Question

A right cylindrical water tank with a diameter of 3 feet and a height of 6 feet is being drained. At what rate is the volume of the water in the tank changing when the water level of the tank is dropping at a rate of 4 inches per minute?

Answer 1

Decreasing @ 2.356 cft/min, nearly, at the instant when the descent of surface is @ 4"/min.

Explanation:

Volume at time t'

`V(t)=pir^2h(t)=pi(3/2)^2h(t)` cubic feet, where h is the height in feet,

at time t'.

Differentiating with respect to time,

V'=9/4ph'=9/4pi(--4/12)=-3/4pi cubic feet//minute.

When h'=-4''/minute=-4/12=-1/3'/minute,

`V'=` 3/4pi=-2.356# cft/min, nearly.

Note that there is no need to use use of initial surface height 6'.

The nozzle draining speed is governed by Bernoulli'equation.