Calc Air Pressure in Tank with Fluid Level & Height

In summary: I told you to forget about the tank, and to focus on the column of liquid on the left. The ideal gas law will not be part of the solution to this problem. Looking at the equation for pressure, P=N*V, you can see that the pressure at the bottom of the column of liquid, Pb, is equal to the pressure at the top of the column of liquid, Pt, plus the pressure of the atmosphere, Pa. So Pb=Pt+Pa. So the pressure at the bottom of the column of liquid would be 58680N.m^-2.
  • #1
jderulo
34
0

Homework Statement



What is the headspace pressure (air)?

Closed tank part filled with fluid under pressure, there are tubes that indicate the fluid level and pressure. The tube on the left is open to atmosphere.

fluid s.g. 1.2
x = 5m
y= 1.7m

111111111.png

Homework Equations



See below

The Attempt at a Solution



Assuming atmospheric pressure and rho*g*h come into play?
 
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  • #2
...
 
Last edited:
  • #3
Why? I was wondering whether to use boyles law as the tank full of air at atmospheric will have been compressed as the tank filled?
 
  • #4
never mind
 
  • #5
?
 
  • #6
?
 
  • #7
Can you please provide an exact statement of the problem.
 
  • #8
Hi the exact statement contains no further info except a couple of filler words such as the, and etc.

Though it doesn't state about it being heads pace or air pressure it's just the area above the fluid.
 
  • #9
If atmospheric pressure is present at the top of the left column of water, what is the pressure in the left column of water at the level of the dashed line in the tank?

Chet
 
  • #10
Atmospheric??
 
  • #11
jderulo said:
Atmospheric??

The pressure at the top of the column is atmospheric...The pressure lower in the column is found via Pascals law
 
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  • #12
...
 
Last edited:
  • #13
jderulo said:
1.2*9.81*y ?
Let's check. If that's the pressure at the level of the dotted line, what is the pressure at the bottom of the tank? And also, based on your result, what is the pressure at the top of the left column of fluid?

If you are not able to solve this problem, you need to go back to your textbook and re-read the sections on hydrostatic pressure. If you encounter difficulties with understanding those sections of the textbook, we are prepared to help answer specific questions you may have.

Chet
 
  • #14
I fail to see how I can elaborate further with the info give. I have numerous textbooks, the unconventional setup is throwing me somewhat.
 
  • #15
jderulo said:
I fail to see how I can elaborate further with the info give. I have numerous textbooks, the unconventional setup is throwing me somewhat.

Can you state in your own words what the 'h' in the equation in your OP represents?
If not, can you find a definition in one of your textbook?
 
  • #16
Head of liquid (the x and y values)
 
  • #17
'h' is the height of fluid above the point of measurement.

So what is the height of fluid above the point you are interested in (the dotted line)?
 
  • #18
Interested in the area above the dotted line, 5metres
 
  • #19
Correct.
So what now? Can you reach the answer?
 
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  • #20
No that is where I am stuck, I can calculate the fluid pressure but the air pressure I am lost.

1200kg.m^-3 * 5m * 9.81m.s^-2 = 58680N.m^-2
 
  • #21
jderulo said:
No that is where I am stuck, I can calculate the fluid pressure but the air pressure I am lost.

1200kg.m^-3 * 5m * 9.81m.s^-2 = 58680N.m^-2
Are you aware that pressure is continuous across the interface between the air in the head space and the liquid immediately below?
 
  • #22
Chestermiller said:
Are you aware that pressure is continuous across the interface between the air in the head space and the liquid immediately below?

Hi Chestermiller

Yes, I guess so - but again totally lost as to how I can progress further? Sorry!
 
  • #23
jderulo said:
Hi Chestermiller

Yes, I guess so - but again totally lost as to how I can progress further? Sorry!
At what location(s) do you think your calculated pressure of 58680N.m^-2 is found?

Let's forget about the tank for the moment, and just focus exclusively on the left column of fluid. You already indicated that the pressure at the very top of this column of fluid is atmospheric. As you move downward from the top of this column, does the pressure get higher or lower (think what happens when you go below the surface in a swimming pool)? Suppose you go downward to a point 5 m below the top surface of the liquid in the column. What would the pressure at this location be equal to (over and above atmospheric pressure)?

Chet
 
  • #24
Chet the calculated pressure would be at the bottom of the tank.

The pressure would get higher. But my assumption was to use the ideal gas law to calculate the air pressure but this then doesn't fit the 5m into my equation?. How can I go 5m below the top surface of liquid when there is only 1.7m of liquid?? The 5m is air?
 
