Answer:
Explanation:
Given that solid circular rod rotates at constant speed and neglecting losses throughout the system, power is calculated as the product of torque and angular speed. That is to say:

There is a formula that relates torque with shear stress:

Where
is the torsion module, whose formula for a solid circular cross section is:

The tension module is calculated herein:

Maximum allowed torsion is found by isolating it from shear stress equation:


Then, maximum transmissible power is determined directly:

Answer
For isotropic material plastic yielding depends upon magnitude of the principle stress not on the direction.
Tresca and Von Mises yield criteria are the yield model which is widely used.
The Tresca yield criterion stated that yielding will occur in a material only when the greatest maximum shear stress reaches a critical value.
max{|σ₁ - σ₂|,|σ₂ - σ₃|,|σ₃ - σ₁|} = σ_f
under plane stress condition
|σ₁ - σ₂| = σ_f
The Von mises yielding criteria stated that the yielding will occur when elastic energy of distortion reaches critical value.
σ₁² - σ₁ σ₂ + σ₂² = σ²_f
Answer:
The radius of a wind turbine is 691.1 ft
The power generation potential (PGP) scales with speed at the rate of 7.73 kW.s/m
Explanation:
Given;
power generation potential (PGP) = 1000 kW
Wind speed = 5 mph = 2.2352 m/s
Density of air = 0.0796 lbm/ft³ = 1.275 kg/m³
Radius of the wind turbine r = ?
Wind energy per unit mass of air, e = E/m = 0.5 v² = (0.5)(2.2352)²
Wind energy per unit mass of air = 2.517 J/kg
PGP = mass flow rate * energy per unit mass
PGP = ρ*A*V*e

r = 210.64 m = 691.1 ft
Thus, the radius of a wind turbine is 691.1 ft
PGP = CVᵃ
For best design of wind turbine Betz limit (c) is taken between (0.35 - 0.45)
Let C = 0.4
PGP = Cvᵃ
take log of both sides
ln(PGP) = a*ln(CV)
a = ln(PGP)/ln(CV)
a = ln(1000)/ln(0.4 *2.2352) = 7.73
The power generation potential (PGP) scales with speed at the rate of 7.73 kW.s/m