Mechanics question on equation of continuity

[emilypearson]

Homework Statement

A large vertical cylindrical rainwater collection tank of cross sectional area A is filled to a
depth h. The top of the tank is open and in the centre of the bottom of the tank is a small hole
of cross sectional area B (B<<A). Derive expressions for (i) the flow speed and (ii) the volume
flow rate of the water flowing out of the small hole.

It is mainly part i) I am struggling with, as once I have an expression for the flow speed, the volume flow rate should be easy enough(I hope!)

Homework Equations

I have come up with

dV=Av₁dT=Bv₂dT
h=vdT

The Attempt at a Solution

Av₁dT=Bv₂dT
integrate both sides with respect to t
∫Av₁dT=∫Bv₂
if I leave t as a constant ...
Av₁=Bv₂
v₂=Av₁/B
However this doesn't seem right as there is no mention of a initial velocity in the question .. please give me some pointers :)

 

[conquest]

Are you sure the relevant equations are correct? For one there is water coming frmo the top and flowing out at the bottom right so it might be a good idea to put a minus sign somewhere (although you could just put that in v). Also should it be dV= Av1dT + Bv2dT
So the change in volume is what flows in minus (or that is in the v2) what flows out through the bottom.