Question

Two sites are being considered for wind power generation. On the first site, the wind blows steadily at 7 m/s for 3000 hours per year. On the second site, the wind blows steadily at 10 m/s for 2000 hours per year. The density of air on the both sites is 1.25 kg/m3 . Assuming the wind power generation is negligible during other times.Calculate the maximum power of wind on each site per unit area, in kW/m2 .

Answer 1

Given :

`$V_1 = 7 \ m/s$`

Operation time,
`$T_1$` = 3000 hours per year

`$V_2 = 10 \ m/s$`

Operation time,
`$T_2$` = 2000 hours per year

The density, ρ =
`$1.25 \ kg/m^3$`

The wind blows steadily. So, the K.E. =
`$(0.5 \dot{m} V^2)$`

`$= \dot{m} * 0.5 V^2$`

The power generation is the time rate of the kinetic energy which can be calculated as follows:

Power =
`$\Delta \ \dot{K.E.} = \dot{m} (V^2)/(2)$`

Regarding that
`$\dot m \propto V$`. Then,

Power
`$ \propto V^3$` → Power = constant x
`$V^3$`

Since,
`$\rho_a$` is constant for both the sites and the area is the same as same winf turbine is used.

For the first site,

Power,
`$P_1= \text{const.} * V_1^3$`

`$P_1 = \text{const.} * 343 \ W$`

For the second site,

Power,
`$P_2 = \text{const.} * V_2^3 \ W$`

`$P_2 = \text{const.} * 1000 \ W$`