Page 34 - Fluid Mechanics and Thermodynamics of Turbomachinery

Introduction: Dimensional Analysis: Similitude 15
up to 9.0 were readily obtained and, it was claimed, even better values might be
possible, but at the cost of reduced head and efficiency. It is likely that supercavi-
tating pumps will be increasingly used in the search for higher speeds, smaller sizes
and lower costs.

Compressible gas flow relations

Stagnation properties
In turbomachines handling compressible fluids, large changes in flow velocity
occur across the stages as a result of pressure changes caused by the expansion or
compression processes. For any point in the flow it is convenient to combine the
1 2
energy terms together. The enthalpy, h, and the kinetic energy, c are combined
2
and the result is called the stagnation enthalpy,
1 2
h 0 D h C c .
2
The stagnation enthalpy is constant in a flow process that does not involve
a work transfer or a heat transfer even though irreversible processes may be
present. In Figure 1.8, point 1 represents the actual or static state of a fluid in
an enthalpy entropy diagram with enthalpy, h 1 at pressure p 1 and entropy s 1 . The
fluid velocity is c 1 . The stagnation state is represented by the point 01 brought
about by an irreversible deceleration. For a reversible deceleration the stagnation
point would be at point 01s and the state change would be called isentropic.

P 01s
h P 01
01s
01

P 1

1

s
FIG. 1.8. The static state (point 1), the stagnation (point 01) and the isentropic stagna-
tion (point 01s) of a fluid.