Circulation Theory

Vortex Theory

Flow around rotating cylinder

image

Where velocity is higher

Lower pressure

Magnus Effect

Force acting on the cylinder

Kutta-Joukowski Equation

L=ρΓV0

\( \Gamma \)

strength of circulation flow

\(2 \pi c \)

\( V_0 \)

Uniform flow velocity

no need to consider

blade shape

Creation of vortices

at the edges

Free tip vortices

Betz

Smallest energy loss

Induced velocity

when helicoidal vortex sheet

pushed astern along shaft axis

rotated about shaft axis

Maximum efficiency

inflow velocity

same for every blade