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?

  • $\begingroup$ 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

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.

  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.