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866 ENGINEERING THERMODYNAMICS

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(ii) If for any flow system the Mach number is less than about 0.4, the effects of compressibility
may be neglected (for that flow system).

Example 16.3. Find the sonic velocity for the following fluids :

(i)Crude oil of specific gravity 0.8 and bulk modulus 1.5 GN/m^2 ;

(ii)Mercury having a bulk modulus of 27 GN/m^2.

Sol. Crude oil : Specific gravity = 0.8 (Delhi University)

∴ Density of oil, ρ = 0.8 × 1000 = 800 kg/m^3

Bulk modulus, K = 1.5 GN/m^2

Mercury : Bulk modulus, K = 27 GN/m^2

Density of mercury, ρ = 13.6 × 1000 = 13600 kg/m^3

Sonic velocity, Coil, CHg :

Sonic velocity is given by the relation :

C =

K

ρ [Eqn. (16.11)]

∴ Coil = 1.5 10

800

×^9

= 1369.3 m/s (Ans.)

CHg = 27 10

13600

×^9

= 1409 m/s (Ans.)

Example 16.4. An aeroplane is flying at a height of 14 km where temperature is – 45°C.
The speed of the plane is corresponding to M = 2. Find the speed of the plane if R = 287 J/kg K
and γ = 1.4.
Sol. Temperature (at a height of 14 km), t = – 45°C.
T = – 45 + 273 = 228 K
Mach number, M = 2
Gas constant, R = 287 J/kg K
γ = 1.4
Speed of the plane, V :
Sonic velocity, (C) is given by,
C = γRT (assuming the process to be adiabatic) ...[Eqn. (16.14)]
= 1.4××287 228 = 302.67 m/s

Also M =

V

C ...[Eqn. (16.15)]

or, 2 =
V
302 67.
or, V = 2 × 302.67 = 605.34 m/s =
605 34 3600
1000

. ×
= 2179.2 km/h (Ans.)

16.5. Propagation of Disturbance in Compressible Fluid

When some disturbance is created in a compressible fluid (elastic or pressure waves are also

generated), it is propagated in all directions with sonic velocity (= C) and its nature of propagation

depends upon the Mach number (M). Such disturbance may be created when an object moves in a

relatively stationary compressible fluid or when a compressible fluid flows past a stationary object.