TITLE.PM5

COMPRESSIBLE FLOW 897

dharm

\M-therm\Th16-2.pm5

C =

p RT

ρ= ... for isothermal process

C =

γ

ρ

p= γRT ... for adiabatic process.

7. Mach number, M =
   V
   C
   (i) Subsonic flow : M < 1, V < C... disturbance always moves ahead of the projectile
   (ii) Sonic flow : M = 1, V = C... disturbance moves along the projectile
   (iii) Supersonic flow : M > 1, V > C... The projectile always moves ahead of the disturbance.
   Mach angle is given by : sin α =
   C
   VM=

1

.

8. The pressure, temperature and density at a point where velocity is zero are called stagnation pressure (ps),
   temperature, (Ts) and stagnation density ρs. Their values are given as :

ps = po L 1 +FGH 2 −^1 IKJ 02 1

NM

O

QP

γ −

γ

M γ

ρs = ρo 1 1

2 0

2

1

+F −^1

HG

I

KJ

L

N

M

O

Q

P

γ M γ−

Ts = To 1

1

2 0

+F −^2

HG

I

KJ

L

N

M

O

Q

P

γ M

where p 0 , ρ 0 and To are the pressure, density and temperature at any point O in the flow.

9. Area-velocity relationship for compressible fluid is given as :
   dA
   A =

dV

V (M

(^2) – 1)
(i) Subsonic flow (M < 1) : dVV > 0 ; dA
A
< O ; dp < 0 (convergent nozzle)
dV
V
< 0 ; dA
A

0 ; dp > 0 (divergent diffuser)
(ii) Supersonic flow (M > 1) : dVV > 0 ; dA
A
0 ; dp < 0 (divergent nozzle)
dV
V
< 0 ; dA
A
< 0 ; dp > 0 (convergent diffuser)
(iii) Sonic flow (M = 1) : dA
A
= 0 (straight flow passage since dA must be zero)
dp = zerozero i.e. indeterminate, but when evaluated,
the change of pressure dp = 0, since dA = 0 and the flow is frictionless.

10. Flow of compressible fluid through a convergent nozzle :
    (i) Velocity through a nozzle or orifice fitted to a large tank :

V 2 =^2

1

(^11)
1
2
1
1
γ
γρ
γ
γ
−
F
HG
I
KJ
−F
HG
I
KJ
L
N
M
M
M
O
Q
P
P
P
−
pp
p