What is the cross section area of the water?

[yy205001]

what is the cross section area of the water??

Homework Statement

Determine an expression for the cross sectional area A of the fluid in the tank as a function of D and H.

Homework Equations

A=pi*r²

The Attempt at a Solution

i try to let the radius equal to the height but then the fluid's height goes lower, it doesn't form a circle anymore. So i have no ideas how to do this.Please help.

 

[Mark44]

Homework Statement

Determine an expression for the cross sectional area A of the fluid in the tank as a function of D and H.

Homework Equations

A=pi*r²

The Attempt at a Solution

i try to let the radius equal to the height but then the fluid's height goes lower, it doesn't form a circle anymore. So i have no ideas how to do this.Please help.

What is the shape of the tank? In your drawing, the cross-section is half a circle, but is the tank spherical or cylindrical or what? To get an expression for the cross-sectional area of the water, you need to know the shape of the tank.

 

[DryRun]

I believe the tank is a half sphere? So, the volume of the sphere is: $$\frac{2}{3}\pi r^3$$

 

[Mark44]

Correction added.

I believe the tank is a half sphere? So, the volume of the hemisphere is: $$\frac{2}{3}\pi r^3$$

Nothing in the OP's post says anything about the actual shape of the tank.

 

[DryRun]

If you click on the attached picture in the first post, it does say "hemispherical" in the lower-right corner. In that case, H= r (radius if sphere) and D = 2r (diameter).

 

[Mark44]

So it does. I missed that.