Page 60 - Mechanical Engineers' Handbook (Volume 4)

3 Fluid Statics 49

Figure 3 Barometer. Figure 4 Open manometer.

3.3 Aerostatics
The U.S. standard atmosphere is considered to be dry air and to be a perfect gas. It is defined
in terms of the temperature variation with altitude (Fig. 8), and consists of isothermal regions
and polytropic regions in which the polytropic exponent n depends on the lapse rate (tem-
perature gradient).
Conditions at an upper altitude z and at a lower one z in an isothermal atmosphere
1
2
are obtained by integrating the expression dp gdz to get
p 2 g(z z )
2
1
exp
p 1 RT
In a polytropic atmosphere where p/p ( / ) ,
n
1
1
p 2 n 1 z z 1 n /(n 1)
2
1 g
p 1 n RT 1
from which the lapse rate is (T T )/(z z ) g(n 1)/nR and thus n is obtained
1
1
2
2
from 1/n 1 (R/g)(dt/dz). Defining properties of the U.S. standard atmosphere are listed
in Table 2.

Figure 5 Differential manometer. Figure 6 Flat inclined surface submerged in a
liquid.