# Homework Help: Help with Newton Question

1. Oct 13, 2012

### Hirohito

1. The problem statement, all variables and given/known data

A tank in the form of a right-circular cone standing on end with its vertex down, is leaking water through a hole its circular bottom.

• a. Suppose the tank is 20 feet high moreover has a radius 8 feet wide moreover the circular hole has a radius 2 inches. In problem 1.3 you were asked to demonstrate that the differential equation governing the height h of water leaking from a tank is

dh/dt = -5/6h3/2

In this model, friction as well as contraction of the water at the hole were taken into account with c = 0.3, moreover that g was taken to be 32 ft/s2. If the tank was initially full, how long shall it take the tank to empty?

b. Suppose the tank has a vertex angle of 60o in addition that the circular hole has a radius of 2 inches. Determine the differential equation governing the height h of water. Use c = 0.6 as well as g = 32 ft/s2. If the height of the water is initially 9 feet, how long will it take the task to empty?

2. Relevant equations

dh/dt = -5/6h3/2

3. The attempt at a solution

Not yet. I just came into this site after being referred to by a friend, moreover I seriously need help in differential equations. Can someone help?

2. Oct 14, 2012

### Simon Bridge

Welcome to PF;
Solving the differential equation seems to be a matter of integration - applying the initial value.

I look forward to seeing your initial attempts at the problem.