Water turbines - notes on calculations
Figure: General water turbine sketch. Physical setting of a turbine casing with respect to a dam. Water levels indicated.
We can see there are several simple relations among quantities just defined
To simplify calculations we usually considers water an incompressible fluid with no phase changes possible and we solve the well known equations, the conservation laws the fluid obeys.
Coservation of linear momentum is expressed by the Navier-Stokes equation. In this case (incompressible fluid, steady state) it can take the form
At the outlet the situation is a little bit complicated. After the flow (with high total pressure) exits the draft tube it mixes with water (with low total pressure) surrounding the draft tube. We usually take simplifying steps and assume the static pressure of exiting flow equals the hydrostatic pressure of surrounding water, i.e. we write