Question

How many characteristic line/lines can pass through a point P in a streamline?

(a) 1

(b) 2

(c) 3

(d) 4

This question was addressed to me during an online interview.

I'm obligated to ask this question of Supersonic Nozzle Design topic in portion Numerical Techniques for Nonlinear Supersonic Flow, Elements of Hypersonic Flow, Couette and Poiseuille Flow of Aerodynamics

Answer 1

Correct option is (b) 2

To explain I would say: For a point in a streamline, there exists two characteristic liens according to this formula:

\((\frac {dy}{dx})\)char = tan⁡(θ ± μ)

Where, θ is the angle made between the tangent to the point P and horizontal

μ is local Mach angle = sin^-1(1/M)

Thus the two characteristic lines have slope tan⁡(θ + μ) and tan⁡(θ – μ). The one which is inclined above the streamline is labelled as C+ and the characteristic line inclined below the streamline is C–.