Basics of Fluid Mechanics, 2014a

12.2. OBLIQUE SHOCK 509
In the oblique shock, the first angle shown is
M x M ys M yw θ s θ w δ
P 0y
P 0x
2.0000 0.58974 1.7498 85.7021 36.2098 7.0000 0.99445
and the additional information by the minimal info in the Potto-GDC is
M x M yw θ w δ
P y
P x
T y
T x
P 0y
P 0x
2.0000 1.7498 36.2098 7.0000 1.2485 1.1931 0.99445
In the new region, the new angle is 7 ◦ +7 ◦ with new upstream Mach number of
M x =1.7498 resulting in
M x M ys M yw θ s θ w δ
P 0y
P 0x
1.7498 0.71761 1.2346 76.9831 51.5549 14.0000 0.96524
And the additional information is
M x M yw θ w δ
P y
P x
T y
T x
P 0y
P 0x
1.7498 1.5088 41.8770 7.0000 1.2626 1.1853 0.99549
An oblique shock is not possible and normal shock occurs. In such a case, the
results are:
M x M y
T y
T x
ρ y
ρ x
P y
P x
P 0y
P 0x
1.2346 0.82141 1.1497 1.4018 1.6116 0.98903
With two weak shock waves and a normal shock the total pressure loss is
P 04
= P 04 P 03 P 02
=0.98903 × 0.96524 × 0.99445 = 0.9496
P 01 P 03 P 02 P 01
The static pressure ratio for the second case is
P 4
= P 4 P 3 P 2
=1.6116 × 1.2626 × 1.285 = 2.6147
P 1 P 3 P 2 P 1
The loss in this case is much less than in a direct normal shock. In fact, the loss
in the normal shock is above than 31% of the total pressure.
End Solution