Page 158 - 48Fundamentals of Compressible Fluid Mechanics

120 CHAPTER 8. ISOTHERMAL FLOW

flow "$#
direction

c.v. !
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Fig. 8.1: Control volume for isothermal flow

The momentum equation written as following

(8.2)
wetted area

where is the cross section area (it doesn’t have to be a perfect circle a close

('*)

Perhaps more quantitative enough shape is sufficient.). The shear stress is the force per area that acts on
discussion about how “circu-
lar” the shape should be. is the area that shear stress
acts on. The second of thermodynamics reads
the fluid by the tube wall on the fluid. The
(8.3)
)

The mass conservation is reduced to
(8.4)

Again it is assumed that the gas is a perfect gas and therefore, equation of
state expressed as following:
(8.5)

8.2 Dimensionless Representation
In this section the equations are transformed into the dimensionless form and pre-
sented in a dimensionless form. First it must be recalled that the temperature is
it seems obvious to write this constant and therefor, equation of state reads
equation perhaps to consult
with others.