Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

18 Fluid Mechanics, Thermodynamics of Turbomachinery
FIG. 1.9. The ideal adiabatic change in stagnation conditions across a turbomachine.
is obtained. Hence Dh0s = CpT01[(p02/p01) (g-1)/g - 1]. Since Cp = g R/(g - 1) and a 2 01 = g RT01,
then
The flow coefficient can now be more conveniently expressed as
As m . ∫ r01D 2 (ND), the power coefficient may be written
Collecting together all these newly formed non-dimensional groups and inserting them
in eqn. (1.14b) gives
(1.15)
The justification for dropping g from a number of these groups is simply that it
already appears separately as an independent variable.
For a machine of a specific size and handling a single gas it has become customary,
in industry at least, to delete g, R, and D from eqn. (1.15) and similar expressions. If,
in addition, the machine operates at high Reynolds numbers (or over a small speed
range), Re can also be dropped. Under these conditions eqn. (1.15) becomes
(1.16)
Note that by omitting the diameter D and gas constant R, the independent variables in
eqn. (1.16) are no longer dimensionless.
p
p