Page 189 - Fluid Mechanics and Thermodynamics of Turbomachinery

170 Fluid Mechanics, Thermodynamics of Turbomachinery

FIG. 6.1. Radial equilibrium flow through a rotor blade row.

FIG. 6.2. A fluid element in radial equilibrium (c r D 0).

Writing dm D rd dr and ignoring terms of the second order of smallness the
above equation reduces to,
1 dp c 2
D . (6.1)
dr r
If the swirl velocity c and density are known functions of radius, the radial pressure
variation along the blade length can be determined,
tip dr
Z
p root D c 2 . (6.2a)
p tip

root r
For an incompressible fluid
tip dr
Z
p tip p root D c 2 . (6.2b)
root r
The stagnation enthalpy is written (with c r D 0)
1
2
2
h 0 D h C .c C c / (6.3)
2 x
therefore,
dh 0 dh dc x dc
D C c x C c . (6.4)
dr dr dr dr