While learning betz’s law, I notice thrust forces at the inlet and outlet of control volume are both represented as densityareavelocity^2, which is different from thrust force caused by air pressure difference at the two sides of turbine itself, since air pressure at inlet and outlet of control volume are same while thrust forces at inlet and outlet are different.
As far as I know, thrust force represents force that changes air flow momentum (plz correct me if I am wrong), but after searching on google for a long time, I still don’t know clearly what it is in essence if it is not related to air pressure difference.
Kindly let me know your thoughts. Many thx
There are not different thrust forces at the inlet and outlet of the control volume. Instead, the thrust force of the rotor can be written as the difference in linear momentum between the inlet and outlet, i.e.,
T = rhoS_1V_1^2 - rhoS_2V_2^2,
or equivalently from Bernoulli’s equation,
T = 1/2rhoS*(V_1^2 - V_2^2),
using your nomenclature. This thrust force is equivalent to the pressure difference between the upwind and downwind sides of the rotor.