Page 45 - 48Fundamentals of Compressible Fluid Mechanics

1.3. HISTORICAL BACKGROUND 7
19
conditions to a more general form .
Here, the second law has been around for over 40 years and yet the
significance of it was not was well established. Thus, it took over 50 years for
20
Prandtl to arrive at and to demonstrate that the shock has only one direction .
Today this equation/condition is known as Prandtl’s equation or condition (1908). In
fact Prandtl is the one who introduced the name of Rankine-Hugoniot’s conditions
not aware of the earlier developments of this condition. Theodor Meyer (Prandtl’s
student) derived the conditions for oblique shock in 1908 21 as a byproduct of the
expansion work.

It was probably later
that Stodola (Fanno’s adviser)
realized that the shock is the in-
tersection of the Fanno line with
the Rayleigh line. Yet, the su-
personic branch is missing from
his understanding (see Figure
1.1). In fact, Stodola suggested
the graphical solution utilizing
the Fanno line.

The fact that the
conditions and direction were
known did not bring the solu-
tion to the equations. The “last
nail” of understanding was put
by Landau, a Jewish scientist
who worked in Moscow Univer-
sity in the 1960’s during the
Fig. 1.1: The shock as connection of Fanno and
Communist regimes. A solution
Rayleigh lines after Stodola, Steam and Gas
was found by Landau & Lifshitz Turbine
and expanded by Kolosnitsyn &
Stanyukovich (1984). to be add to oblique shock
chapter.
Since early of the 1950 the relationship between the the oblique shock
deflection angle and shock angle and Mach number was described as not possible
to obtained. There were up recently (version 0.3 of this book) several equations
that tied various properties/quantities. The first analytical solution connecting the
angles with upstream Mach number was published in this book version 0.3. The
probable reason that analytical solution was not published because the claim in the

19 To add discussion about the general relationships.
20 Some view the work of G. I. Taylor from England as the proof (of course utilizing the second law)
21 Theodor Meyer in Mitteil. ¨ub. Forsch-Arb. Berlin, 1908, No. 62, page 62.