Deriving Equation for Water Depth After Tank Hole Poked

[gboff21]

Homework Statement

A vertical cylindrical tank of cross-sectional area A_1 is open to the air at the top and contains water to a depth h_0. A worker accidentally pokes a hole of area A_2 in the bottom of the tank.
Derive an equation for the depth of the water as a function of time t after the hole is poked. Use A_1,A_2 h_0 and appropriate constants

Homework Equations

P=h_0$$\rho$$g
V=h_0A_1

The Attempt at a Solution

I have no idea where to go after deriving the above equations.

 

[skeptic2]

Can you derive a formula for the volume of water that flows through the hole per unit of time based on the pressure?

 

[gboff21]

Could you use P=FA and Ft=impulse?

 

[yinx]

This is a fluid mechanics questions. i believe you need the continuity equation and bernoulli's equation to solve it.

Continuity Equation: A1*V1= A2*V2

Bernoulli's Equation: P_1+h_1pg+(1/2)pv_1^2 = P_2+h_2pg+(1/2)pv_2^2
Capital P= pressure
Small p = rho (density)