I'm struggling to confirm the Velocity in an open channel flow with 0 percent slope. Water enters the channel from an open pipe. The rectangular channel dimensions (66' Long x 3.33' W x 6.75' D) and Q (15 MGD) are known. The channel is concrete and empties into a larger basin via free fall (i.e. no weir at end). I would use mannings; however with no slope I'm stumped. Any help would be appreciated.

P.S. This is a real world problem at a waste water treatment plant I'm working on.

Thanks in advance. C

  • $\begingroup$ Please confirm, the floor of the channel is above the water level in the basin it empties into? $\endgroup$
    – mart
    Feb 22, 2017 at 10:42
  • $\begingroup$ The height of water will build up at the inlet to give you enough hydrostatic pressure to drive the flow. Then you need to balance the pressure drop along the length against the hydrostatic pressure/head. $\endgroup$
    – ericksonla
    Feb 26, 2017 at 18:24
  • $\begingroup$ mart - Yes, it free falls into the basin below at the end of the channel. $\endgroup$
    – user10149
    Feb 27, 2017 at 15:04

2 Answers 2


My open channel hydraulics are a little rusty having ended up in project management for a few years.

Assuming sub-critical flow, i.e. the Froude number is less than 1. This is reasonable unless the inlet to your channel is horizontal and the water is entering at high velocity.

The depth of flow is governed by a control structure at the down stream end. Two conditions could exist - either the water free falls into the basin, or the discharge is flooded and the downstream level is the same as the basin.

Assuming free-fall, calculate the critical depth of the flow. This is the same as a weir equation, setting the height of the weir above the invert of the channel as zero.

The normal equations for flow in an open channel fall apart when the depth is critical. To overcome this, go say 3 depths back upstream and add 10% to the depth. Now split the remaining length of channel into small segments, and working upstream calculate the frictional losses in the next segment, hence the change in total head, hence the change in depth. Use the new depth for the start of your next segment. Do this all the way upstream to the inlet.


Assume a slope of 1:500 it is impossible in reality to build a completly flat pipe. Construction tolerances accept that a flat pipe is in a gradient of 1:500. Flow calculations to this will prove adequately precise.


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