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?

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    $\begingroup$ Please show both give the same value for Q calculation. $\endgroup$ – StainlessSteelRat Feb 12 at 22:42
  • $\begingroup$ 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 Feb 13 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 Feb 22 at 0:34

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.

  • $\begingroup$ 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 Feb 27 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 Feb 28 at 0:17

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