# Tank pressure

## 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 See below

## The Attempt at a Solution

Assuming atmospheric pressure and rho*g*h come into play?

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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?

never mind

?

???

Chestermiller
Mentor
Can you please provide an exact statement of the problem.

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.

Chestermiller
Mentor
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

Atmospheric??

billy_joule
Atmospheric??
The pressure at the top of the column is atmospheric...The pressure lower in the column is found via Pascals law

• Chestermiller
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Chestermiller
Mentor
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

I fail to see how I can elaborate further with the info give. I have numerous textbooks, the unconventional setup is throwing me somewhat.

billy_joule
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?

Head of liquid (the x and y values)

billy_joule
'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)?

Interested in the area above the dotted line, 5metres

billy_joule
Correct.
So what now? Can you reach the answer?

• Chestermiller
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

Chestermiller
Mentor
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?

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!

Chestermiller
Mentor
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

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?

Chestermiller
Mentor
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