Open channel flow in a circular pipe has a maximum flow $Q_{max}$ at a flow depth approximately 93.8% of the pipe diameter. Calculating flow Q from depths 92.5% and 94.9% both give the same value for Q.

So, if we know that the flow is Q, or if we are designing for a flow of Q, how do we determine which flow depth be correct in practice?

  • 2
    $\begingroup$ Please show both give the same value for Q calculation. $\endgroup$ Commented Feb 12, 2021 at 22:42
  • 1
    $\begingroup$ The flow can transition between those two Manning's normal depths. What part of the design is critical to a specific value for depth? $\endgroup$
    – DavidJ
    Commented Feb 13, 2021 at 1:43
  • $\begingroup$ @DavidJ Neither is critical in my case; I have a project building an open channel flow calculator. Depth to flow is deterministic but not the case in flow to depth? (Incomplete but you can get the idea here: eduk8r.org/fluids/calcs/openChannel ) $\endgroup$
    – dmorg
    Commented Feb 22, 2021 at 0:34
  • $\begingroup$ Open channel flow in a circular pipe, when has a circular pipe been considered an open passageway of fluids? Please review and revise your question so there is no misunderstanding. $\endgroup$
    – r13
    Commented Jul 26, 2021 at 21:23
  • $\begingroup$ The water level in the pipe is determined by Q but also, crucially, by the slope of the pipe and by the water level at the downstream end. Water level will in most cases vary along the length of the pipe (water flows downhill, if the pipe has no slope the free surface will). You need to wrap your head around these things before you can build a channel flow calculator. $\endgroup$
    – mart
    Commented Jul 27, 2021 at 7:23

1 Answer 1


To solve for depth, given flow, one can use VT Chow’s equations to iteratively solve for theta. The two solutions will be found on either side of theta Qmax.

Concurrent Depths

How to resolve.

Chow on internet

  • $\begingroup$ Yes, I can solve for depth iteratively; that is not my problem. Given that there can be two 'alternate' depths that yield the same discharge (when the flow yields depths close to 94% full), I was interested in which depth 'wins out.' If I read your earlier comment (Feb 13) correctly, depths may fluctuate between the two depths? $\endgroup$
    – dmorg
    Commented Feb 27, 2021 at 20:22
  • $\begingroup$ Chen does not indicate a preferred depth. When I consider the headwater above the crown that would occur at the entrance transition, I envision that there would be depth surges. $\endgroup$
    – DavidJ
    Commented Feb 28, 2021 at 0:17
  • $\begingroup$ Does VT Chow’s work include circular pipe flow as asked by OP? You should show the link then. $\endgroup$
    – r13
    Commented Jul 26, 2021 at 21:52
  • $\begingroup$ Thanks for the info. Appreciated. $\endgroup$
    – r13
    Commented Jul 28, 2021 at 1:27

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