## Compressible Fluid Mechanics - Glossary (Under Construction)

## Compressibility starts to become significant for Mach Numbers greater than 0.3 - all supersonic flows are compressible

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Adiabatic Processes## A perfect gas where c

Calorifically Perfect Gas_{v}and c_{p}are constants.## The compressibility, tau, is given by

Compressibility

link effect on speed of sound

Energy Equation

Enthalpywhere e isinternal energy, p is pressure and v is the volume per unit mass, i.e. the reciprocal of density.For a perfect gas, enthalpy is a function of temperature only

h = h(T) For a calorically perfect gas, this becomesh = c where_{p}Tc_{p}is the specific heat at constant pressureThe

total enthalpyfor a steady, adiabatic, inviscid flow is given at any point by in other words, the total enthalpy is the sum of the static enthalpy and the kinetic energy at that particular point.The total enthalpy is constant along a streamline.

If all the streamlines of a flow originate from a common uniform freestream, then the total enthalpy is the same for each streamline. Consequently, for a steady, adiabatic flow, the total enthalpy is constant throughout the entire flow.

From

we can see that under these same conditions, the total temperature will also be constant throughout the flow.

## Isentropic Mach Number The Mach number is a measure of the directed motion of the gas compared with the random thermal motion of the molecules. Mach Wave Shock Wave A shock wave will only occur in supersonic flows - it is an extremely thin region, in practise, about 10 - 5 cm across which flow proplerties can change enormously. In practise, it usual mathematically to model shocks as a line discontinuity. In general these properties will increase across a shockwa wave pressure density temperature entropy whereas as the following properties will go down velocity The flow in front of the shock waave will always be supersonic. Behind a normal shock the flow will always be subsonic, although with an oblique shock wave, the flow can be iether subsonic or supersonic. Shock Wave (Normal) Shock Wave (Oblique) Second Law of Thermodynamics Speed of Sound related to speed of molecular movement. two a pressure and density are related via the perfect gas equation of state. i.e. funtion of temperature only lower compressibility higher speed of sound

Entropy## is equivalent to the Principle of Conservation of Energy.

First Law of ThermodynamicsThe heat added and work done on a system will raise the temperature

For a reversible process

which produces ## For a perfect gas , the internal energy is a function of temperature only.

Internal Energy

e = e(T) For a calorically perfect gas, this becomese = c where_{v}Tc_{v}is the specific heat at constant volume## An isentropic process is both adiabatic and reversible.

IsentropicIsentropic relations can be summarized as

## The Mach number is a measure of the directed motion of the gas compared with the random thermal motion of the molecules.

Mach NumberIt is given by

where u is the flow velocity and a is the speed of sound

Mach Wave## A shock wave will only occur in supersonic flows - it is an extremely thin region, in practise, about 10

Shock Wave^{- 5}cm. across which flow proplerties can change enormously. In practise, it usual mathematically to model shocks as a line discontinuity. In general these properties will increase across a shock wavewhereas as the following properties will go down

- pressure
- density
- temperature
- entropy
The flow in front of the shock wave will always be supersonic. Behind a normal shock the flow will always be subsonic, although with an oblique shock wave, the flow can be iether subsonic or supersonic.

- velocity

Shock Wave (Normal)

Shock Wave (Oblique)## Inviscid, frictionless

Reversible Processes

Second Law of Thermodynamics## Staring off from

Specific Heat at constant pressure

c _{p}- c_{v}= Rwe can show that

## Staring off from

Specific Heat at constant volume

c _{p}- c_{v}= Rwe can show that

## The speed of sound increases proportionally to the absolute temperature.

Speed of Sound

where c is speed of sound, k is a constant and T is absolute temperature

Since temperature varies within the troposphere, the speed of sound will vary with altitude also. At sea level it is 1224 km/hr and at 9100 meters altitude it is 1090,8 km/hr. The Earth's troposphere ends near 11000 meters, and since the temperature in the stratosphere is fairly constant, the speed of sound is also approximately a constant - 1060 km/hr.

related to speed of molecular movement. two a pressure and density are related via the perfect gas equation of state. i.e. funtion of temperature only lower compressibility higher speed of sound