Question

Fig. 4.1 shows a small wind-turbine used to generate electricity.
Fig.4.1 The wind-turbine drives an electric generator.
The wind blows with a velocity of 7.0m/s at right angles to the plane of the turbine. The mass of air passing per second through the turbine is 6.7kg.
(a) (I) Calculate the kinetic energy of the air blown through the turbine por second. kinetic energy
- (II) Only 8% of this energy is converted to electrical energy. Calculate the power output of the electric generator. ​

Answer 1

Answer:

The kinetic energy of the air blown through the turbine per second is

166.15J/s.

The power output of the electric generator is 13.292W.

Explanation:

(I) To calculate the kinetic energy of the air blown through the turbine per second, we can use the formula for kinetic energy:

KE= 1/2mv²

where:

KE is the kinetic energy,

m is the mass of air passing per second through the turbine,

v is the velocity of the air.

Given:

m=6.7kg/s (mass of air passing per second),

v=7.0m/s (velocity of the air).

Substituting the given values into the formula:

KE= 1/2×6.7×(7.0)²

KE= 1/2×6.7×49

KE=166.15J/s

(II) Since only 8% of this kinetic energy is converted to electrical energy, the power output of the electric generator can be calculated using the formula:

Power=Energy conversion efficiency×Kinetic energy

Given:

Energy conversion efficiency =0.08 (8%),

Kinetic energy =166.15J/s.

Substituting the given values into the formula:

Power=0.08×166.15

Power=13.292W