# Time to Drain a Tank Using Torricelli's Law

Time to Drain a Tank Using Torricelli's Law

Liquid flows out of a tank at a rate given by Toricelli's law, =-πa, where is the volume and the height of the water in the tank (both functions of time), is the radius of the tank, is the radius of the hole in the bottom of the tank, = 9.81 , the acceleration due to gravity, and is the time. The volume is given by and the solution of the differential equation gives . Thus the length of time required to drain the tank, so that , is given by seconds.

dV

dt

2

2gh

V

h

r

a

g

m/s

2

t

V(t)=πrh(t)

2

h(t)=h1-t

a

2

r

2

g

2h

2

h(t)=0

t=

2h

g

r

a

2