Page 203 - 48Fundamentals of Compressible Fluid Mechanics

9.7. WORKING CONDITIONS 165

1

Fig. 9.17: The maximum entrance Mach number, % to the tube as a function of super-
sonic branch
is reduces after the
maximum length is excessed. b
As the figure ?? shows the entrance Mach number, N
Example 9.3:
V . b H! and for WYXaZ [ HOQS "
Calculate the shock location for entrance Mach number N
assume that F HIUS
SOLUTION
for F H I
S V is
for this entrance
The solution is obtained by iterative process. The maximum WYX(Z$#%'& [
thus the extra tube,
exceed the the maximum length W`XaZ [
0.821508116. Hence, WYX(Z [
, At the left side is when the shock occurs at
b
is W`XaZ [
Mach number. The maximum for N
H QS*),+-
H(
"=Q
). Hence, the value of left
QS*),+-
"=Q H Q0S I I.
H Q0S "
. The right side is when the shock is at the entrance at which the
A : W`XaZ [H<
E
(flow chocked and no any additional WYX(Z [
WYXaZ [
H Q0S/)0+1
"
Q
is 9 S/90+9 6 6 ) VS/9 7 7 Q^S Q
Q- =V 1 7 8 7 8
Q0S I I.
extra WYXaZ [
and N32
is calculated for N
side isE
O

4
4
5
5
Q0S -" "1"
I ^S V
^S Q
Q
Q

b
With N

4

]
5
7 8
6
7
5
]
7;:
7 8 :
6<:
:
:
"^S V
V "
" S -91"
Q^S 1" "0"
" S/)V-+
QS V " -"
I
S I.+=V
IUS +0I-V
" Now the solution is some-
where between the negative of left side to the positive of the right side. 20
The extra A : WYXaZ [ < is "^S V
V "
QS_I I.
H "^S IaQ
The solution of the above utilizing results in the following table
E

4
4
4
4

L
L
Q^S 9)Q=)
Q^S +=V-
Q^S "1"
IUS QUQ
Q
I
S +)^I
^S Q
Q
Q
20 What if the right side is also negative? The flow is choked and shock must occur in the nozzle
L
L
before entering the tube. or in very long tube the whole flow will be subsonic.