Hydrostatic pressure on triangular plate

Homework Statement

A triangle with base 3 m and height 4 m is submerged vertically in water so that the tip is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it.

Homework Equations

$$\int_{a}^{b}{\rho}g(x)w(x)dx$$

The Attempt at a Solution

I keep getting the wrong answer. Does it look like I'm setting it up right?

Using similar triangles

I have $$a = \frac{3}{4\sqrt{2}}\left(4-xi^{*}\right)$$

$$wi^{*}=2\left(\frac{\sqrt{3}}{2}-a\right)$$

$$a\mbox{re}a=wi\; \Delta x=\left( \sqrt{3}\; -\; 3\frac{\sqrt{2}}{2}+\frac{3}{4\sqrt{2}}x \right)$$

Pressure = 1000gx

Force = P*A

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vela
Staff Emeritus
Homework Helper
No. I'm not sure where you're getting the sqrt(3)/2 from in your formulas for a and w. Also, why not use similar triangles to find w directly as a function of x instead of going through the mess with a?

a=3/8(4-xi)

Sorry, I don't know where I got that either. I must need some rest.

Area=3/4xi(delta x)

Does this look right?

vela
Staff Emeritus