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:
The DE then becomes;
separating the variables,
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 ;