Making Pressure Measurements: How to Do It and What to Expect

Before I begin, I would like to welcome you to the team! I am Matt Hanley. I had this job prior to you, and have been tasked with making this page to instruct you on how to carry out the duties of your job. I will also let you know what your readings should end up looking like. That way, you will be able to see whether or not the measurements are accurate. Above, you will see the apparatus you will be working with shortly. I wish you luck as you begin your journey at this nameless but grand company!

One of the many ways to find change in pressure is by using gages. Notice I said "gages" and just "gage." On your tube apparatus, you should notice two different gages. A high gage on the left, and a short gage on the right. It should look something like the one pictured. You will have two different units on your gage like the one in the picture does. For our purposes, you will only use the kilopascal (kPa) readings. In the gage in the picture, you would read the inside circle, which is colored red. You must find where on the gage the needle is pointing. Use your simple math skills to find out what each tick mark means. For example, if there are five tick marks across ten kilopascals, that means each tick adds two kilopascals. Using this knowledge, you should be able to read the pressure reading on the gages. Record the reading on both of the gages and save them for some equations I will cover later. The left gage's pressure should be p1, and the right's should be p2.

The next type of measurement I will cover is a manometer. If you look at the tube apparatus, around the middle, you will notice a part of the pipes filled with a metallic liquid. This liquid is mercury. If you look even closer, you will also notice that there is a set of measurements on the side of the tube holding the mercury. When there is flow, and it is time for you to take a reading, the mercury will rise and fall, depending on which side of the tube you are looking at. The mercury in the left side will rise, and the right side will fall. Now, you will look at the level of the mercury. Record the height of the mercury on each side from the top of the curve seen in the liquid. This curve is called a meniscus, and is caused by capillary action. The left side recording will be positive, and the right will be negative. You will use these recordings for calculations in the future. The picture shows the heights and equations that are important for reading the manometer. The left reading will be hL, and the right side will be hR.

On the ground you will notice a large tub, into which the water flows. This is a scale, and the top of the scale can be seen right above it on the wall. There is an arm on which you will be placing weight that can be found here. Included is a picture of one of these scale arms. As fluid fills the scale, the arm will move upwards. As soon as the arm hits the top rubber stop, add a weight to the balance pan, and start a timer. Take note of the weight you placed on the balance pan. You will be mostly using a one pound weight, which translates to 100 pounds of liquid in the scale. All of the weights have a 100 times multiplier, so a two pound weight translates to 200 pounds of liquid. When you add the weight, the arm will move down onto the bottom rubber stop. Once the scale fills up with enough liquid, the arm will start to move back up towards the top rubber stop. Once it touches the rubber stop, stop your timer. After this, make sure to open up the escape valve for the scale so that the floor does not get flooded. Record your time and the weight of the liquid you just measured, which in this case, is 100 pounds. We will use these values soon.

Bourdon Gage Calculations:

Pressure A = p1 + Yw*(a1 − aA)

Pressure B = p2 + Yw*(b2 − bB)

Yw = 9810N/m^3 = 62.4lb/ft^3, a1 = .81m, aA = .613m, b2 = 2.376m, bB = 2.183m, Yhg/Yw = 13.55

Use these equations to find pressures A and B. You will then subtract Pressure B from Pressure A. This is your reading for pressure difference.

Manometer Calculations:

Pressure A − Pressure B = Yw*(bB − aA) + (Yhg-Yw)*(hL − hR)

Using the same values as you did in the gage calculations and your values from your Manometer readings, you will be able to find the pressure difference.

Weight-Time Calculations:

Volumetric Flow Rate = W/(Yw*Time)

Finding the volumetric flow will help you analyze your pressure readings better, as you will see in a graph soon.

Comparison of Pressure Measurements

The first graph shows the values you recorded from both the Bourdon gages and the manometer. I included a straight line with a slope of unity along with my recordings. If the two ways to read the pressure were perfectly aligned, the dot would land on the unity sloped line. You should strive to get as straight of a line as you can in your data. How far your line strays from the unity sloped line can only be controlled so much. Discrepancies can come from human error, or uncalibrated measurement devices.

Q vs. Change in Pressure

The second graph shows the volumetric flow you should have calculated for earlier. It is shown against both the Bourdon gage readings and the manometer readings. As you might be able to see, the trend lines for this graph are exponential rather than linear. These trendlines are very similar. It would most likely take much more data points to be able to tell which reading is more reliable, as the range of my data shown is not wide. The differences in the data can be chalked up to human error, and the calibration of the measurement devices, as I stated before.

Weight-Time Precision

You can check the precision of your weight-time measurements by following the example below:

Find the volumetric flow using your shortest and longest time data points

a) Qs = 100lbs / (62.4* ) = .00107ft^3/s

b) Ql = 100lbs / (62.4* ) = .0009461ft^3/s

Estimate your precision (e) by finding the quotient of the maximum difference divided by the average value

c) e = (.00107-.0009461) / (.5*(.00107+.0009461)) = .123 * 100 = 12%

The typical precision in engineering calculations is a value below 10%. My calculation precision was above the limit, so they are not typical of engineering calculations. This does not mean your calculations should also be this way.

I hope you make good use of these instructions, good luck!

Resources:

https://www.walmart.com/ip/Pool-Spa-Filter-Water-P... (Gage Picture)

UIUC TAM 335 Lab Manual