How Is Power Extracted from Wind Turbines?

AI Thread Summary
Power extraction from wind turbines involves calculating the kinetic energy of the wind before and after it passes through the turbine blades. The initial wind conditions are given as a density of 1.2 kg/m³ and a speed of 8 m/s, while the conditions after passing the blades show a reduced speed of 3 m/s and a density of 1.8 kg/m³. The formula for power extraction is P = 1/2 * p * A * v³, where A is the surface area of the turbine blades. Additionally, there is a request for assistance in calculating the surface area of wind turbine blades, with inquiries about relevant formulas or software tools. Understanding these calculations is crucial for optimizing wind turbine efficiency.
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Homework Statement


Air of density 1.2kgm-3, speed 8ms-1 is incident on blades of wind turbine. Radius of blades 1.5m. After passing blades, wind speed is reduced to 3.0ms-1 and density 1.8kgm-3. How much power is extracted from wind?

Homework Equations


P=1/2 pAv3

The Attempt at a Solution


P=1/2 x 1.2 x pi x 1.52x 83. But I don't know what to do with the information about the wind after passing blades.
 
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I've solved it - thank you for your time :)
 
How to calculate surface area of wind turbine blade

i want to calculate surface area of wind turbine blade,

can anyone help me out,any formula or software for it?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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