Theory of Compressible FlowsM.S. Mechanical & Process
Engineering4th Semester
IntroductionGAS DYNAMICSIt is the branch of fluid mechanics
concerned with causes and effects arising from the motion of
compressible fluids particularly gases.Fluid MechanicsStaticsFluid
DynamicsAerodynamicsHydrodynamicsGas DynamicsIn this subject we are
concerned with following fundamental physical lawsLaw of
conservation of massNewtons second law of motionFirst law of
thermodynamicsSecond law of thermodynamicsAbove laws are applicable
to all fluids and all flow processesAbove laws are applied to a
fluid utilizing the continuum concept
ContinuumDue to elastic collisions limits of velocity are
between zero and very high velocity Continuum concept may not be
applicable for a gas at low pressure (High altitudes)Distance b/w
two consecutive collisions is mean free pathMean free path is
inversely related to molecular diameterAll materials, solid or
fluid, are composed of molecules discretely spread and in
continuous motion. However, in dealing with fluid-flow relations on
a mathematical basis, it is necessary to replace the actual
molecular structure by a hypothetical continuous medium, called the
continuumContinuum postulate assumes that every differential
element of body of fluid contains a large number of molecules such
that the average statistical properties of molecules in the
differential volume represent macroscopic properties of fluid in
region of that differential volume.
Continuum, contd.For continuum postulate to hold, mean free path
() 0.01 gas is a combination of discrete particles
CompressibilityAmount by which a substance can be compressed is
given by a property compressibilityCompressibility is fractional
change in volume per unit change in pressureIsothermal
CompressibilityRise in temp is controlled by some heat transfer
mechanismIsentropic CompressibilityCompressibility in the form of
densityLiquid d is smallGas d Is small for low speed flowIs large
for high speed flowAnother index
whereCollisions between the fluid molecules causes the
propagation of sound wavesPropagation of sound waves is affected by
molecular density of the mediumWhere molecular density is low,
dissipation of energy occurs without colliding with any molecule
(free particle flow)It is an important quantity in gas dynamicsWe
shall study further details about speed of sound in Chapter 3For
Ideal GasThe Acoustic SpeedThe speed at which a sound wave or small
pressure disturbance is propagated in the fluid medium
It is the ratio of local fluid speed V to its acoustic speed
Mach Number
