1) calculate the WSEL over the weir with the weir equation and known weir geometry
2) use that as a downstream boundary condition for a standard step method or direct step method GVF analysis

Your sketch is actually a pretty straight forward homework problem from many civil hydraulics texts. The only thing missing is weir geometry. (sharp crested?) Most of my students could answer this in around an hour of work, with a spreadsheet. The diameter of the pipe is irrelevant, only the flow is needed.

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Thanks beej67.

This is a sharp crested weir. I have already determined the WSE in the channel. The issue is the upstream end. The water is falling vertically down (The velocity and the surface area will vary) until it meets the channel before it spreads radially out and then flowing downstream the channel. What would happen at the point of contact? what would be the WSE profile? HGL? Energy loss? Will the water splash out of the channel

The appropriate and responsible engineering answer to that question is "hell if I know." There's no easy answer to it, because it's a rapidly varying flow (RVF) situation that's typically not handled in civil design. It's the sort of thing computational fluid dynamics nerds will spend a month modeling and then wondering if they got it right. It's certainly erosive as you've drawn it, though. The most I could do is tell you the velocity at which the water would hit the bottom of the flume if the flume was empty.

I would suggest doing one of two things with your design to handle the situation. Either design a concrete splash pad lower than the ditch section to act as an energy dissipator, or extend the pipe down to the bottom of the flume and put a 180 degree turn in it, so it discharges pointing 'up,' like a fountain, and spreads all directions from there. Either solution, if done properly, will dissipate energy without throwing too much onto your flume walls. In fact, you could use a momentum analysis to determine exactly how high the 'fountain' solution goes if you really felt like it. Go dig out your undergrad fluid mechs textbook and look up the example problem they all seem to have with a fire hose nozzle - same math.

Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East - http://www.campbellcivil.com

you have not given enough information at this point. velocity of the water impacting the bottom of the channel is unknown since the pump discharge line is presumably under pressure. If you knew the velocity of the jet, then you could at least estimate the energy grade line elevation and have an idea of how high the channel walls should be. Since you have a weir blocking the flow, flushing velocity will not be adequate, you will trap sediment behind the weir. Also, you have not given the depth of tailwater which will affect the energy dissipation of the jet.

Since this is something I recently encountered, some ideas:
1) A weir will block sediment, an open flume or an undershot weir might be better to pass the sediment and still keep the tailwater depth where you want it

2) With sufficient mixing and turbulence from the jet plus high enough mass flow rate, sediment will move through the channel.

3) Consider a screen or partial cover over the channel to prevent splashing and for safety

4) if the jet velocity is too high, you can reduce it using a larger pipe size

5) an energy dissipater at the upstream end may be necessary if you don't have deep enough tailwater. an impact basin might work (which is similar to the undershot weir)

Thanks cvg.

The weir can be lowered periodically to flush the sediments trapped behind.

The maximum velocity at the 90 bend is 2.1 m/s. Based on this I can estimate the total energy at the 90 bend, and, also at the point the jet hits the channel. I am reluctant to create a pool at this location. My preference is to have a uniform channel bottom. After reading the comments I now thinking of curving the pipe until the pipe outlet is facing the channel and then closing the channel up to a 2.0 m length to confine the turbulent region. The 2.0 m length is only a guess.

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You could model this scenario in EPA SWMM.

at the very least, I would calculate the length of hydraulic jump and use that to estimate the length of your cover. since you are angling the pipe downstream, your hydraulic jump will get pushed farther downstream. not sure that is the best option for energy dissipation and 2 meters sounds too short.

Lan, your second sketch looks a lot more reasonable.

As mentioned above, check to see whether you're subcritical or supercritical. Design your ditch height and freeboard for the subcritical case and your channel liner for the higher velocities of the supercritical case. Consider looking up USBR stilling basin design guidelines as well, they'll have a lot of good information for your case.

Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East - http://www.campbellcivil.com