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Mechanics: Fluid

Fluid

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`Fluid Properties Compressibility Speed of Sound Mach Number`

Fluid Properties

Compressibility

Compressibility is used to described the easy of volume change for a fixed massed of fluid due to a pressure change. Bulk modulus is usually used to characterize the compressibility in an analogous manner to Young's modulus of elasticity for solids. For a given mass, the volume change of a fluid is inversely proportional to its density. And the bulk modulus is expressed as

and can be approximated by a differential change as

or

For ideal gas compression or expansion under constant temperature,i.e. isothermal process,

imply

And for the compression or expansion is reversible and adiabatic, i.e. frictionless and no heat exchange with surroundings under isentropic process,

where ;

imply

If the pressure changes are small, gases can be treated as incompressible fluid.

Speed of Sound

Speed of sound which describe the speed of pressure wave propagation in the fluid, is an important parameter in compressible flow. When a piston moves forward, the generated pressure wave will travel through the fluid at the speed of sound . When the piston moves a constant incremental velocity , there will have a small increase in local pressure at the wave front and a small difference in the fluid states across the wave front. Considering a moving control volume that encloses the wave front,  fluid will move toward the wave front into the control volume at a relative speed of and fluid will also move away from the wave front and leave the control volume at a relative speed of

From the conservation of mass,

From the steady flow energy balance equation, by neglecting potential energy change and there is no heat or work crosses the boundaries,

Imply

The small disturbance can also be assumed as an isentropic process, imply

Therefore or

and it can be expressed as
or

and the seed of sound is a function of temperature only.

Mach Number

Mach number, Ma, is defined as the ratio of the fluid flow speed to the speed of sound in the same fluid at the same state, i.e. and is another important parameter in compressible flow.

ID: 100100008 Last Updated: 3/2/2010 Revision: 0

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