# Math Help - Torricelli's law

1. ## Torricelli's law

Suppose that a cylindrical tank has a radius of 3 ft and it has a hole in the bottom with radius 1 in. How long will it take for the water, initially 9 ft deep, to drain completely?

My working:

$A(y) \frac{dy}{dt}=-a\sqrt{2gy}$

$\pi*3^2 \frac{dy}{dt}=-\pi*(1/12)^2*\sqrt{2*32y}$

$1296\frac{dy}{\sqrt{y}} =-8dt$

$162*2\sqrt{y}=-t+C$

$324\sqrt{y}=-t+C$

$y(0)=9$

$324*\sqrt{9}=C$

$C=972$

$324\sqrt{y}=-t+972$

Substituting $y = 0$,

$0=-t+972$

$t=972s$

Never mind! I figured it out.