Toricelli's Law Proof for Water Leaking from a Reservoir

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toricellis law ? proof ??

Homework Statement

Let y(t) and V(t) be the height (in m) and the volume of the water (m^3), respectively, in a resevoir at time t (in s). If the water leaks out through a hole of area a ( in m^2) at the bottom of the resevoir, Toricelli's Law states that dV/dt= -a(squareroot(2gy)) where g is the acceleration due to gravity.

Suppose that the resevoir is a cylinder of height 5m and radius 50cm and that the hole in the bottom is circular with radius 2.5cm. If we take g=10m/s^2, show that y satisfies dy/dt= -1/200(squareroot(5y))

Homework Equations

The Attempt at a Solution

Well i figured the volume of the cylinder is (5/4)pi and area of small circle is 0.00196m^2 i don't know what to do next ?? please help ..

 

[AKG]

Express V(t) in terms of y(t).