**A tank in the form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom.When friction and contraction of the water at the hole are taken into account,the height h of water in the tank is described by **

**where 0 <c <1. How long will it take the tank take to empty if c =0.6? Given that the tank is 10 feet high and has radius 2 feet and the circular hole has radius 0.5 inch and g=32 ft/s^2.**

We begin by combining all the constants as follows:

therefore,

The DE then becomes;

separating the variables,

integrating,

we can rewrite the above equation as follows

Where L is the constant of integration.

but h(0)=H ; substituting this into the above equation we have

Thus the equation becomes

For the tank to empty , h=0 .therefore,

solving for t ;