1. Supplemental Learning Module ME 303 Fluid Mechanics
COHERENT APPLICATION THREADS
CATs
Wind Turbines
Supplemental Learning Module
ME 303 Fluid Mechanics
Control Volume Analysis and the Betz Limit
Don Wroblewski
Associate Professor, Mechanical Engineering
Associate Chair, Aerospace Engineering
Undergraduate Program

2. BETZ LIMIT SETUP A1 A2 A F P V2 V V1 Wind Speed downstream of rotor
Wind Speed through rotor
Wind Speed downstream of rotor
Streamtube A1 A2
Undisturbed Wind Speed A
Rotor area F
Force exerted by rotor on wind V1 P
Power extracted at rotor

3. BETZ LIMIT ASSUMPTIONS
Wind velocity is always axial (normal to flow areas)
Steady State, Uniform Flow
Incompressible, adiabatic flow
Ideal rotor
Zero mass
Zero drag
No Wake V2 F V V1 A1 A A2 P

4. Apply following to control volume
BETZ LIMIT ANALYSIS
Apply following to control volume
Conservation of mass: relates V’s to A’s
Momentum equation: relates F to V’s and A’s
Energy equation: relates P to V’s and A’s
Other: P=VF
Control volume V2 F V V1 A1 A A2 P

5. Betz Limit Results Coefficient of Performance
Coefficient of Performance vs Velocity Ratio V2 V V1