A flat plate is placed in a supersonic stream, aligned with the flow direction. Weak Waves caused by roughnes on the plate are observed. Determine the Mach number of the supersonic stream when the waves are at the following angles. Comment on the trend. (i) 60 degrees (ii) 30 degrees (iii) 15 degrees Solution The weak waves that are formed in a supersonic flow are called as mach waves. If angle made my these waves is theta, then sin(theta) = 1 / Mach number Mach number = 1 / sin(theta) a) For 60 degrees Mach number = 1 / sin(60) = 1.154 b) For 30 degrees Mach number = 1 / sin(30) = 2 c) For 15 degrees Mach number = 1 / sin(15) = 3.863 We can visualize that as much number increases, angle of wave decreases which is indded true. .

1. A flat plate is placed in a supersonic stream, aligned with the flow direction. Weak Waves
caused by roughnes on the plate are observed. Determine the Mach number of the supersonic
stream when the waves are at the following angles. Comment on the trend.
(i) 60 degrees
(ii) 30 degrees
(iii) 15 degrees
Solution
The weak waves that are formed in a supersonic flow are called as mach waves.
If angle made my these waves is theta, then
sin(theta) = 1 / Mach number
Mach number = 1 / sin(theta)
a) For 60 degrees
Mach number = 1 / sin(60) = 1.154
b) For 30 degrees
Mach number = 1 / sin(30) = 2
c) For 15 degrees
Mach number = 1 / sin(15) = 3.863
We can visualize that as much number increases, angle of wave decreases which is indded true.