Calibration of a Flowmeter - Haylee Cox

Hello, congratulations on the new position! In order to acclimate you to the environment of the company and the duties you will be completing, I have created a small tutorial below. If you have any questions on flowmeter calibrations, check this guide as it may be useful. Happy callibrating!

When given the data from a hydraulic flowmeter experiment, you can easily plot the flow rate, Q, with respect to the manometer deflection, h in a program such as Excel. In this case, we are using linear scales on the plot to obtain information. Next, you can pass a smooth curve through the data using the necessary trend line option (power, log, linear, etc.), which is used as the calibration curve for the flowmeter.

Similarly, you can plot the same data from the hydraulic flowmeter using logarithmic scales. You can then plot a power trendline along the data and use this as an additional calibration curve. As seen on the plot above, the power trend line shows a very linear relationship between flow rate and manometer deflection. Because of the linearity of the data set, we know that a power-law relationship exists, denoted as Q = K(h)^m. This indicates that: "there is a relationship in which a relative change in one quantity(flow rate or manometer deflection) gives rise to a proportional relative change in the other quantity, independent of the initial size of those quantities." If there is not a linear relationship on your plot, you know that a power-law relationship does not apply.

Next, you can plot the discharge coefficient (Cd) as a function of the Reynolds number (Re) on linear-log scales, which are two values obtained from the hydraulic flowmeter experiment. The Reynolds number for each test run can be found using the following formula: Re = (V1*D)/ v, where V1 is there velocity in the pipe, D is the diameter of the pipe, and v is the viscosity of the fluid. This plot can be used to make conclusions about the experiment, as discussed in the next step.

As stated, the plot given in Step 4 (discharge coefficient as a function of the Reynolds number), can allow you to make conclusions about the data given. It is shown on our plot that the discharge coefficient remains within a range of .2, increasing as the Reynolds number increases, and then decreasing. There are no sporadic jumps in the data. Additionally, it is noted that the ideal value of the discharge coefficient is derived to be 1. Clearly, our discharge coefficient never even comes close to this unity value, but do not be worried, as this value is not typically achieved experimentally. Most likely, this is because the theory behind the derivation fails to include realistic fluid behaviors and forces, including frictional forces and drag forces along the walls of the pipe. The theory could be adjusted to account for these real world applications. If you really wanted to achieve unity for the discharge coefficient, you would have to use calculations with a smaller Reynolds number and therefore a smaller flow rate, but the flow rate can only be lessened so much before data stops being collected.

Lastly, a paddlewheel flowmeter calibration curve can be created with linear scales. In order to do so, plot the voltage output (V) of the paddlewheel versus the flow rate (Q) that was calculated using the weight-time measurements. From this plot we can see a clear rising flow rate (flow rate at which curve starts to incline) as well as a maximum flow rate (highest flow rate) on the curve. From here, the corresponding velocities for each of these points can be found in the data that the company will give you. The rising flow rate velocity here is found to be .00708 m/s and the maximum fluid velocity is found to be .02353 m/s, which make sense by just glancing at the curve shown above. It is noted that there is no cutoff flow rate or associated velocity. You can observe this by seeing that the flow rate never begins to decline on this plot; if you wanted to achieve a falling cutoff flow rate point, you should consider taking a wider range of data with higher flow rates.

Assumptions on the performance of the paddlewheel flowmeter can be made based on the plot gathered in the previous step. In order check on the reliability (precision) of the flowmeter, you can look and see how consistent the data is with respect to the trend line created. In this case, the data remains fairly equidistant from the trend line with a few exceptions at the beginning of the curve, indicating that the paddlewheel flowmeter is reliable to some extent. In order to check how accurate the flowmeter is, you can see how close the data actually is to the trend line. In this case, the data is slightly closer to the trend line toward the middle and end of the curve, indicating that higher flow rates infer higher accuracy.