# Hydraulic, Fluids at Rest Problem (barrel)

## Homework Statement

In the figure below, an open tube of length L = 1.8 m and cross-sectional area A = 4.6 cm2 is fixed to the top of a cylindrical barrel of diameter D = 1.2 m and height H = 1.8 m. The barrel and tube are filled with water (to the top of the tube). Calculate the ratio of the hydrostatic force on the bottom of the barrel to the gravitational force on the water contained in the barrel.

P=phg

F=mg=pvg

F=pa

F1/A1 = F2/A2

## The Attempt at a Solution

Okay, this problem has been giving me a major headache.

I tried to solve this by finding the gravitational force in barrel, which I assumed as:
mg = pvg = (1000kg/m^3)(0.6m^2*pi*1.8m)(9.8m/s^2) = 19940.256 N

Then I "attempted" to set up an equation to find the hydrostatic force on the bottom of the barrel, where I got stuck:
F1/A1=F2/A2
-> Atmospheric pressure/area of the tube = Hydraulic pressure/are of the bottom of the barrel
->???????

I already know that the answer is 2, but I need to learn HOW and WHY it is so.

pics at http://www.webassign.net/hrw/hrw7_14-31.gif

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Doc Al
Mentor
Then I "attempted" to set up an equation to find the hydrostatic force on the bottom of the barrel, where I got stuck:
F1/A1=F2/A2
-> Atmospheric pressure/area of the tube = Hydraulic pressure/are of the bottom of the barrel
->???????
First find the water pressure at the bottom of the barrel. What does hydrostatic pressure depend on? At what depth below the water surface is the bottom of the barrel?

Would the water pressure at the bottom of the barrel be:

pressure of the tube on the top + pressure of the water in thebarrel
-> pgAh + pgAh -> (1000kg/m^3)(9.8m/s^2)(0.00046m^2)(1.8m) + (1000kg/m^3)(9.8m/s^2)(0.6m^2)(pi)(1.8m)
-> 20021.4 ?????

Does hydrostatic pressure depend on the area where pressure is applied onto??

The bottom of the barrel is 1.8m away from the top of the barrel (not including the tube)

Can someone please explain the whole process step by step?
I really feel like I'm getting lost here :-(

First find the water pressure at the bottom of the barrel. What does hydrostatic pressure depend on? At what depth below the water surface is the bottom of the barrel?
Would the water pressure at the bottom of the barrel be:

pressure of the tube on the top + pressure of the water in thebarrel
-> pgAh + pgAh -> (1000kg/m^3)(9.8m/s^2)(0.00046m^2)(1.8m) + (1000kg/m^3)(9.8m/s^2)(0.6m^2)(pi)(1.8m)
-> 20021.4 ?????

Does hydrostatic pressure depend on the area where pressure is applied onto??

The bottom of the barrel is 1.8m away from the top of the barrel (not including the tube)

Can someone please explain the whole process step by step?
I really feel like I'm getting lost here :-(

Doc Al
Mentor
Would the water pressure at the bottom of the barrel be:

pressure of the tube on the top + pressure of the water in thebarrel
-> pgAh + pgAh -> (1000kg/m^3)(9.8m/s^2)(0.00046m^2)(1.8m) + (1000kg/m^3)(9.8m/s^2)(0.6m^2)(pi)(1.8m)
-> 20021.4 ?????
No. The area doesn't matter for caculating pressure.

Does hydrostatic pressure depend on the area where pressure is applied onto??
No. (You'll need the area when you find the force, but not the pressure.)

The bottom of the barrel is 1.8m away from the top of the barrel (not including the tube)
What matters is how far below the water surface the bottom is. There's water in the tube!

No. The area doesn't matter for caculating pressure.

No. (You'll need the area when you find the force, but not the pressure.)

What matters is how far below the water surface the bottom is. There's water in the tube!

So... the water pressure at the bottom of the barrel is:

P = phg = (1000kg/m^3)(3.6m)(9.8m/s^2) = 35280(Pa??)

and since F = p*a,

(35280)(area of the bottom of the barrel) = force
(35280)(0.6^2)(pi) = 39880.512 N

and the grativational force on the water contained in the barrel is:

mg = pvg = 19940.256 N

so, the ratio of the hydrostatic force on the bottom : gravitational force = 39880.512/19940.256 = 2 !!!!!

Wow!!!! Thank you so much :-)!

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Doc Al
Mentor
So... the water pressure at the bottom of the barrel is:

P = phg = (1000kg/m^3)(3.6m)(9.8m/s^2) = 35280(Pa??)
Good. But don't forget to add in atmospheric pressure.

and since F = p*a,

(35280)(area of the tube???) = force?
Since you want the force on the bottom of the barrel, use the area of the bottom of the barrel (not the tube).

and the grativational force on the water contained in the barrel is:

mg = pvg = 19940.256 N

am I following you correctly?
Yes.

Good. But don't forget to add in atmospheric pressure.

Since you want the force on the bottom of the barrel, use the area of the bottom of the barrel (not the tube).

Yes.

Thank you so much!
I think now I know the concept behind this probelm :-)