# Problem understand Pressure

## Homework Statement

So imagine a barrel with the area on top = ∏r^2
There is a tube of water 12 meters high ontop of the barrel.
What is the net force exerted on the barrel?

F = PA
F = Density*Height*Gravity*(Area of barrel)
How come the volume of water in the tube isn't a factor in the net force? Only the area of the top of the barrel matter? I used this equation and I got the right answer. My teacher said the volume of water in the tube DOESN"T matter, and I don't understand how that is possible. More total water = more total force?? Apparently not... Help me understand :)

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Your teacher is very misleading if that's what he said, the sheer volume of water does not always affect the pressure. The height of the water is in the equation, pressure changes with depth. As you get deeper underwater there becomes more and more pressure; however, if you make the volume of water larger but don't increase the depth (add more surface area of water) then the pressure at the bottom doesn't change. So for example you increase the height of the tube of water to 13 meters then your pressure and volume of water changes but if you simply add more water to the tube but don't change the height of the water (larger diameter tube) your volume changes but not your pressure.

Lets say the cross sectional area of the tube is 5 and it's 12 meters high and filled with water
That would produce more net force if the cross sectional area is 2 and it's 12 meters high,, right? Yet this variable is not represented in the equations and I still got the correct answer

Doc Al
Mentor
You might want to have a look at this diagram (from hyperphysics): Note that the shape of the container, and thus the total volume of fluid, has no bearing on the pressure at a given depth below the surface.

See: Static Fluid Pressure

PhanthomJay
Homework Helper
Gold Member
Lets say the cross sectional area of the tube is 5 and it's 12 meters high and filled with water
That would produce more net force if the cross sectional area is 2 and it's 12 meters high,, right? Yet this variable is not represented in the equations and I still got the correct answer
I think the problem is not worded correctly. If you were to add water to the barrel by say just filling it slowly from a water pitcher, the pressure at the top of the barrel would be zero. But if you fill it from the 12 m high thin tube, the pressure at the bot of the tube would be ρgh, where h = 12, and since the pressure would be uniformly distributed at that same value to the underside of the barrel top, the force on that top would be ρgh(A), where A is the area of the barrel top. Might be enough to cause the barrel to burst at its top or sides. Pressure at the bottom of the barrel would be even greater.

I think the problem is not worded correctly. If you were to add water to the barrel by say just filling it slowly from a water pitcher, the pressure at the top of the barrel would be zero. But if you fill it from the 12 m high thin tube, the pressure at the bot of the tube would be ρgh, where h = 12, and since the pressure would be uniformly distributed at that same value to the underside of the barrel top, the force on that top would be ρgh(A), where A is the area of the barrel top. Might be enough to cause the barrel to burst at its top or sides. Pressure at the bottom of the barrel would be even greater.
But it's the force that the water EXERTS onto the barrel lid. So you're telling me if the barrel had an infinite surface area the force would be infinite as well even though the tube is still just that long slim volume?

I do not recommend going for an infinite or even "very large" volume here; it does not simplify anything and introduces instead a lot of complications. In a reasonably sized volume, pressure will depend only on the height of the water column above, and the force exerted onto the lid will be proportional to that pressure and the area of the lid.

D H
Staff Emeritus
But it's the force that the water EXERTS onto the barrel lid. So you're telling me if the barrel had an infinite surface area the force would be infinite as well even though the tube is still just that long slim volume?
Let's get rid of that appeal to ridicule and replace "infinite" with "large":
But it's the force that the water EXERTS onto the barrel lid. So you're telling me if the barrel had an large surface area the force would be large as well even though the tube is still just that long slim volume?
Now that's exactly right. It's the principle behind a hydraulic jack.

Dick
Homework Helper

## Homework Statement

So imagine a barrel with the area on top = ∏r^2
There is a tube of water 12 meters high ontop of the barrel.
What is the net force exerted on the barrel?

F = PA
F = Density*Height*Gravity*(Area of barrel)
How come the volume of water in the tube isn't a factor in the net force? Only the area of the top of the barrel matter? I used this equation and I got the right answer. My teacher said the volume of water in the tube DOESN"T matter, and I don't understand how that is possible. More total water = more total force?? Apparently not... Help me understand :)
Your formula does involve volume. Height*(Area of barrel)=Volume of water. But if area of the barrel and height are fixed you can't change volume independently.