Page 164 - 48Fundamentals of Compressible Fluid Mechanics

126 CHAPTER 8. ISOTHERMAL FLOW
8.4 Comparison with Incompressible Flow

Meta
he Mach number of the flow in some instances is relatively small. In these
cases, one should expect that the isothermal flow to have similar characters
as the flow of incompressible flow. For incompressible flow, the pressure loss
is expressed as follows

(8.37)

represent the

ratio of the traditional . To obtain similar expression for the isothermal

and
and pressures has to be derived. From

Now note that for incompressible flow
equation (8.37) one can obtained that
flow, a relation between
and
(8.38)

Substituting this expression into (8.38) yield

(8.39)

"

discuss why the pressure ra- Because is always positive there is only one solution to above equation
tio must be greater then kM2
even though M2. In case the no solution and in case only one solution to M2.
Expending the solution for small pressure ratio drop, , by some
mathematics.
denote
(8.40)

Now equation (8.39) can be transformed into

(8.41)

" "
(8.42)

(8.43)