# Fluid Pressure problem

1. Feb 25, 2012

### NoobDoingMath

Hi I have a midterm study guide question. This one has stumped me for a while and probably the only one undone.

1. The problem statement, all variables and given/known data
Suppose there is a semi-circular plate of radius 5 ft that rests on its
diameter and is tilted at 45 degree angle to the bottom of a tank lled with water to depth
6 feet. Find the force exerted by the water against one side of the plate. (The
weight-density of water is 62.4 lb=ft^3)

2. Relevant equations
So I'm reading the book and I know that to solve the problem Force is weight-density of water (62.4) times the depth (6-y) and the area.

Now the problem is I'm not quite sure how to approach the area. I just can't seem to grasp the image of the tank. Not to mention the 45 degree angle really confused my approach. I was under the assumption that its a 6ft tall cylinder with length 10ft and a plate on the bottom tilted at 45 degrees

3. The attempt at a solution
Problem seems simple, but I can't seem to figure out the 45 degree plate to find the area.

What i have is:

Integral from 0 to 6 of (62.4)(6-y)(area)

Now this is assuming that I approached this correctly.

2. Feb 25, 2012

### tiny-tim

Welcome to PF!

Hi NoobDoingMath! Welcome to PF!
Yes, that's basically correct.

You seem to be confused about the area …

I suggest in future you always use the slicing method.

In this case, slice the plate into horizontal slices of vertical distance dy …

then find the area of that slice (it'll be dy√2 times the width, won't it?)

3. Feb 25, 2012

### NoobDoingMath

Still a little bit confused, and I want to see if I'm understanding correctly. My "math English" isn't too good. :shy:

So √2 is a result of the 45-45-90 triangle right?
Therefore the slice is √2dy*width

The width is 10ft since its radius is 5 and the plate rest on its diameter?

Resulting my solution to be:

∫(62.4)(6-y)(10√2)dy a=0, b=6

My answer would become:

11232√2

4. Feb 26, 2012

### tiny-tim

Hi NoobDoingMath!

(just got up :zzz:)
Nooo, you're not thinking straight.

Or, rather, you are thinking straight, and you should be thinking circular!

The width has to be the width of the slice

that's the whole point of slicing …

you add the area of each slice, and that depends on y, doesn't it?

Try again!

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