# Hydraulic siphon spillway entry and exit velocity magnitude and profiles

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.

• $\xi$ will likely vary strongly with velocity.
– Rick
Sep 15 '15 at 18:03
• 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? Sep 16 '15 at 19:02
• 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?
– Rick
Sep 16 '15 at 19:19
• 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. Sep 18 '15 at 6:34
• 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.
– Rick
Sep 18 '15 at 13:10