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####

Piston Velocity

When a piston is moving, it creates a shock that moves at a speed
greater than that of the piston itself.
The unknown data are the piston velocity, the temperature, and,
other conditions ahead of the shock.
Therefore, no Mach number is given but pieces of information
on both sides of the shock.
In this case, the calculations for

*U*_{s}
can be obtained from
equation (

5.24) that relate the
shock velocities and Shock Mach number as

Equation (

5.64) is a quadratic equation for

*M*_{sx}.
There are three solutions of which the first one is

*M*_{sx}=0
and this is immediately disregarded.
The other two solutions are

The negative sign provides a negative value which is
disregarded, and the only solution left is

or in a dimensionless form

Where the ``strange'' Mach number is

*M*_{sx}′ =
U_{x}′ /C_{x}.
The limit of the equation when

*c*_{x}⇒ ∞
leads to

As one additional ``strange'' it can be seen that the shock is close
to the piston when the gas ahead of the piston is very hot.
This phenomenon occurs in many industrial applications,
such as the internal combustion engines and die casting.
Some use equation (5.68) to explain
the next Shock-Choke phenomenon.

** Next:** Shock-Choke Phenomenon
** Up:** General Velocities Issues
** Previous:** General Velocities Issues
** Index**
Created by:Genick Bar-Meir, Ph.D.

On:
2007-11-21