Calculating this gauge pressure reading

In summary, the conversation discussed the use of a U-tube manometer and a pressure gauge to determine the pressure of a volume of air trapped in a tank. The participants also discussed how to form equations and establish relations in order to find the correct gauge pressure, ultimately resulting in a correct answer of 33.5 kPa.
  • #1
Bolter
262
31
Homework Statement
See below
Relevant Equations
pressure = rho x g x h
specific weight = rho x g
Hi everyone!
How do I go about solving this problem?

Screenshot 2020-09-30 at 13.04.21.png

Screenshot 2020-09-30 at 13.05.09.png


I tried working out the gauge pressure using this but I have a few unknowns which won't make this possible such as what is the length of x which I labelled in the figure

IMG_5299.JPG


Any help would be appreciated! Thanks
 
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  • #2
The U-tube manometer is telling you the pressure of the volume of air trapped in the tank.
The pressure gauge should be telling you the static pressure at that height of liquid, which surface is being pressured down by the trapped air.
 
  • #3
Lnewqban said:
The U-tube manometer is telling you the pressure of the volume of air trapped in the tank.
The pressure gauge should be telling you the static pressure at that height of liquid, which surface is being pressured down by the trapped air.

Ok I get that, but I am not entirely sure how I can form an equation with that statement. Do I begin off by setting up an expression on the left and right side of the figure then equate them?
 
  • #4
The trapped pocket of air in the tank is simultaneously in contact with the surface of both liquids, having a unique pressure.
I would establish relations for each side around that common pressure.

I believe that height x is irrelevant, do you agree?
 
Last edited:
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  • #5
Lnewqban said:
The trapped pocket of air in the tank is simultaneously in contact with the surface of both liquids, having a unique pressure.
I would establish relations for each side around that common pressure.

I believe that height x is irrelevant, do you agree?

Thanks I got the right answer from making relations on both sides and then equalling those 2. Gauge pressure turned out to be 33.5 kPa

IMG_5300.JPG
 
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  • #6
You are welcome. :smile:
Your result is correct.
 
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Related to Calculating this gauge pressure reading

1. How do you calculate gauge pressure reading?

To calculate gauge pressure reading, you need to know the atmospheric pressure and the pressure of the gas or fluid you are measuring. Subtract the atmospheric pressure from the total pressure to get the gauge pressure reading.

2. What is the formula for calculating gauge pressure?

The formula for calculating gauge pressure is P gauge = P total - P atmosphere, where P gauge is the gauge pressure reading, P total is the total pressure, and P atmosphere is the atmospheric pressure.

3. What is the difference between gauge pressure and absolute pressure?

Gauge pressure is measured relative to atmospheric pressure, while absolute pressure is measured relative to a perfect vacuum. This means that gauge pressure can be positive or negative, while absolute pressure is always positive.

4. How do you convert gauge pressure to absolute pressure?

To convert gauge pressure to absolute pressure, you need to add the atmospheric pressure to the gauge pressure reading. This will give you the absolute pressure reading.

5. What units are used for measuring gauge pressure?

Gauge pressure is typically measured in units of pounds per square inch (psi), kilopascals (kPa), or bar. Other units such as millimeters of mercury (mmHg) or atmospheres (atm) may also be used.

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