Hydraulic siphon spillway entry and exit velocity magnitude and profiles

Question

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.

.

Answer 1

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.

Answer 2

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.