5. Air flow passes through a turbine and is bounded by the streamlines shown in Fig. 2. The flow enters with uniform velocity U, î and exits with a velocity profile v(r) = U. () i for r

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5. Air flow passes through a turbine and is bounded by the streamlines shown in Fig. 2. The flow
t for r< R2. The
enters with uniform velocity U, î and exits with a velocity profile 7(r) = U (
turbine is held in place by an external force F and gravity may be neglected.
a) Derive a relationship between R1 and R2.
b) Using the momentum equation, find an expression for F in terms of the velocity and
radii.
c) Consider the GE Haliade-X turbine which has a span of 150 m. If the wind is blowing
30 kph, find F. You may use 1.225 kg/m³ as the atmospheric density.
Transcribed Image Text:5. Air flow passes through a turbine and is bounded by the streamlines shown in Fig. 2. The flow t for r< R2. The enters with uniform velocity U, î and exits with a velocity profile 7(r) = U ( turbine is held in place by an external force F and gravity may be neglected. a) Derive a relationship between R1 and R2. b) Using the momentum equation, find an expression for F in terms of the velocity and radii. c) Consider the GE Haliade-X turbine which has a span of 150 m. If the wind is blowing 30 kph, find F. You may use 1.225 kg/m³ as the atmospheric density.
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