Page 160 - 48Fundamentals of Compressible Fluid Mechanics

122 CHAPTER 8. ISOTHERMAL FLOW
Meta End

The dimensionalization of the mass conservation equation yields

(8.15)

Differentiation of the isotropic (stagnation) relationship of the pressure (4.11) yields

where is the stagnation equa-
tions? put them in a table
put explanation how to derive
this expression.
(8.16)

"

%
Differentiation of equation (4.9) yields:

(8.17)

Notice that

in isothermal flow. There is no change in the actual
temperature of the flow but the stagnation temperature increases or decreases
depending on the Mach number (supersonic flow of subsonic flow). Substituting

for equation (??) yields:
(8.18)
%

Rearranging equation (8.18) yields %

(8.19)

%

Utilizing the momentum equation also requires to obtain a relation between

) yields

the pressure and density and recalling that in isothermal flow (
(8.20)

From the continuity conservation leads

(8.21)

The four equations momentum, continuity (mass), energy, state are de-

3
scribed above. There are 4 unknowns (

) and with these four equations
3 Assuming the upstream variables are known.