I have a question about assumption of inlet and outlet pressure in betz’s law.
The upper diagram below is a control volume of one-dimensional air flow. The lower one is its pressure at corresponding places. Wind blows from left to right. And it is assumed air pressures at the far left and the far right are same as ambient pressure.
However, as far as I know, wind is caused by air pressure difference, so I am wondering if it is correct to assume that air pressure at these two far sides are same as ambient pressure (P1). If so, how could wind be caused?
I think the answer to your question is scale. The pressure-gradient zone around the rotor is fairly small scale…perhaps encompassing a couple rotor diameters upwind and downwind of the rotor. The pressure gradient driving wind in the first place tends to be a much larger scale (mesoscale)…over many, many kilometers.