# Homework Help: Mechanics question on equation of continuity

1. Jan 19, 2012

### emilypearson

1. The problem statement, all variables and given/known data
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!)

2. Relevant equations
I have come up with

dV=Av1dT=Bv2dT
h=vdT
3. 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 :)

2. Jan 19, 2012

### 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.