Hydrostatic Force and Pressure

[Seraph404]

Homework Statement

A semicircle with radius 3 m is submerged vertically in water so that the top is 1 m above the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it

I'm not getting the correct answer, so can someone help me to understand my mistake in setting up this problem?

Homework Equations

F = Pressure * Area
Pressure = $$\rho$$*g*d

The Attempt at a Solution

Pressure = $$\rho$$*g*y = 9800*y
Area = 2sqrt(9-y^2)dy

And then I integreated pressure * area from 0 to 2.

This seemed correct to me, but I got the wrong answer. Any hints?

 

[mighty2000]

First, make sure you are using the correct units for pressure and area. Pressure should be in units of Pa (Pascal) and area should be in units of m^2 (square meters).

Next, check your integration bounds. The semicircle is submerged from y=0 to y=2, not 0 to 2. You also need to take into account the distance from the surface, so the integration bounds should be from y=1 to y=3.

Finally, double check your calculation for the area. The correct formula for the area of a semicircle is (pi*r^2)/2, not 2sqrt(9-y^2).

Once you make these corrections, you should get the correct answer.