Page 249 - 48Fundamentals of Compressible Fluid Mechanics

13.3. OBLIQUE SHOCK 211

show that the common solution is the weaker shock, in which the flow turn to lesser
7
extent .
(13.7)

"

The above velocity–geometry equations also can be expressed in term of Mach
"

number as

E c
(13.8)

(13.9)

E c
(13.10)

B

(13.11)

B

The total energy across oblique shock wave is constant, and it follows that

the total speed of sound is constant across the (oblique) shock. It should be noted
E c

because the temperatures
on both sides of the shock are different, . B
B

"
As opposed to the normal shock, here angles (the second dimension) have

B

B
to be solved. The solution of this set of four equations (13.8) through (13.11) are

function of four unknowns of , , , andc . Rearranging this set set with utilizing
that although "
the Mach number
the the geometrical identity such as results in

(13.12)

c
E

instead of into the normal shock relationship and results in

The relationship between the properties can be found by substituting
(13.13)

E E
7 Actually this term is used from historical reason. The lesser extent angle is the unstable and the

weak angle is the middle solution. But because the literature referred to only two roots the term lesser

extent is used.