5
2nd YEAR FLUIDS / COMPRESSIBLE FLOW
3
m ( UOUT - UIN ) = r SF
r A C [ ( C - DU ) - C ] = P A - ( P + DP ) A
P = r C DU
USING CONTINUITY TO ELIMINATE U :
- AS ALSO SEEN IN SURFACE WAVES, STRONG WAVES (HIGH ) TRAVEL FASTER THAN WEAK WAVES.
- IN THE LIMIT OF 0 THE VELOCITY OF A WEAK WAVE BECOMES :
C2 = a2 = �P / �r (3.1)
- THE ABOVE EQUATION SUGGESTS THAT THE SPEED OF SOUND, a, DEPENDS ON THE RELATIONSHIP BETWEEN THE FLUID PRESSURE AND DENSITY.
- IN LIQUIDS, WHERE DENSITY CHANGES VERY LITTLE WITH PRESSURE, THE SPEED OF SOUND IS CONSIDERABLY HIGHER THAN IN GASES.
