How to calculate divided irrigation discharge from a Parshall flume

How do I calculate the discharge from a Parshall flume that flow over a bulkhead (XY) into three partitions (A, B and C) divided 25%/50%/25%. There is no restriction of flow when the pipe gates are open (the incoming volume does not exceed the capacity in any of the partitions). The partitions A & C feed 8" pipe, while the partition B feeds a 10" pipe. When either A or B partitions are closed (using gates A1 and C1), a downstream gate (A2 and C2) can be opened to dump that partition's portion into the 10" pipe (Section C).

1. If gate C1 is closed (effectively shutting off the water to that pipe), and the downstream gate C2 is closed, what percentage of the water goes into Pipe A and B? (My guess is A 33% and B 66%)

2. If gate C1 is closed (effectively shutting off the water to that pipe), and the downstream gate C2 is open, what percentage of the water goes into Pipe A and B? (My guess is A 25% and B 75%)

Thanks, Chris

• Include into your diagram if the flow over the bulkhead is free flow over a weir (=liquid level on lower side lower than weir). – mart Apr 16 '19 at 6:31
• I'm not sure what a weir is, but the water does flow freely and evenly over the bulkhead (when all the gates are open). – Chris Apr 17 '19 at 12:20
• In your case, the bulkhead appears to act as a weit, see this answer for how to determine flow: engineering.stackexchange.com/a/8039/61 – mart Apr 18 '19 at 10:50

Hydraulics get complicated fast, the beaty of weirs (that's the function of your bulkhead hear) is that you simplify the hydraulics, as you separate the flow upstream of the weir from the flow conditions downstream the weir: As long as water level downstream is a bit below the crest, flow conditions upstream can be calculated backwards from the weir withour regarding downstream conditions. This is why you can build flow distributing structures as per your drawing: Flow into one compartment depends only on weir length (again, only so long as the water level downstream is below the weir crest). You "pay" for this with hydraulic losses.

Your guesses is correct, provided two things:

• the wall partinioning B & C is higher than the resulting water level in those compartments.
• There's enough distance between upstream of the bulkhead for the flow to evenly distribute, or the flow velocity is low (how much distance? How low? I don't know. You want even distribution along the bulkhead). Given the shape of your flume upstream, I'd assume that you are good.

If gate C1 is closed (effectively shutting off the water to that pipe), and the downstream gate C2 is closed, what percentage of the water goes into Pipe A and B? (My guess is A 33% and B 66%)

Reservoir C will fill up to the water level upstream of the bulkhead, then flow over the bulkhead into the compartments A and B will be proportional to bulkhead lengths. IF the bulkhead between B and C is lower than that level, you will have an additional flow into compartment B, to be calculated by the weir formula. You need to check the hydraulic losses for the pipes from reservoir A and B and calculate the water levels in A and B at the relevant flow rates.

If gate C1 is closed (effectively shutting off the water to that pipe), and the downstream gate C2 is open, what percentage of the water goes into Pipe A and B? (My guess is A 25% and B 75%)

IF the hydraulic losses from the pipes A or B are so high that the water level rises above weir crest, you'd need to account for a lower discharge coefficient and the math gets hariy fast.

• Thank you! The irrigation water upstream is consistent, and the partitioning walls B & C are higher than the weirs themselves. The Reservoirs A, & C are deeper than the Parshall Tailwater channel and Reservoir B is deeper still. The gates A1, B1 & C1 effectively close off the outlet pipes. With that said, is it safe to assume Gates A2 & C2 to dump reservoir A & C's portion of the water into reservoir B when their pipe gates (A1 & C1) are closed? Again, Thank you! – Chris Apr 19 '19 at 12:43
• Yes. When A1 & C1 are closed, the only way the water can take is through pipe B (or over the walls of the structure when the lvel is too high). – mart Apr 19 '19 at 19:05