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## Homework Statement

A tank of cross-sectional area ##A## contains a liquid having density ##\rho##. The liquid squirts freely from a small hole of area ##a## at a distance ##H## below the free surface of the liquid.

If the liquid has no internal friction(viscosity), with what speed does it emerge?

## Homework Equations

##p = H\rho g ##

##F = \frac{\Delta (mv)}{\Delta t}##

## The Attempt at a Solution

##F = pa = aH\rho g ##

Again, ## F = \frac{\Delta (mv)}{\Delta t} = v \cdot \frac{\Delta m}{\Delta t}## ; because, ##v## is constant;

Now, ## \frac{\Delta m}{\Delta t} = \frac{a (\Delta x) \rho }{\Delta t} = a \rho v ## ; because, ##\frac{\Delta x}{\Delta t} = v ##

So, ## aH\rho g = v \cdot a \rho v = a \rho v^2 ##

Finally, ## v = \sqrt{Hg}##

But, it doesn't match the answer.

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