This page is intended for college, or high school students.
For younger students, a simpler explanation of the information on this page is
available on the
As an object moves through a gas, the gas molecules are deflected
around the object. If the speed of the object is much less than the
speed of sound
of the gas, the density of the gas remains constant and the flow of
gas can be described by conserving
speed of the object approaches the speed of sound, we
on the gas. The density of the gas varies locally as the gas is
compressed by the object.
For compressible flows with little or small
flow turning, the flow process is reversible and the
The change in flow properties are then given by the
(isentropic means "constant entropy").
But when an object moves faster than the speed of sound,
and there is an abrupt decrease in the flow area,
are generated in the flow.
Shock waves are very small regions in the gas where the
change by a large amount.
Across a shock wave, the static
increases almost instantaneously.
The changes in the flow
properties are irreversible and the
of the entire system increases.
Because a shock wave does no work, and there is no heat addition, the
and the total temperature are constant.
But because the flow is non-isentropic, the
total pressure downstream of the shock is always less than the total pressure
upstream of the shock. There is a loss of total pressure associated with
a shock wave as shown on the slide.
Because total pressure changes across the shock,
we can not use the usual (incompressible) form of
across the shock. The
and speed of the flow also decrease across a shock wave.
If the shock wave is perpendicular to the flow direction, it is called a
normal shock. There are equations which describe
the change in the flow variables. The equations are derived from the
Depending on the shape of the object and the speed of the flow, the shock wave may
be inclined to the flow direction. When a
shock wave is inclined to the flow direction it is called an oblique
shock. On this slide we have listed the equations which describe the change
in flow variables for flow across an oblique shock.
The equations presented here were derived by considering the conservation of
mass, momentum, and energy
for a compressible gas while ignoring viscous effects.
The equations have been further specialized for a two-dimensional flow
without heat addition. The equations only apply for
those combinations of free stream Mach number and deflection angle for which
an oblique shock occurs. If the deflection is too high, or the Mach too low,
a normal shock occurs.
For the Mach number change across an oblique shock there are
two possible solutions; one supersonic and one subsonic. In nature, the
supersonic ("weak shock") solution occurs most often. However, under some
conditions the "strong shock", subsonic solution is possible.
Oblique shocks are generated by the nose and by the
leading edge of the wing and tail of a supersonic aircraft.
Oblique shocks are also generated at the trailing edges of the aircraft as
the flow is brought back to free stream conditions.
Oblique shocks also occur downstream of a
if the expanded pressure is different from free stream conditions.
In high speed
oblique shocks are used to compress the air going into the engine. The air
pressure is increased without using any rotating machinery.
On the slide, a supersonic flow at Mach number M
approaches a shock wave which is
inclined at angle s. The flow is deflected through the shock by an amount
specified as the deflection angle - a. The deflection angle is determined by
resolving the incoming flow velocity into components parallel and
perpendicular to the shock wave.
The component parallel to the shock is assumed to remain constant across the shock,
the component perpendicular is assumed to decrease by the normal shock relations.
Combining the components downstream of the shock determines the delflection angle.
The right hand side of all these equations depend only on the free stream
Mach number and the shock angle. The shock angle depends in a complex way on
the free stream Mach number and the wedge angle. So knowing the Mach number
and the wedge angle, we can determine all the conditions associated with
the oblique shock.
The equations describing oblique shocks
were published in NACA report
Here's a Java program based on the oblique shock equations.
You can use this simulator to study the flow past a wedge.
Input to the program can be made
using the sliders, or input boxes at the upper right. To
change the value of an input variable, simply move the slider. Or
click on the input box, select and replace the old value, and
hit Enter to send the new value to the program.
Output from the program is displayed
in output boxes at the lower right. The flow variables are presented as ratios
to free stream values. The graphic at the left shows the wedge (in red)
and the shock wave generated by the wedge as a line. The line is colored
blue for an oblique shock and magenta when the shock is a normal shock. The black
lines show the streamlines of the flow past the wedge. Notice that downstream
(to the right) of the shock wave, the lines are closer together than upstream.
This indicates an increase in the density of the flow.
There is more complete
program that is avaliable at this web site. The program solves for flow past a
wedge and for flow past a
normal shock conditions.
Another simulation, called
describes the intersection and reflection of multiple shock waves.
You can also download your own copy of the program to run off-line by clicking on this button: