Page 186 - 48Fundamentals of Compressible Fluid Mechanics

148 CHAPTER 9. FANNO FLOW

*,+.-0/1
2 =?>A@CB
shock 3,4657 89 :<;
!#"$&%(''
)
atmosphere
conditions
d-c nozzle
Fig. 9.4: The schematic of Example 2

vessel. The vessel conditions are is at 29.65 [Bar], 400 K. With these conditions
a pipe inlet Mach number is 3.0. A normal shock wave occurs in the tube and the
flow discharges to the atmosphere, determine;

(a) the mass flow rate through the system;

(b) the temperature at the pipe exit; and
].

and H\QS .
(c) determine the Mach number that a normal shock wave occurs [N
Take k = 1.4, R = 287ED F
Q
Q
SOLUTION
(a) Assuming that the pressure vessel very much larger than the pipe therefore,
the velocity in the vessel can be assumed small enough so it can be neglected.
Thus, the stagnation conditions can be approximated as the condition in the
tank. It further assumed that the flow through the nozzle can be approximated

The mass flow rate through the system is constant and for simplicity reason
b
b
as isentropic. Hence, L H VUQUQ
and H K
point 1 is chosen in which, S3

NHG
The density and speed of sound are unknowns and needed to be computed.
H
With the isentropic relationship the Mach number at point one is known the
following can be found either from table or program 6

6 It should pay attention that in the program the variable whatInfo = infoStagnation ; and not whatInfo
= infoStandard ;