1.

What is the relation between the induced velocity in far wake region (w) and that at the rotor disk (v) for hovering condition?(a) w=v(b) w=v^2(c) w=2v(d) w=v/2I had been asked this question during an interview.My query is from Momentum Theory in section Helicopter Dynamics of Aerodynamics

Answer»

The correct choice is (c) w=2v

To explain: The momentum equation for the rotor is given by:

T=\(\dot {m}\)w

Which can be REARRANGED as:

\(\frac {T}{\dot {m}}\)=w (equation 1)

And the ENERGY equation is given by:

TV=\(\frac {1}{2}\dot {m}\)

Which is rearranges as:

\(\frac {T}{\dot {m}}=\frac {1}{2}\)vw^2 (equation 2)

On EQUATING equation 1 and 2 we get w=2v

Thus, the induced velocity in the wake region is TWICE that of the velocity at the rotor disk.


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