I'm working on a pipe design problem using Bernoulli's equation, from first principles. The pipe is from a water storage reservoir (point 1) and discharges into a river (point 2). These are my two reference points respectively.

Now I know that the velocity at the reservoir is zero (point 1) as the water level is assumed to be stationary, but is the velocity at point 2 equal to the speed of the river?

This seems to make sense from my understanding as the movement of water in the river would carry some energy which must be considered.

  • $\begingroup$ Is the discharge end immersed in the river? Parallel to flow or perpendicular? $\endgroup$
    – Solar Mike
    Mar 30, 2018 at 15:27
  • $\begingroup$ It would be immersed in the river, and perpendicular to the flow. $\endgroup$
    – S User
    Mar 31, 2018 at 0:06
  • $\begingroup$ The velocity at P2 is governed by the pipe size and the flow rate in any case. There may be some discharge factor that gets added into the pipe resistance depending on the discharge conditions, but that's how this is accounted for - with a pipe fudge factor, like with elbows and transitions. $\endgroup$
    – Phil Sweet
    Aug 17, 2020 at 9:45
  • $\begingroup$ As @PhilSweet hinted, the word "pipe" implies significant viscous forces, and if significant viscous forces are encountered between point 1 and point 2, applying Bernoulli's equation between those points won't work. $\endgroup$ Apr 15, 2021 at 8:42

1 Answer 1


If the water discharges there is a flow, then it has a velocity depending on head and pipe specification.

In these types of plumbing of gravity pipes they leave a gap at the discharge so as not to create a siphone. So no consideration of flow of river.

  • $\begingroup$ The syphon effect can be planned for and used... $\endgroup$
    – Solar Mike
    Mar 31, 2018 at 5:31
  • 1
    $\begingroup$ draining into a river with drainage submerged is not approved in many municipalities for less than 25 years flooding. $\endgroup$
    – kamran
    Mar 31, 2018 at 6:26
  • 1
    $\begingroup$ And in places where it is permitted... $\endgroup$
    – Solar Mike
    Mar 31, 2018 at 6:56
  • $\begingroup$ It's interesting and is the subject of many tests and hydrology software. If a pipe drains into another larger pipe the confluence flow and velocity and pressure would be that of the larger pipe, like Bernoulli test instrument in the lab. However in draining into a river we deal with vertices and eddies and a complex system. if the outlet is inserted parallel to the flow there will be shear cone of mixing the two flows. this shear cone will be streamlined and smooth in small velocities and turbulent and frothy in large velocities. The effect on the upstream flow in the pipe is not significant. $\endgroup$
    – kamran
    Mar 31, 2018 at 7:07
  • $\begingroup$ Having worked on a feed pipe that had a siphon to draw the water up over the dam wall to feed the pelton turbine I know how stuff works.... laminar flow, turbulent flow , critical , Reynolds numbers, schlieren images ... $\endgroup$
    – Solar Mike
    Mar 31, 2018 at 9:28

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