For an ideal rotor with wake rotation

PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · Energy resources and conversion · Energy resources and conversion

Energy from Physics, Ch Natural energy flows: rotors, turbines, waves, channels and hot rock

Problem

For an ideal rotor with wake rotation, the best induction factors at local speed ratio

x

satisfy

a'(1+a')x^2=a(1-a)

and

a'=(1-3a)/(4a-1)

. ((a)) At

x=1

, find

a

and

a'

. ((b)) The integrand of

C_P

a'(1-a)x^3

, would be

\tfrac{4}{27}x

on a rotor whose every annulus reached the Betz share with no swirl. Find the ratio

a'(1-a)x^2/(4/27)

x=1

, and say what it means for the part of a blade that runs at

x=1