Assume we have a pipe with a diameter of 10mm. Water is flowing through that pipe and we know that the water pressure at the 'open' end of the pipe is 2 atm. How would one go about calculating the flowrate of water? Reasonable assumptions are allowed.

I at first thought of using Poiseuille's equation, but that requires you to have a container length. Right now I have found no way to calculate flow in my situation.

  • $\begingroup$ Do it for unit length ie 1. $\endgroup$ – Solar Mike Jun 3 '20 at 7:31
  • $\begingroup$ also see: waterprofessionals.com/learning-center/flow-rate-calculator $\endgroup$ – Solar Mike Jun 3 '20 at 8:16
  • $\begingroup$ Thank you for the reply @Solar Mike, unfirtunately the problem with those calculators is that they require the water velocity? which I don't have. Could you please elaborate a bit on why would using a unit length on 1 meter of pipe work? To me it still seems we are just calculating fluid flow rate through a pipe with 1 meter length, not an open ended pipe. I'm sorry if this should be obvious and I don't understand. $\endgroup$ – emos-egavas Jun 3 '20 at 10:39
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    $\begingroup$ A picture or a more clear definition of the inlet and outlet locations would be helpful. Can you describe why 1 meter of pipe is not the same as an open ended pipe to you? Alternatively, you can give us more details on what your "situation" is. As it stands, I would have to assume some length to use any equation that I know. $\endgroup$ – J. Ari Jun 3 '20 at 13:41
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    $\begingroup$ To calculate the flow rate, you need the inlet and exit pressures plus the pipe type and diameter. Then it's just a typical pressure head loss determination, probably best done with tables. It's the total system that matters, not a single cross-section. Obviously the flow rate is the same for the entire length of the pipe. $\endgroup$ – Tiger Guy Jun 3 '20 at 16:56

There's Torricelli's equation for hydrodynamic calculations purpose and for calculating the velocity of perfect fluid flow at the $'open' end$ could be presented as: $$V = \sqrt{2gh}$$ $V $ is the velocity, $m/s$

$g $ is the acceleration due to gravity, $m/s^2$

$h $ is the liquid column height (above the 'open' end), $m$

The same conclusion could be drawn from the Bernoulli's incompressible flow equation

  • $\begingroup$ Torricelli's and Bernoulli's equations only work if frictional losses are negligible. Unfortunately, the fluid mechanician's definition of the word "pipe" includes frictional losses not being negligible. $\endgroup$ – Daniel Hatton Apr 1 at 16:02

Sorry, I don't have enough reputation to commenton Nikolay Jolshin's answer. Regardless of the pressure at the exit, if you know the difference in pressure you can use Torricelli's equation.

I just want to add that, depending on the application, you might also need to consider loses due to speed. For example adding a speed coeficient to Torricelli's eq. Many manufacturers provide such coeficient, which from my experience normally dances around 0.98


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