According to Toricellis law water drains from a tank at a ra

According to Toricelli\'s law, water drains from a tank at a rate proportional to the square root of the depth. A spherical tank of radius 1 meter was initially full of water and took and hour to drain. At what time was the tank half full?

Solution

V proportional to squareroot(2r-h)

V=dr/dt= ksquareroot(2r-h)

1/(2r-h) dr=dt

1/(r-h/2)=2t

4r/3=2t

2/3hr=time=40min