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Re[2]: wave momentum



Philip Zell wrote:
=> Pressure, velocity, and temperature do change across a shock front. I think
=a > shock is, by definition, a discontinuity. The changes are described by a
=set of
=> "jump conditions" called the Rankine-Hugoniot equations. Each equation can
=be > expressed in terms of the adiabatic gas constant (gamma) and M1, the Mach
=number
=> for the gas behind the shock
=front. >
=> Pressure: P2 / P1 = 1 + [2*gamma*(M1^2 - 1) / (gamma +
1)] >
=> Density: rho2 / rho1 = [1 + ((gamma + 1)/(gamma - 1))*P2/P1] / [((gamma +
=1) /
=> (gamma - 1)) + P2/P1]
=>
=> Temperature: T2 / T1 = (P2 / P1)[((gamma + 1)/(gamma - 1)) + (P2/P1)] / [1
=+ > ((gamma + 1) / (gamma - 1))*P2/P1]
=>

In response to Zell, Jim McLean wrote

-This is one of the great things about this list: people with different
-knowledge bases and viewpoints all adding to the mix. I was actually
-thinking of astrophysical shockwaves when I wrote my note a few cycles
-back, but I had no idea about these quantities changing.

-Would it be correct to view a sonic boom as a shock wave with Mach
-number 1? For that special case, I get the above ratios all coming
-out to 1.

--
--James McLean
jmclean@chem.ucsd.edu
post doc
UC San Diego, Chemistry


The mach number of a projectile is defined as the ratio of the
projectile's speed to the speed of sound in the medium through which
the projectile moves. A supersonic aircraft can travel at more than
Mach 1. Because the shock wave generated by a supersonic aircraft
moves along with the aircraft, the shock wave must also move at
greater than Mach 1. So, a sonic boom can itself be supersonic with
Mach number greater than 1.


An object traveling at exactly Mach 1 also produces a shock wave,
according to the Physics text by Marion and Hornyak. This means that
there is still a discontinuity in pressure across the shock at M1 = 1.
I don't know how to reconcile this with Jim's application of the
Rankine Hugoniot equations at M1 = 1 to show that P1 = P2. Are any
fluids/aerodynamics jocks reading this?

Philip Zell