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for calculating the volumetric flow rate of a liquid coming out of a tube, I know that If the pipe is too short, the Hagen–Poiseuille equation may result in unphysically high flow rates; the flow is bounded by Bernoulli's principle

So, what exactly is the Volumetric Flow rate due to Bernoulli's principle ( the formula )?

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  • $\begingroup$ Google 'orifice equation ' or 'flow through an orifice'. The practical formulation usually adds a coefficient of discharge that accounts for the specific orifice geometry and vena contracta $\endgroup$ – docscience Sep 6 '15 at 19:14
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Find the velocity using bernoulli's equation

Pressure + G.P.E per unit volume + K.E per unit volume = constant

and apply the equation for flow rate.

Flow rate = Area x Velocity

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    $\begingroup$ Sorry what is G.P.E per unit volume + K.E per unit volume? $\endgroup$ – David 2000 Sep 6 '15 at 17:04
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    $\begingroup$ Gravitational potential energy and Kinetic energy. $\endgroup$ – slhulk Sep 6 '15 at 17:05
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    $\begingroup$ So you mean if I change the cross section I can't have the same velocity ? But my question is the formula that gives me the relation between the volumetric flow rate and pressure and Area and Velocity $\endgroup$ – David 2000 Sep 6 '15 at 17:08
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    $\begingroup$ It is the Bernoulli's equation that I have written in words. :) $\endgroup$ – slhulk Sep 6 '15 at 17:09
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    $\begingroup$ oh u need the flow rate.. Let me edit my answer $\endgroup$ – slhulk Sep 6 '15 at 17:10
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The equation you are looking for is derived on Wikipedia.

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