Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

efficiently converting this energy into pressure energy can be appreciated. The conversion
of the kinetic energy to pressure energy is considered in the following section on
diffusers.
The fraction of the kinetic energy at impeller exit to the specific work input is
where
Define the total-to-total efficiency of the impeller as
where pr is the total-to-total pressure ratio across the impeller, then
Substituting eqns. (7.30), (7.31) and (7.32) into eqn. (7.30) we get
(7.30)
(7.31)
(7.32)
(7.33)
(7.34)
Exercise. Determine rE assuming that b¢ 2 = 0, s = 0.9, h I = 0.8, p r = 4 and g = 1.4.
N.B. It is very convenient to assume that Figures 7.13 and 7.14 can be used to derive
the values of the Mach numbers Mu and M2. From Figure 7.13 we get Mu = 1.3 and
from Figure 7.14, M2 = 1.117. Substituting values into eqn. (7.34),
1 Ê 1. 117ˆ
rE =
2¥ 0. 9Ë
13 . ¯
2
Centrifugal Pumps, Fans and Compressors 235
È 1
+ ( - )
˘
1 4 1
ÎÍ 08 ˚˙
=
1+ ¥
1
135 .
.
0. 5276
2 1. 117
5
Calculations of r E at other pressure ratios and sweepback angles show that its value
remains about 0.52 provided that s and h1 do not change.
EXAMPLE 7.4. Air at a stagnation temperature of 22°C enters the impeller of a centrifugal
compressor in the axial direction. The rotor, which has 17 radial vanes, rotates