I am trying to set up an equation relating the mechanical energy in a hydropower plant to its electrical output. What I picture is the relation between the energy input from the moving water, to the rotational energy of the turbine to the electric output of the generator. I know I can calculate the power P directly using the formula P = d*h*r*g*k, where d is the density of water, h is the height, r is the flow rate, g is the gravity constant and k is an efficiency coefficient. However, I´d like to set up an equilibrium equation where I can vary the flow of water and see the effect on the angular speed of the turbine and furthermore the electric power output from the generator. I guess I could do this by calculating the kinetic energy of the water and translate this into rotational energy of the turbine (using 0.5*I*ω^2 where I is the moment of inertia and ω the angular velocity ?). This energy would in turn be converted into electrical energy less some friction and magnetic resistance. I do however not exactly see how I should insert the time dimension in order to obtain an equation of a system in equilibrium (i.e. where the water flow is constant and the output including friction and resistance is constant). Did I explain this right and can anyone help me with my problem?