The blades of a windmill sweep out a circle of area A. (a) If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it in time t?(b) What is the kinetic energy of the air? (c) Assume that the windmill converts 25% of the wind’s energy into electrical energy, and that A = 30 m2, v = 36 km/h and the density of air is 1.2 kg m–3. What is the electrical power produced?
Answers
Explanation:
Area of the circle swept by the windmill = A
Velocity of the wind = v
Density of air = ρ
(a) Volume of the wind flowing through the windmill per sec = Av
Mass of the wind flowing through the windmill per sec = ρAv
Mass m, of the wind flowing through the windmill in time t = ρAvt
(b) Kinetic energy of air = (1/2) mv2
= (1/2) (ρAvt)v2 = (1/2)ρAv3t
(c) Area of the circle swept by the windmill = A = 30 m2
Velocity of the wind = v = 36 km/h
Density of air, ρ = 1.2 kg m–3
Electric energy produced = 25% of the wind energy
= (25/100) × Kinetic energy of air
= (1/8) ρ A v3t
Electrical power = Electrical energy / Time
= (1/8) ρ A v3t / t
= (1/8) ρ A v3
= (1/8) × 1.2 × 30 × (10)3
= 4.5 kW
Answer:
Explanation:
the blades of windmill sweep out a circle of area A . and wind flows at a velocity v perpendicular to circle .
(a) hence, volume of air passing through the windmill per second = Av
so, volume of air passing through in time t = Av × t
then, mass = density × volume
= P × Av × t
mass of air = PAvt
(b) kinetic energy of air = 1/mv²
= 1/2( PAvt)v²
= PAv³t/2
(c) electric energy produced = 25% of Kinetic energy { wind's energy }
= 1/4 × (PAv³t)/2
= (PAv³t)/8
so, Electric power produced = electric energy produced /time taken for producing
= (PAv³t)/8t
= (PAv³)/8
hence, Electric power = (PAv³)/8
here,
P = 1.2 kg/m³
A = 30 m²
v = 36 km/h = 36×5/18 = 10m/s
Electric power = 1.2 × 30× 10³/8
= 4500 watt