(adsbygoogle = window.adsbygoogle || []).push({}); 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=Av_{1}dT=Bv_{2}dT

h=vdT

3. The attempt at a solution

Av_{1}dT=Bv_{2}dT

integrate both sides with respect to t

∫Av_{1}dT=∫Bv_{2}

if I leave t as a constant ...

Av_{1}=Bv_{2}

v_{2}=Av_{1}/B

However this doesn't seem right as there is no mention of a initial velocity in the question .. please give me some pointers :)

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# Mechanics question on equation of continuity

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