# Lowest pressure that the student's lungs can create?

## Homework Statement

A student sucks on the end of a long tube which is initially filled with air and whose other end is in a large bucket of water which is open to the atmosphere. They manage to draw the water up a vertical distance of 3.36 m above the surface of the water in the bucket. What is the lowest pressure that the student's lungs can create?

[P(atmosphere)=105N/m^2, ρ(water)=1,000 kgm-3, g=9.81 m/s^2]

## Homework Equations

Hydrostatic pressure, P = Po +ρgh

## The Attempt at a Solution

0 + (1000*9.81*3.36) = 33kN/m^2
This is my attempt at the problem. It's considered partially correct since this is the result of the water being sucked from the bottom of the bucket to the top, but it is not the actual pressure in the student's lungs.

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haruspex
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P = Po +ρgh
Think carefully what each of those variables represents in the context of how you are applying the formula in this question.

Think carefully what each of those variables represents in the context of how you are applying the formula in this question.
I had another go at the question assuming that Po = 105 (atmospheric pressure) but again, got the wrong. What am I missing?

haruspex
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I had another go at the question assuming that Po = 105 (atmospheric pressure) but again, got the wrong. What am I missing?
Equations have context. The equation P = Po +ρgh only works if the variables are matched up to the real world according to the relationships the equation assumes. In that equation, what do P, Po etc. refer to? And don't just answer pressure, height etc. What pressures? What height?

Equations have context. The equation P = Po +ρgh only works if the variables are matched up to the real world according to the relationships the equation assumes. In that equation, what do P, Po etc. refer to? And don't just answer pressure, height etc. What pressures? What height?
I'm assuming the height is the vertical distance of 3.36m and 33kN/m^2 is the pressure when the water is being sucked from the bottom of the bucket to the surface, and NOT the pressure in the student's lungs. Is there another height that I need to account for? How would I go about finding it?

haruspex
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33kN/m^2 is the pressure when the water is being sucked from the bottom of the bucket to the surface, and NOT the pressure in the student's lungs
That's not clear - what pressure do you mean? The pressure at the bottom of the bucket? The pressure at the bottom of the tube? The pressure in the tube at the same height as the surface of the water in the bucket? A difference of two pressures?

That's not clear - what pressure do you mean? The pressure at the bottom of the bucket? The pressure at the bottom of the tube? The pressure in the tube at the same height as the surface of the water in the bucket? A difference of two pressures?
The pressure in the tube at the same height as the surface of the water. I just want to know if there's another height that I need to account for?

haruspex
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The pressure in the tube at the same height as the surface of the water.
Ok, but it's wrong.
In the context of the general equation P = Po +ρgh, complete the sentence "where Po is the pressure at point A, P is the pressure at point B, h is the height of ..... above ...., g is acceleration due to gravity and ρ is the density of the fluid at rest and occupying a continuous region including .... and ...."
Then see if you have used the equation correctly.

I also used 0 as Po, and have gotten this response from the assignment.

"This is the pressure difference between the top of the fluid in the tube and the bottom, not the pressure created by the student's lungs."

I'm not sure where to go from here...

haruspex
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I also used 0 as Po, and have gotten this response from the assignment.

"This is the pressure difference between the top of the fluid in the tube and the bottom, not the pressure created by the student's lungs."

I'm not sure where to go from here...
Please try to answer my question. Forget the problem posted for the moment, and try to understand what the equation says:
In the context of the general equation P = Po +ρgh, fill in the blanks in the sentence "where Po is the pressure at point A, P is the pressure at point B, h is the height of .......... above ........., g is acceleration due to gravity and ρ is the density of the fluid; the fluid is at rest and occupying a continuous region including .......... and .........."

Please try to answer my question. Forget the problem posted for the moment, and try to understand what the equation says:
In the context of the general equation P = Po +ρgh, fill in the blanks in the sentence "where Po is the pressure at point A, P is the pressure at point B, h is the height of .......... above ........., g is acceleration due to gravity and ρ is the density of the fluid; the fluid is at rest and occupying a continuous region including .......... and .........."
"h is the height of point B above point A, ... , occupying a continuous region including point B and point A."

haruspex
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"h is the height of point B above point A, ... , occupying a continuous region including point B and point A."
No.
According to the equation, which is greater, P or Po? So will the pressure be greater at A or at B?
Which will be higher?

No.
According to the equation, which is greater, P or Po? So will the pressure be greater at A or at B?
Which will be higher?
Well P is just Po plus an added value, so Po is less than P. Pressure will be greater at point B than at point A.

haruspex
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Well P is just Po plus an added value, so Po is less than P. Pressure will be greater at point B than at point A.
So which is higher, A or B?

So which is higher, A or B?
In terms of Pressure? Well B of course. I would say point B is lower than point A?

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haruspex
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In terms of Pressure? Well B of course. I would say point B is lower than point A?
I meant in height, so you agree A is above B. (But that is not what you answered in post 11.)

Now let's match it to the problem at hand. Pick two points to be A and B. State the equation in terms of pressures at those points.

I meant in height, so you agree A is above B. (But that is not what you answered in post 11.)

Now let's match it to the problem at hand. Pick two points to be A and B. State the equation in terms of pressures at those points.
So P(B) = P(A) +pgh

haruspex
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So P(B) = P(A) +pgh
Sure, but I'm asking you to pick two points in the actual set-up to be A and B for the purposes of applying the equation.

Sure, but I'm asking you to pick two points in the actual set-up to be A and B for the purposes of applying the equation.
So point B would be at the bottom of the straw. While point A would be at the top of the straw or the top of the liquid, or does it matter?

So then would we rearrange the formula to Po = P-pgh, and use this to find the pressure in the lungs of the student?

Because the pressure in the lungs has to be lower than the pressure of the atmosphere for the liquid to rise, so this equation seems correct to me.

EDIT: This led me to the right answer, thanks so much for the help.

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haruspex
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So then would we rearrange the formula to Po = P-pgh, and use this to find the pressure in the lungs of the student?

Because the pressure in the lungs has to be lower than the pressure of the atmosphere for the liquid to rise, so this equation seems correct to me.

EDIT: This led me to the right answer, thanks so much for the help.
OK!

haruspex