## Related questions with answers

Question

In Exercise, use the differential equation for a leaking container, Eq. $\frac{d y}{d t}=-\frac{B \sqrt{2 g y}}{A(y)}$

Water leaks through a hole of area $B=0.002 \mathrm{~m}^2$ at the bottom of a cylindrical tank that is filled with water and has height 3 m and a base of area $10 \mathrm{~m}^2$. How long does it take (a) for half of the water to leak out and (b) for the tank to empty ?

Solution

VerifiedStep 1

1 of 5The model for a leak of a water from the container that has a hole of area $B$ in the bottom, and $A(y)$ is the area of a horizontal cross section at the height $y$ is

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

where $g$ is acceleration due to gravity.

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