I am working on the hydraulic seawater flow though a siphon spillway. My task is to determine at a location in front of the spillway the flow velocity and profile when

  1. The flow enters the spillway
  2. The flow exits the spillway

See attached a drawing of the problem.

Now the basic formula for calculating the flow through the siphon is

$$ \Delta H = \xi \frac{v^2}{2g} $$ where:

$\Delta H$ = pressure head

$\xi$ = total friction losses

v =flow velocity

g = gravitational acceleration

Question is: what is the flow profile and velocity at the location in front of the spillway (see drawing) for a given pressure head, geometry and friction loss factor?

Please note that I am not looking for a full fledged CFD analysis at this stage.

Any help on how to tackle this problem is appreciated.

. enter image description here

  • 1
    $\begingroup$ $\xi$ will likely vary strongly with velocity. $\endgroup$
    – Rick
    Sep 15, 2015 at 18:03
  • $\begingroup$ Would you be able to be more specific? $\xi$ is a combination of frictional and inertial losses. Where do you think the contribution is greatest? $\endgroup$
    – Ruudc
    Sep 16, 2015 at 19:02
  • $\begingroup$ At low speeds (small head differences) it's probably mostly viscous losses, at higher speeds the inertial losses will probably dominate. Are you trying to model this as a 2D problem? If not, what's the width? $\endgroup$
    – Rick
    Sep 16, 2015 at 19:19
  • 1
    $\begingroup$ Yes, that makes sense. I am trying to solve in 3D with a width of 3.2 meter. At the moment I know that the combined inertial losses are $\xi$ = 1.62 and the frictional losses are $\xi$ = 0.38. Though I am still unsure how to determine the velocity magnitude and profile in the region I indicated. The head difference is between 0.5 and 1.5 meter. $\endgroup$
    – Ruudc
    Sep 18, 2015 at 6:34
  • $\begingroup$ How did you get those values for $\xi$? The inlet flow will likely just converge on the inlet pretty uniformly with small amount of viscous loss. At the outlet, the flow will likely continue along it's path gradually spreading with recirculation zones on either side and the top. Calculating these zones would require CFD, though some approximation techniques probably exist. Why do you need the flow profile? If you're just trying to calculate losses, you can probably just assume there's no pressure recovery at the outlet, and there's no losses at in the inlet. $\endgroup$
    – Rick
    Sep 18, 2015 at 13:10

2 Answers 2


The outflow case could be considered assuming a jet confined on one side. That should give a reasonable analytical solution for the ocean side.

The inflow case is trickier, but you should be able to find some research on flow fields upstream of an orifice. The bed confines the inflow, so that's a bit of a unique case. Try looking for studies on an orifice intake with the bed/floor confining the inflow. I would think someone's published flow fields for that case.


As a simplification I would assume that the flow going into the pipe flowed mostly uniformly towards the pipe from all directions, meaning that the flow velocity would drop off rapidly and there would be very little energy loss associated with it.

Conversely, I would assume that the water exiting the pipe would pretty much keep going straight with the same velocity, the kinetic energy in the flow would then be dissipated through viscous and turbulent effects.

Of course this flow profile would be affected by any objects (such as turbines) placed in the way, and at low flow velocities the jet would diffuse over a significantly shorter distance.

If you're looking for a more accurate analysis I think you need to look into jet dynamics, or just use a simulation, though jet simulations are sensitive to choice of turbulent model so make sure to validate your model.


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