Compressible Flow
 

Speed of sound in a medium

 Speed at which ‘infinitesimal disturbances are propagated into an undisturbed medium.
 

Mach cones and "zones of silence"

 In a flow where the velocity is < a (i.e. subsonic flow), disturbances are felt everywhere. When u > a (i.e. supersonic flow), disturbances cannot propagate upstream.

 m is the "Mach Angle"

Bigger disturbances propagate faster (e.g. shocks). This can be seen by considering the dependence of ‘a’ on local properties.

 a = Ö (g RT), If T is substantially higher downstream of the disturbance, ‘a’ downstream is > ‘a’ upstream.

 Also,

constant entropy
 
 

Isentropic Flow Relations

, where 

, where in S.I. units for air
 
 

, specific heat at constant pressure

, specific heat at constant volume

enthalpy
 
 

Quasi-1-dimensional flow

and if M < 1 (subsonic)

dA > 0 Þ du < 0 (compression)

dA < 0 Þ du > 0 (expansion)
 

Velocity-Area Relation

Thus, if M>1,

choked throat: M=1

 or, 
 
 

Normal Shocks

These changes in properties can be calculated using the normal shock relations.
 

Normal shock relations:

 Oblique shocks

All the above hold true for the normal component of velocity. In addition, the tangential component of velocity remains unchanged across the oblique shock.

Limits on b for an oblique shock

Prandtl-Meyer Expansion

Isentropic;

T₀, P₀ constant

At any point, where the Mach # is M,
 

q ₂-q₁ = w (M₁) - w (M₂)

w is tabulated as the Prandtl-Meyer function