862 ENGINEERING THERMODYNAMICS

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\M-therm\Th16-1.pm5

γ

γρ

γ

γ

−

F

HG

I

KJ

−

F

HG

I

KJ

R

S

|

T

|

U

V

|

W

|

−

1

(^11)
1
2
1
1
pp
p =
VV 22 12
22
−
Substituting the values, we get
1.4
1.4− 1 × 122670
1 150
2
30
2
2
1
1
22
−
F
HG
I
KJ
R
S
|
T
|
U
V
|
W
|
=−
−
p
p
1.4
1.4
= 10800
Q
p (^1) RT
1
ρ = =×=^1 290 423 122670
F
HG
I
KJ
429345 1 2
1
0 2857
−
F
HG
I
KJ
R
S
|
T|
U
V
|
W|
p
p
.
= 10800
or
p
p
2
1
0 2857
F
HG
I
KJ
.
= 1 –
10800
429345 = 0.9748
or
p
p
2
1
= (0.9748)1/0.2857 = (0.9748)3.5 = 0.9145
or p 2 = 35 × 0.9145 = 32 kN/m^2 (Ans.)
Temperature, T 2 :
For an isentropic process, we have
T
T
2
1

p
p
2
1
(^111)
F 0 9145 (^1) 0 91450 2857 0 9748
HG
I
KJ

γ− −
γ
(. ) (. ).
.4
.4.
∴ T 2 = 423 × 0.9748 = 412.3 K
or t 2 = 412.3 – 273 = 139.3°C (Ans.)

16.3. Propagation of Disturbances in Fluid and Velocity of Sound

The solids as well as fluids consist of molecules. Whereas the molecules in solids are close
together, these are relatively apart in fluids. Consequently whenever there is a minor disturbance,
it travels instantaneously in case of solids ; but in case of fluid the molecules change its position
before the transmission or propagation of the disturbance. Thus the velocity of disturbance in case
of fluids will be less than the velocity of the disturbance in solids. In case of fluid, the propagation
of disturbance depends upon its elastic properties. The velocity of disturbance depends upon the
changes in pressure and density of the fluid.
The propagation of disturbance is similar to the propagation of sound through a media. The
speed of propagation of sound in a media is known as acoustic or sonic velocity and depends upon
the difference of pressure. In compressible flow, velocity of sound (sonic velocity) is of paramount
importance.

16.3.1. Derivation of sonic velocity (velocity of sound)

Consider a one-dimensional flow through long straight rigid pipe of uniform cross-sectional
area filled with a frictionless piston at one end as shown in Fig. 16.1. The tube is filled with a
compressible fluid initially at rest. If the piston is moved suddenly to the right with a velocity, a
pressure wave would be propagated through the fluid with the velocity of sound wave.