Measuring Pressure Differences and Flow Rates

I used to be the company's expert at measuring all quantities involving pressure differences and flow rates. Now that I am being promoted to a new position, you will have to fill in my shoes. At first the job may seem daunting, but with time and practice you will come to learn that it is challenging in a fun and proactive way. I have put this together to teach you in the simplest of ways how to calculate measurements as well as what to expect data to look like once measured correctly. I will demonstrate this using one of the experiments I recently worked on. The objective of this lab was relatively straightforward: using both a bourdon gage and a differential manometer, I needed to calculate a series of pressure differences and flow rates and see which device gave me the more accurate data of the two. I have put together all my data from the lab, conducted my calculations with precision, and received accurate results compared to what I had originally expected all throughout my trials.

Supplies

The tools needed for this lab were simple. The supplies I used included a bourdon gage, a differential manometer, a stopwatch, and something to note all my data on, either an iPad or a notebook. I then needed a calculator to calculate and assemble all the calculations I had done after collecting my data. At the end, I put together all my data into my computer and plotted graphs of the results from both the bourdon gage as well as the differential manometer. You can use Microsoft Excel or Google Sheets for this step. I chose Google Sheets.

Step 1: Plotting a Graph of the Pressure Difference, As Determined by the Bourdon Gage Method, As a Function of the Pressure Difference, As Determined by the Differential Manometer Method

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Step 2: Plotting a Graph of the Pressure Differences Calculated by Both Methods As Functions of the Volumetric Flow Rate

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Step 3: Describing the Apparent Dependence of Pressure Difference on Flow Rate

As we can see from the data as well as the trends of the graph, we can tell that the differential pressure measurement method that appears to be more reliable is the manometer. The results from the manometer have less deviation, more consistency, and appear more visibly linear than the results from the bourdon gage. From these observations alone, we can figure the manometer to be more accurate in the readings. Manometers are generally much easier to use and leave less room for error when compared to bourdon gages.

When analyzing the range of pressure differences over which method is more reliable, the results from the manometer have less standard deviation than the bourdon gage. As the volumetric flow rate increased, so did the pressure differences. However, the results from the manometer increased more consistently and far more steadily than the results from the bourdon gage with much less sway away from the line of unity. The bourdon gage results had a higher standard deviation and the range was wider. The manometer had narrower results which proved the manometer produced more consistent, accurate results.

The only possible explanation for the differences between the two methods? The manometer is a more advanced unit of measurement than the bourdon gage. It yields more accurate results, proves itself far more reliable than the bourdon gage, and is far more technologically advanced and suited for experiments like these when attempting to produce the most accurate results possible. The manometer was able to narrow down the values far more and significantly better than the bourdon gage. It left less room for any errors or mishaps.

Step 4: Estimating the Precision of the Measurements

It is always important to see how precise our measurements are at the end of every experiment. For these reasons, we estimate how well we calculated our results through a series of calculations. By using one of our weight-time data sets, we can calculate the flow rate easily.

The weight throughout our experiment remained the same, sitting at an even 100 LB. We obtained five different time intervals in order of each trial: 43.124 seconds, 48.55 seconds, 54.61 seconds, 69.54 seconds, and 82.58 seconds. The more trials we conducted, the longer the duration lasted. Our objective now is to calculate two different flow rates: one by using the shortest time measurement and the other by using the longest time measurement. The shortest time measurement value is denoted as Qs, and the longest time measurement value is denoted as Ql. The formula for flow rate is simple: mass/time.

The shortest time measurement was 43.124. 43.124/100 = 0.43124. Qs now has a value of 0.43124.

The longest time measurement was 82.58 seconds. 82.58/100 = 0.8258. Ql now has a value of 0.8258.

Next, we estimate the precision "e" of our measurements by finding the quotient of the maximum difference divided by the average value. The formula is denoted as e = (Qs-Ql)/(0.5*(Qs+Ql)). When plugging in our values for Qs and Ql, we obtain -0.62 for e.

The prompt asked to keep the value of e to two significant figures. When comparing this precision to typical engineering calculations, it stands out. Usually when doing such calculations with quantities that have such precise values, it is best to be as accurate as possible. Using no more than two significant figures is not common as many problems tend to use more, but it is not rare.