Energy extraction limit in open-channel flow (Fr = 0.3094)

[eXtrem]

TL;DR

Maximum energy extraction in subcritical open-channel flow occurs at Fr = 0.3094, giving a 34.52% limit — potentially a Betz-type limit for open channels.

Hello,

I would appreciate feedback on a theoretical result concerning energy extraction from subcritical open-channel flow.

Using a control-volume approach with conservation of mass and momentum, I obtained an extremum corresponding to a Froude number:

Fr = 0.3094 (rectangular channel)

This extremum defines the maximum fraction of total head that can be converted without triggering a transition to critical flow.

The corresponding maximum energy extraction is 34.52%, which may be interpreted as a Betz-type limit for open-channel flow under subcritical conditions.

The result is derived under standard shallow-water assumptions and does not rely on turbine-specific modeling.

Preprint available on ResearchGate

https://www.researchgate.net/publication/400628197_An_Ext

I would be grateful for technical comments, especially regarding:
• the physical interpretation of the extremum
• possible relation to classical hydraulic limits
• assumptions that might restrict generality

Thank you.