Problem statement
When does the maximum flow occur in a pipe? Intuition might suggest that it occurs when the pipe is flowing full—i.e., when the depth of flow h equals the diameter D of the pipe.
Write a function that takes the ratio 
and produces the flow rate as a fraction of the value for a full pipe. For example, when the input is 1/2, the output should be 1/2, and when the input is 1, the output should be 1. Assume that Manning’s equation applies and Manning’s roughness coefficient is constant.
and produces the flow rate as a fraction of the value for a full pipe. For example, when the input is 1/2, the output should be 1/2, and when the input is 1, the output should be 1. Assume that Manning’s equation applies and Manning’s roughness coefficient is constant. See Test 13 for the answer to the initial question.
Background
Steady uniform flow in a channel is often computed with Manning’s equation, which results from a balance between the component of the fluid’s weight in the flow direction and friction on the walls of the channel. The shear stress on the channel walls is computed with an empirical relation. Manning’s equation for the flow Q is
where n is Manning’s roughness coefficient, 
is the hydraulic radius, 
is the slope of the channel, A is the cross-sectional area of the flow, and P is the wetted perimeter (i.e., the perimeter of the solid wall of the channel that is touching the water.) The coefficient C is 1 for SI units and 1.5 (or 1.49) for U.S. customary units.
is the hydraulic radius, is the slope of the channel, A is the cross-sectional area of the flow, and P is the wetted perimeter (i.e., the perimeter of the solid wall of the channel that is touching the water.) The coefficient C is 1 for SI units and 1.5 (or 1.49) for U.S. customary units. Solution Stats
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Is something broken on Cody right now? I submitted a solution (several iterations of it, in fact) well over an hour ago, and the problem shows up as solved for me, but no solutions are visible and my profile doesn't show that I solved this either.
Yes, there seems to be a problem. No solutions have been displayed for 2 solvers, nor is your comment visible on the comment section of Recent activity.
I'll inform the devs about this.
Hi Dyuman, I tried solving other problems, and my solutions, although correct, is also not counted. Are the devs working on this?
@Dyuman thank you.
@Ramon it appears work's being done on this; Solutions for this problem are showing up for me now, and recent comments are starting to show up again as well (albeit incomplete and with the wrong timestamps).
We are currently looking into this issue. Thank you for being patient!
Thanks, Arunika!
@Christian, Dyuman and Ramon, I've got some updates. So an unexpected issue occurred on 4/9/23 which caused a pretty big backlog of updates in our queue. That queue is slowly being processed, so the delayed updates to your profiles will self-resolve in the next few hours.
We are currently working on speeding this up, but aside from an inconvenient delay, we assure you your progress will not be lost. We apologize for this inconvenience and we hope you understand!
Looks like things are back to normal now, Thanks Arunika!
Totally understood, Arunika. Thanks again to you and everyone for fixing this so quickly!