Bernoulli's eqn for a fish passage

[Shuff]

I'm doing a project for my University. Making a design for a fish friendly dam structure that will let fish pass downstream without getting through the turbine.

Quick sketch:

(1/2 u_1^2+p_1+gz_1 )_inlet=(1/2 u_2^2+p_2+gz_2 )_funnel+(1/2 u_3^2+p_3+gz_3 )_fishway

(1/2 u_2^2+p_2+gz_2 )_funnel=(1/2 u_4^2+p_4+gz_4 )_(turbine exit)

These are the two Bernoulli equations I have set up. Are they useable for this case?
If p1 is 20 meters under water surface, can one apply the basic 1 bar per 10meters, or will the water flow u1 play a major role on the p1?

p=F/A=(m⋅g)/A=(V⋅ρ⋅g)/A=(h⋅A⋅ρ⋅g)/A=ρ⋅g⋅h

Can p3 be assumed to be 1atm since it is so close to free air?

Also, how can p2 be calculated/assumed?

The problem I’m having is that I have too many unknowns. The u1 has to be assumed/given, but how can I calculate both u2 and u3. I guess the percentage of the area in the funnel and the fish tunnel ratio is not precise enough to calculate the ratio (funnel has ex. 80% more area than fishway so it has 4 times more flow). Since they are not located the same distance etc.

 

[LightHero]

The Bernoulli equation can be used to calculate the unknowns. The pressure at points 1 and 3 will depend on the elevation of the water surface and the depth of the points relative to the water surface. Pressure 2 can be assumed to be equal to pressure 4 since they are located on the same side of the turbine. U1 and U4 can be calculated using the continuity equation, which states that the flow rate before the turbine must be equal to the flow rate after the turbine. You can then calculate U2 and U3 by using the Bernoulli equation.