# Hydraulic, Fluids at Rest Problem (barrel)

• azrida
In summary, the hydrostatic force on the bottom of the barrel is greater than the gravitational force.
azrida

## 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

Last edited:
azrida said:
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 :-(

Doc Al said:
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 :-(

azrida said:
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!

Doc Al said:
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 Nand 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 :-)!

Last edited:
azrida said:
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.

Doc Al said:
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 :-)

## 1. How do you calculate the pressure in a hydraulic system?

The pressure in a hydraulic system can be calculated using the formula P=F/A, where P is the pressure, F is the force applied, and A is the cross-sectional area of the container or barrel.

## 2. What is the principle behind the operation of a hydraulic system?

The principle behind a hydraulic system is Pascal's Law, which states that a change in pressure at any point in a confined fluid will be transmitted equally to all points in the fluid.

## 3. How does the size of the barrel affect the pressure in a hydraulic system?

The size of the barrel does not directly affect the pressure in a hydraulic system. The pressure is determined by the force applied and the cross-sectional area of the container, not the size of the container.

## 4. Can the height of the fluid in the barrel affect the pressure in a hydraulic system?

Yes, the height of the fluid in the barrel can affect the pressure in a hydraulic system. The pressure increases as the height of the fluid increases due to the weight of the fluid pressing down on the bottom of the barrel.

## 5. How does the density of the fluid affect the pressure in a hydraulic system?

The density of the fluid does not directly affect the pressure in a hydraulic system. However, a denser fluid will require more force to move, which can indirectly affect the pressure in the system.

• Introductory Physics Homework Help
Replies
2
Views
773
• Classical Physics
Replies
3
Views
733
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
2K
• Classical Physics
Replies
8
Views
2K
• Introductory Physics Homework Help
Replies
21
Views
8K
• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
4K
• Introductory Physics Homework Help
Replies
2
Views
5K