Page 59 - Fluid Power Engineering

Properties of W ind 37

9
8 7
Wind speed in m/s 6 5 4 3 Shear=0.15

1 2 Shear=0.25
0
0 10 20 30 40 50 60
Height above ground level in meters

FIGURE 3-8 Plot of wind speed as a function of height with wind speed =
10 m/s at 200-m elevation.

roughness conditions on the surface (see Fig. 3-8). A location with
high roughness will have lower wind speed at 10 m because of higher
friction compared to a location with lower roughness. However, if
the higher roughness location has the same wind speed as the lower
roughness location at 10-m elevation, then the higher roughness loca-
tion (b) must have higher wind speed at higher elevations compared
to location (a).

Density of Air as a Function of Elevation
3
The other parameter that influences power is air density, P = ρ Av /2.
The relationship between P and ρ is linear. If ρ, the air density is lower
by 10%, then the power will be lower by 10%. Air density depends on
pressure, temperature, and relative humidity. As elevation increases,
both pressure and temperature decrease. To derive the relationship,
begin with the ideal gas law:

pV = nRT (3-13)

3
where p is pressure in Pascals, V is volume in m , n = number of
moles, R is the gas constant which is 287.05 J/(kg · K), and T is the
◦
temperature in Kelvin (K = C + 273.15).
n
Density = , number of moles per unit volume.
V
p
ρ = (3-14)
RT