Page 165 - 48Fundamentals of Compressible Fluid Mechanics

8.4. COMPARISON WITH INCOMPRESSIBLE FLOW 127

and remember that

now we have to expend into series around
(8.44)

and for example the first derivative of

(8.45)

similarly it can be shown that
equation (8.43) now can be

approximated as
#

(8.46)

rearranging equation (8.46) yield

(8.47)

and further rearrangement yield

(8.48)

in cases that is small when chi is small provide dis-
cussion
(8.49)

The pressure difference can be plotted as a function of the
for given value

. Equation (8.49) can be solved explicitly to produce a solution for

of
(8.50)

A few observations can be made about equation (8.50) The larger value of

the solution is not physically possible because
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