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First post on this forum. Greetings from the Netherlands :)

I am currently in the process of designing a turbine used in locks in several canals. The turbine is powered when the lock chamber is being emptyed during the lockage.

The goal is to calculate the water level in the lock chamber and the flow rate through the turbine at any given time assuming the turbine has a fixed power level and all of the water flows through it. I've made an attempt at finding a solution, but I would like to know if I'm on the right track.

The water level in the lock chamber decreases as water is flowing out of it. The flow rate and thus the power produced by the turbine decreases as time progresses. However, as the turbine is converting energy into electricity, it in turn is decreasing the flow rate even further. Correct?

From Bernoulli we know:

g*hl = v

^{2}/2+g*ht

hl is the water level in the lock chamber or "elevation head", and hk is the head loss produced by the turbine.

We also know:

P = ρ*Q*g*ht

ht=P/(ρ*A*v*g)

(Head loss produced by the turbine equals power divided by the density of water times the surface area of the pipe times the flow speed times acceleration due to gravity)

This gives:

g*hl = v

^{2}/2+P/(ρ*A*v)

Which can be written as:

0.5*ρ*A*v

^{3}- ρ*A*hl*g*v + P = 0

This formula can then be used to iterate hl and the flow rate.

Is this formula describing the flow rate A*v and the water level hl correctly for this scenario? Am I missing something?

Thanks guys!

Slendermann