What is engine power vs propeller thrust relation?
Power P, stationary thrust T, propeller swept area A, and air density rho are linked by this expression, derived from first principles and momentum theory:
T^3 = 2 · P^2 · A · rho
That's the maximum power available assuming a 100% prop efficiency.
Things change if the prop is moving forward, as in a flying plane. With the forward speed component, the blades have their angle of attack reduced in proportion to that forward speed. The blades work as wings, and a wing profile has a coefficient of lift that changes with the AoA. Drag does also change with a growing AoA, Hence, for every section of a fixed-pitch prop's blade, there's an optimum L/D at a given combination of rotating and forward speeds that gives the best efficiency. For a fixed angular speed of the prop, there is a given forward airspeed at which the prop works with maximum efficiency, that efficiency –and hence the thrust– dropping asymptotically as the forward speed grows...
Concerning the power delivered by a propeller in forward motion, it's the product of the thrust and speed...