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** Index**
##

The Properties in the Adiabatic Nozzle

When there is no external work and heat transfer,
the energy equation, reads

Differentiation of continuity equation,

, and dividing by the continuity
equation reads

The thermodynamic relationship between the properties
can be expressed as

For isentropic process

and
combining equations (

4.25) with
(

4.27) yields

Differentiation of the equation state (perfect gas),

, and dividing the results
by the equation of state (

) yields

Obtaining an expression for

*dU/U*
from the mass balance equation (

4.26)
and using it in equation (

4.28) reads

Rearranging equation (

4.30) so that the
density, dρ,
can be replaced by the static pressure,
dP/ρ yields

Recalling that

and substitute the speed of sound into
equation (

4.31) to obtain

Or in a dimensionless form

Equation (

4.33) is a differential
equation for the pressure as a function of the cross section area.
It is convenient to rearrange equation
(

4.33) to obtain a variables
separation form of

**Subsections**

** Next:** The pressure Mach number
** Up:** Isentropic Converging-Diverging Flow in
** Previous:** Isentropic Converging-Diverging Flow in
** Index**
Created by:Genick Bar-Meir, Ph.D.

On:
2007-11-21