# Controlling the flow from a draining tank

• yttuncel

## Homework Statement

Torricelli’s law says that if you drain a tank like the one in the figure shown, the rate y
at which water runs out is a constant times the square root of the
water’s depth x. The constant depends on the size and shape of the
exit valve.

Suppose that for a certain tank. You are trying to
maintain a fairly constant exit rate by adding water to the tank
with a hose from time to time. How deep must you keep the water
if you want to maintain the exit rate

a. within 5.7 L/min of the rate y0=28.3L/min
b. within 2.8 L/min of the rate y0=28.3L/min

## The Attempt at a Solution

I could not understand neither the question nor the method i should use. Should it be done via epsilon-delta method? Or simply by differentiating ?

Last edited:
Figure not attached.

I'm guessing you have an initial rate, q0, at the initial height, y0:
q(y0)=q0

Now see if you can write the rate in terms of the height, based on the information it is proportional to the square root of the height