Engineering Hydrodynamic force on hinged flap gate

[Kapper]

Homework Statement

I am trying to find an expression for the hydrodynamic torque the water is exerting on a hinged flap gate. the gate is partially submerged and water can flow around the gate in all directions. I Am not sure how to set up this equation

Relevant Equations

Conservation of momentum, Hydrostatic pressure

I have attempted to use the law of conservation of momentum.

The Areas are the lengths marked with the red striped line times the length into the paper, and the Forces F1 and F_hydro are the hydrostatic pressure and hydrodynamic forces respectively (acting on the plate) (The x y components is relative to the coordinate frame given in drawing).

I want to have an equation that works for all angles, which includes both static and dynamic situations.
I can't get this to make sense I think I should use angular momentum instead of linear But I have no idea how to derive that.

 

[256bits]

What is F1, or FHydro?
And what coordinate system orientation are you using?

That is the first step in solving thee problems so that others are not guessing on the analysis.

Other than that, are you being asked to solve the force with water flow, or just at the instance when the gate will open?

 

[Kapper]

Sorry I've made an update