Time to Drain a Tank Using Torricelli's Law

height of water (m)

2

radius of tank (m)

2.5

radius of spigot (m)

0.01

Liquid flows out of a tank at a rate given by Toricelli's law,

dV

dt

=-π

2

a

2gh

, where

V

is the volume and

h

the height of the water in the tank (both functions of time),

r

is the radius of the tank,

a

is the radius of the hole in the bottom of the tank,

g

= 9.81

m/

2

s

, the acceleration due to gravity, and

t

is the time. The volume is given by

V(t)=π

2

r

h(t)

and the solution of the differential equation gives

h(t)=h

2

1-

2

a

2

r

g

2h

t

. Thus the length of time required to drain the tank, so that

h(t)=0

, is given by

t=

2h

g

2

r

a

seconds.