# 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