Posted by **Claire** on Wednesday, November 3, 2010 at 6:02am.

A cylindrical tank 2m diameter and 4m long with its axis horizontal, is half filled with water and half filled with oil of density 800kg/m^3. Determine the magnitude and position of the net hydrostatic force on one end of the tank.

The answers should be 27.9kN, 1.26m from the top.

Can someone please explain how to work it out?

- Fluid Mechanics -
**MathMate**, Wednesday, November 3, 2010 at 11:12am
For a uniform liquid, the pressure at a depth of h equals ρh.

For a tank of radius r (length does not matter) containing a mixture of oil and water, the hydrostatic pressure at any point h below the top is

p1(h)=0.8h for 0<h≤r, and

p2(h)=0.8h+(h-r)(1-0.8) for r<h≤2r

The width of the tank at any height h from the top is

w(h)=sqrt(r²-(r-h)²)

The magnitude of the hydrostatic force, F, is the sum of the integrals

F=∫ 0 r p1(h)dh + ∫r 2r p2(h)dh

=2.646g N

The total moment about the top:

Fh=∫ 0 r x*p1(h)dh + ∫r 2r x*p2(h)dh

=3.353g N-m

The position can be found by dividing Fh/F = 1.267 m from the top.

Note that 2.646g gives 26.0 N as opposed to the 27.9 N given in your answer.

Check my calculations/the answer given in the book.

## Answer this Question

## Related Questions

- Calc - A cylindrical slime tank is placed so that the axis of the cylinder is ...
- CALCULUS - A cylindrical oil storage tank 12 feet in diameter and 17feet long is...
- fluid mechanics - A dam has been constructed of a large cylindrical pipe 10ft in...
- fluid mechanics - A dam has been constructed of a large cylindrical pipe 10ft in...
- Calculus (Definite Integrals - Force) Please Help - A cylindrical oil storage ...
- solid mensuration - A cylindrical tank with flat ends has a diameter of two ...
- Geometry - A spherical storage tank has a diameter of 48 ft and is full of water...
- Calculus - A cylindrical tank, with height of 15 m and diameter 4m, is being ...
- Math - Using 3.14 for pi, rounding to the nearest tenth, if necessary. A ...
- MATHS - A cylindrical water tank of diameter 1.4m and height 2.1m is being feed ...

More Related Questions