  • #25
jderulo said:
Chet the calculated pressure would be at the bottom of the tank.
No. That is not the pressure at the bottom of the tank.
The pressure would get higher. But my assumption was to use the ideal gas law to calculate the air pressure but this then doesn't fit the 5m into my equation?. How can I go 5m below the top surface of liquid when there is only 1.7m of liquid?? The 5m is air?
I told you to forget about the tank, and to focus on the column of liquid on the left. The ideal gas law will not be part of the solution to this problem. Looking at the column of liquid on the left in your figure, did you notice that little triangular "symbol thingie" at the very top of the left column. The left column is full of liquid all the way up to that triangular "symbol thingie." Above that point there is air at atmospheric pressure, but below that point there is liquid. Were you aware of that?

Chet
 
  • #26
Chestermiller said:
No. That is not the pressure at the bottom of the tank.

I told you to forget about the tank, and to focus on the column of liquid on the left. The ideal gas law will not be part of the solution to this problem. Looking at the column of liquid on the left in your figure, did you notice that little triangular "symbol thingie" at the top of the left column. The left column is full of liquid all the way up to that triangular "symbol thingie." Above that point there is air at atmospheric pressure, but below that point there is liquid. Were you aware of that?

Chet

No I wasn't - I had incorrectly assumed the liquid level in the column was the same as in the tank. Thought the triangle symbol was maybe a smudge of a scan. The head is 6.7m?

I am guessing at this point to move onto the tank? If so, a 6.7m head factored into my rho * g * h equation then gives me the pressure at the interface inside the tank?
 
  • #27
jderulo said:
No I wasn't - I had incorrectly assumed the liquid level in the column was the same as in the tank. Thought the triangle symbol was maybe a smudge of a scan. The head is 6.7m?

I am guessing at this point to move onto the tank? If so, a 6.7m head factored into my rho * g * h equation then gives me the pressure at the interface inside the tank?
No. You went downward 6.7 m from the top water surface in the column. This puts you at the bottom of the tank. Now you've got to go back up 1.7 m to get to the water surface in the tank.

Chet
 
  • #28
Chestermiller said:
No. You went downward 6.7 m from the top water surface in the column. This puts you at the bottom of the tank. Now you've got to go back up 1.7 m to get to the water surface in the tank.

Chet

OK - so 9.4m. That makes sense. I didn't realize we added the head backupwards.

I am right in thinking the answer is 110657N.m^-2 ?
 
  • #29
jderulo said:
OK - so 9.4m. That makes sense. I didn't realize we added the head backupwards.

I am right in thinking the answer is 110657N.m^-2 ?
No. If you go back upwards, you have got to subtract, not add.
 
  • #30
Chestermiller said:
No. If you go back upwards, you have got to subtract, not add.

58860N.m^-2 ? Assuming a head of 5m?
 
  • #31
jderulo said:
58860N.m^-2 ? Assuming a head of 5m?
Yes. That's the air pressure in the tank headspace (over and above atmospheric pressure).

Chet
 
  • #32
Thanks Chet - I had that value earlier, was you trying to see if I understood it?

The y value, the 1.7m - seems odd that I do not include that. I always thought we had to use all the data in chem eng problems. At least I have in the past!
 
  • #33
jderulo said:
Thanks Chet - I had that value earlier, was you trying to see if I understood it?

The y value, the 1.7m - seems odd that I do not include that. I always thought we had to use all the data in chem eng problems. At least I have in the past!
Why do you think they put the y into the problem description?
 
  • #34
Chestermiller said:
Why do you think they put the y into the problem description?
Not really sure can only assume it would make the solution glaringly obvious if it wasn't there...?
 
  • #35
jderulo said:
Not really sure can only assume it would make the solution glaringly obvious if it wasn't there...?
Exactly.
 

FAQ: Calc Air Pressure in Tank with Fluid Level & Height

1. How do you calculate air pressure in a tank with fluid level and height?

The formula for calculating air pressure in a tank with fluid level and height is P = ρgh, where P is pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column. This formula assumes that the tank is open to the atmosphere and that there is no air inside the tank.

2. Can you calculate air pressure in a tank with fluid level and height if the tank is closed?

Yes, you can calculate air pressure in a closed tank using the ideal gas law, which states that PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. You will need to know the volume of the tank, the number of moles of air inside the tank, and the temperature of the air.

3. How does the fluid level and height affect the air pressure in a tank?

The fluid level and height directly affect the air pressure in a tank. As the fluid level increases, the height of the fluid column also increases, resulting in an increase in air pressure. Conversely, as the fluid level decreases, the height of the fluid column decreases, resulting in a decrease in air pressure.

4. What units are typically used to measure air pressure in a tank with fluid level and height?

The most common units used to measure air pressure in a tank with fluid level and height are pounds per square inch (psi) or kilopascals (kPa). However, other units such as atmospheres (atm) or millimeters of mercury (mmHg) may also be used.

5. Can the air pressure in a tank with fluid level and height change over time?

Yes, the air pressure in a tank with fluid level and height can change over time. This can be due to a variety of factors such as changes in temperature, changes in the fluid level, or changes in the amount of air inside the tank. It is important to regularly monitor and adjust the air pressure in a tank to ensure safe and efficient operation.

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