Page 154 - 48Fundamentals of Compressible Fluid Mechanics

116 CHAPTER 7. NOZZLE FLOW WITH EXTERNAL FORCES
7.1 Isentropic Nozzle ( )
put cv. figure
The energy equation for isentropic nozzle provides

external
work or
potential
difference,

(7.1)

i.e.
leads to

#

Utilizing equation (4.27) when
(7.2)

at any point of the flow. The equation (7.2) becomes when the %
# %
For the isentropic process

(7.3)

%

%

The continuity equation as developed earlier (mass conservation equation
isn’t effected by the gravity)
(7.4)

to the right

yields

Substituting
from equation (7.4), into equation (7.2) moving
hand side, and diving by

(7.5)

Rearranging equation (7.5) yields

(7.6)

And further rearranging yields

(7.7)