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**1. Homework Statement**

A tank is in a shape of a cylinder with a circular cross-section of area A. Initially the depth of water in the tank (the head) is h0. At time t = 0 water is allowed to leave the tank ffrom a valve at the bottom. The rate at which the water leaves the tank is proportional to the head of the water at that instant; the constant of proportionality, k, is related to the discharge coefficient or the tank.

Derive an expression for the head of water in the tank at any time t after it is allowed to empty.

How long does it take for the tank to lose 1/2 its water? How long does it take for the tank to empty.

**2. Homework Equations**

Code:

```
dy/dx = -ky
y = Ce^(-kt)
```

**3. The Attempt at a Solution**

dh/dt = -k(h - h0)

h(time) = (h - h0)e^(-kt)

ln ((h - h0) / h(time)) = kt

and this is where i get stuck thats even if i've got the first bit right???

any help would be great!

:)