Page 60 - Fluid Power Engineering

38 Chapter Three

3
Density expressed in kg/m is
p M
ρ = (3-15)
RT 1000
where M is the molecular weight of dry air in grams = 28.9644 g/mole
and R expressed in moles is 8.31432 J/(mol K)
In the troposphere (elevation up to 11 km from sea level), the
variations in temperature are described by:

T = T 0 − Lh (3-16)

where T 0 = 288.15 K and L, the temperature lapse rate is 6.5 K/km,
and h is the elevation from sea level in kilometers.
gM
Lh RL

p = p 0 1 − (3-17)
T 0
2
where p 0 is 101,325 Pa, g is gravitational constant, 9.80665 m/s .
gM

Lh RL 1 M
ρ = p 0 1 − (3-18)
T 0 R (T 0 − Lh) 1000
Table 3-6 contains values of density using Eq. (3-18). Density is lower
by 2% at 200 m and 17.8% lower at 2000 m. Since power is directly

Height, m Density, kg/m 3
0 1.224999
5 1.224411
10 1.223824
50 1.21913
100 1.213282
150 1.207456
200 1.201651
250 1.195867
500 1.167268
1000 1.111642
1500 1.058067
2000 1.00649
TABLE 3-6 Density of Air as Function of Elevation for Dry Air