Investigate and based on rotor momentum/ actuator disk theory, what is the theoretical velocity magnitude, w far downstream in the wake of the rotor?

Background
This is an open-ended problem, as such there is no single proper way to devise a solution. The objective is to allow you to think critically and research ideas for a potential way to solve the problem. Credit will be given on your effort and reasoning behind your solution.

Problem Statement
Suppose you are asked to measure the wind velocity, w (in two components along the x and y directions; u and v respectively) far downstream in the wake of a hovering helicopter rotor where the wind changes minimal direction at a maximum frequency of 10 Hz. Suppose that the mean induced velocity (vi) remains nearly constant at 15 m/s at the plane of the rotor.

Questions

1. Investigate and based on rotor momentum/ actuator disk theory, what is the theoretical velocity magnitude, w far downstream in the wake of the rotor?
2. Suppose you are asked to measure the velocity components u and v using inexpensive electronic components. How might you design/ build a simple wind sensor(s) that could measure the wind velocity and direction? Use sketches to present your ideas, you can assume that you can calibrate your chosen sensor/ actuator voltage output to a physical measured variable.
3. If your wind velocity is changing direction at a maximum frequency of 10 Hz, what is the minimum frequency that you should sample your wind measurement in order to properly capture/ reproduce the wind fluctuations?

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