Thread: Work it, I need a glass of water....Solving for F(h)

Water is pumped into a spherical tank of radius 5 ft from a source located 2 ft below a hole at the bottom. Density of water=62.4. Find the work F(h) to fill the tank to a height h from the bottom of the tank.

I know F(0)=0 and F(10)=228708 by computing the work to fill the tank. It is clearly going to be a continuous function and it fills faster in the middle, the domain will be 0<=h<=10, but how do I find the equation for this? I know I can still use the same geometry I did for finding F(10), with center at the center of the sphere, but I am confused how to get a function out of this.

Originally Posted by twittytwitter

Water is pumped into a spherical tank of radius 5 ft from a source located 2 ft below a hole at the bottom. Density of water=62.4. Find the work F(h) to fill the tank to a height h from the bottom of the tank.

I know F(0)=0 and F(10)=228708 by computing the work to fill the tank. It is clearly going to be a continuous function and it fills faster in the middle, the domain will be 0<=h<=10, but how do I find the equation for this? I know I can still use the same geometry I did for finding F(10), with center at the center of the sphere, but I am confused how to get a function out of this.

consider a representative horizontal slice of water in the tank between the bottom and height ...



let the side view of the sphere be the circle ...



weight of the slice is

note that , so the distance the slice is to be lifted is

work to lift all the slices ...