I am investigating the open jets of small wind tunnels and the study of small scale wind turbines and need to know how to calculate the distance "x" where the jet flow manages to flood the machine.
Yes, there are equations to calculate the optimal jet flow distance for wind turbines. The optimal jet flow distance is the distance between the end of the wind turbine blade and the start of the jet flow, which is where the flow becomes fully developed.
One equation that can be used to calculate the optimal jet flow distance is the momentum theory equation, which relates the axial momentum of the incoming flow to the axial momentum of the flow leaving the rotor. The equation is given as:
Vj = 2*sqrt(T/ρA)
where Vj is the optimal jet flow velocity, T is the rotor torque, ρ is the air density, and A is the swept area of the rotor.
Once the optimal jet flow velocity is known, the optimal jet flow distance can be calculated as the product of the optimal jet flow velocity and the time required for the flow to become fully developed. The time required for the flow to become fully developed is dependent on the Reynolds number and other flow properties, and can be determined through empirical relationships or computational fluid dynamics (CFD) simulations.