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Feedback    Next: The pressure Mach number Up: Isentropic Converging-Diverging Flow in Previous: Isentropic Converging-Diverging Flow in   Index

## The Properties in the Adiabatic Nozzle

When there is no external work and heat transfer, the energy equation, reads (4.25)

Differentiation of continuity equation, , and dividing by the continuity equation reads (4.26)

The thermodynamic relationship between the properties can be expressed as (4.27)

For isentropic process and combining equations (4.25) with (4.27) yields (4.28)

Differentiation of the equation state (perfect gas), , and dividing the results by the equation of state ( ) yields (4.29)

Obtaining an expression for dU/U from the mass balance equation (4.26) and using it in equation (4.28) reads (4.30)

Rearranging equation (4.30) so that the density, dρ, can be replaced by the static pressure, dP/ρ yields (4.31)

Recalling that and substitute the speed of sound into equation (4.31) to obtain (4.32)

Or in a dimensionless form (4.33)

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 (4.34)

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