Question

Could someone please help me understand this question and specifically what it means by proportional:

Water leaks from the bottom of a tank at a rate proportional to the depth h of the water in the tank. Write down an equation describing this if V is the volume of the water in the tank after time 't' and if the tank is a cylinder show that dh/dt is proportional to h

Answer 1

do u know anything about Torricelli's law

Answer 2

if water leaks at the bottom of the tank (dV/dt) at a rate proportional to the depth h of the water in the tank ..how can i write something here..

Answer 3

\[\frac{ dv }{ dt }=-a \sqrt{2gh}\]

Answer 4

and

Answer 5

nope! havent met that before .. what does the right side of the equation mean/stand for?

Answer 6

\[A(h) \frac{ dh }{ dt}=-k \sqrt{h} \]

Answer 7

where K is a constant

Answer 8

Thanks for that

Answer 9

-a is area btw