rate directly using what we know about pressure difference, we should also measure the flow rate directly using the weight-time method as an additional source of information we use in the analysis. As you can see, there is a scale in the laboratory near the manometer. The leverage of the scale is adjusted to 1 : 200 such that one pound of weight on the scale is equivalent to 200 pounds of water flowing into the tank in the basement. Given a weight placed on the scale, we can start our stopwatch as we open the valve and stop recording when the weight is balanced such that the mark on the scale is pointed by the lever. The weight of liquid moved during the time interval, which is 200 times weight on the scale, divided by the time it takes to balance the scale, in second, would give us the flow rate. Although human error would cause certain inaccuracy, but it should not affect the precision.

## Step 7: Change the Flow Rate at Certain Successive Order

Now we change the flow rate to 90%, 80% to 10% of the maximal flow rate. The way we do so is by observing the manometer deflection. By the Bernoulli's equation, we know the pressure difference is proportional to the manometer deflection and square of velocity of fluid on the streamline, so as velocity, which is proportional to flow rate, drops to 90% of the maximum, the manometer deflection would be 90% square, so we can just adjust the valve until manometer deflection is 90% square of the maximum one. We change the flow rate according to this formula for flow rate between 10% and 90% of the maximum, and repeat step 3, 4, 5, 6 for each flow rate. By the end of the experience, we should have complete data on the flow rate of the liquid and a set of well calibrated flow meters.

## Step 8: Analyze Graphs (Lab Report 1, 2 ,4, 6)

Now we have finished data collection, we can plot the data and analyze their implication. We see that when plotting in log-log scale, flow rate vs deflection graph shows a linear trend. This is an important implication that the relationship between flow rate and deflection could be modeled as the power of deflection, and we can measure its slop to obtain the exponent on deflection to find a more symbolic equation to model their relationship. We can also calculate flow velocity from the flow rate measurement. The maximum flow rate in this experiment is 0.02012 meter cube per second, and slowest is 0.00316 meter per second. Given the throat of both Venturi meter and orifice plate has diameter of 88.9 mm, we use the fact that volumetric flow rate = flow velocity * cross-sectional area, we get the maximum is 3.24141 meter per second and the cut off minimum is 0.50909 meter per second.

## Step 9: Discussion (Question

Now we have seen the plot obtained from our data, we see that discharge coefficient ranges from 0.454 to 0.589. This shows that discharge coefficient is not an unity and it has huge discrepancy at different flow rate. This implies that our model for volumetric flow rate on orifice flow meter is not accurate that we can't simply apply our model on Venturi pipe to orifice plate pipe. This is because the orifice plate is an interruptive protrusion in the pipe. This protrusion does not change the streamline gradually, and it generates more collision than that of Venturi pipe, causing more kinetic energy loss to the form of heat energy. We should correct this by taking the energy loss due to collision into account. We should not assume that we have steady flow in the orifice plate pipe and we should assume the discharge coefficient is a variation of volumetric flow rate because higher velocity would cause more drastic collision and thus more energy loss in the system.

However, a good news is that we see, in the linear scale, that output voltage from the peddle wheel is nearly a linear function with respect to flow rate, as is true in vice versa, and axis intercept is small. Because the rotary velocity of the peddle wheel should, in theory, be linearly proportional to the flow rate due to conservation of angular momentum, and our plot shows conformity to the theorem throughout entire flow rate region, I would argue peddle wheel makes very accurate measurement at both low and high flow rate and could be used as a reliable tool in the future flow rate measurement.

I hope this manual helps clarifying what you need when taking flow rate measure with out lab devices, and I with you good luck and hope we would have great time working together.

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