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is it possible to calculate the flow of water out of a pipe where gravity is the only force acting upon the water and therefore generating the flow. The pipe diameter is X and there is minimal fall (say 6 inches?).

The real life scenario here is that I am trying to calculate the flow of water out of a washing machine waste when the filter plug is removed at the bottom?

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  • $\begingroup$ It would be quite handy if you could provide a sketch of your scenario. $\endgroup$
    – Andrew
    Apr 13 '18 at 12:43
  • $\begingroup$ Sorry Andrew... not sure how to attach a sketch to a comment? Any ideas?? $\endgroup$ Apr 17 '18 at 14:37
  • $\begingroup$ You could edit your question and add a scan or you can provide a link of the uploaded file in the comment section. $\endgroup$
    – Andrew
    Apr 17 '18 at 15:15
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The Bernoulli equation will give you a pretty good estimate. It says that: $$ P_{1} + \frac{1}{2}\rho v_{1}^{2} + \rho g h_{1} = P_{2} + \frac{1}{2}\rho v_{2}^{2} + \rho g h_{2} $$ You pick 2 points in a flow (1 and 2). In this case, you can ignore the pressure terms, $P$, and focus on velocity, $v$, height, $h$, and gravitational acceleration, $g$. In this case, you can use the free surface of the water in the machine as point 1, meaning that $P_{1} = v _{1} = 0$, $h_{1}= 0.15 m$, then point 2 is at the outlet of your pipe, and $P_{2} = h_{2} = 0$. Then: $$ v_{2} = \sqrt{2gh_{1}} $$ gravitational acceleration is $9.81m/s^2$. If you want to add a (probably small) degree of accuracy to your calculations , the so-called head-loss calculations are useful. You can use this calculator: https://apps.engineeringtoolbox.com/head-loss-water-pipe-a_15.html

Which will give you a pressure loss in kPa, and velocity loss in m/s. You can adjust your prediction as: $$ v_{adjusted} = v_{2} - v_{loss} $$ so your average flow velocity will You'll notice, though, that you need to know the flow rate:$$Q_{2} = v_{2}\pi r_{pipe}^{2}$$ before you can calculate the head loss.

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  • $\begingroup$ Hey EMiller, Thanks for your advice. Much appreciated. However would you mind elaborating a little more. $\endgroup$ Apr 16 '18 at 15:31
  • $\begingroup$ How do I know what the velocity is? $\endgroup$ Apr 16 '18 at 15:35
  • $\begingroup$ Is there a standard for gravitational acceleration? $\endgroup$ Apr 16 '18 at 15:36
  • $\begingroup$ Where do I add the diameter of the pipe as surely this will make a difference? $\endgroup$ Apr 16 '18 at 15:36
  • $\begingroup$ @David C Bradley , I've edited my answer. hopefully it's more clear. The pipe diameter will play a role in head loss, but mostly it's used to calculate the cross-sectional area of the pipe, so that the flow rate can be calculated from the velocity. $\endgroup$
    – EMiller
    Apr 17 '18 at 13:43

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