Cylindrical barrel Hydrostatic Pressure

[BrianSauce]

Homework Statement

A circular cylindrical barrel is half full with oil. If the diameter of the base is 8.0 m, find the net force against each end if ρo = 800 kg/m3. The cylinder is on its side.

Homework Equations

F=P*A
P=ρgdy

The Attempt at a Solution

P = ρo*g*h, where h is the radius which is 4 meters.
A = half the area of a circle, 1/2πr2
F=ρogh*1/2πr2

The answer is incorrect, what am I doing wrong?

 

[Erebus_Oneiros]

Pressure is a function of depth, so is Force. To find the net force you need to write the expression for force for an elemental depth and then integrate from 0 to radius r.

 

[BrianSauce]

F=1/2πr²ρ_og∫₀^r-√r²-y²
?

 

[Erebus_Oneiros]

That doesn't look right to me.

F= ρg∫₀^r 2h * √(r²-h²) dh

a simple substitution of variables solves this integral.

Another way that this problem can be solved is to find the center of pressure and then multiply the area with the pressure at (c.o.p).

Hope it helped.

 

[BrianSauce]

I understand the center of pressure part. Since this is a semicircle I could find the pressure at the center of mass and then just multiply it by the area. I will use this to solve it. I don't understand your integral though; where did 2h come from?

 

[Erebus_Oneiros]

Check the attached image.

Using c.o.p is fine but it isn't by first principles. Also if the center of pressure isn't already given then you need to integrate to find it.

 

[BrianSauce]

Thank you for your help, to me finding center of masses for symmetrical objects seems a little more intuitive than what you did. However, for an object that isn't symmetrical I'll have to use your method. Either way thank you very much.