Power Plant Engineering

NON-CONVENTIONAL ENERGY RESOURCES AND UTILISATION 117

Axial thrust (Fx) in newtons Fx max = (π/9) ρD^2 Vi^2 = π/9 (1.226 × 120^2 × 10^2 )

= 616,255 N.

Example 12. A 10 m/s wind is at 1 standard atmosphere and 15°C. Calculate:

1. The total power density in the wind stream.


2. The maximum obtainable power density.


3. A reasonably obtainable power density.


4. Total power produced if the turbine diameter is 120 m.
   Solution. The air density,

ρ =

P

RT

= (1.01325 × 10^5 )/[287 (15 + 273)] = 1.226 kg/m^3.

1. Total power density

ρtotal

A

=

3

2

ρVi

= 1.226 × (10)^3 /2 = 613 W/m^3

2. Maximum power density

max

A

ρ

=

8

27

ρVi^3

= (8/27) × 1.226 × (10)^3 = 363 W/m^3.

3. Assuming ηηηηη = 40%
   Actual power density,

P

A

= 0.4 wt

P

A







= 0.4 × 613 = 245 W/m^3.

4. Total power produced,

P =

P

A







2

4

πD

= 0.245 × π(120)^2 /4 = 2770 kW.
Example 13. A 10 metre diameter rotor has 30 blades, each 0.25 metre wide. Calculate its
solidity.

Solution. Solidity = [(No. of blade × width)/(π × dia of rotor)] × 100 in %

Given that

Number of blade = 30

Width = 0.25 m

Diameter of rotor = 10 m