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How many characteristics pass through a point in the flow field if the Mach number is greater than 1?(a) 1(b) 2(c) 4(d) 0This question was posed to me in homework.I would like to ask this question from Two Dimensional Irrotational Flow in section Numerical Techniques for Steady Supersonic Flow of Aerodynamics

Answer»

Correct option is (b) 2

The best explanation: The characteristic curve is given by the relation

\(\frac {DY}{dx_{char}} = \frac {- \frac {uv}{a^{2}} ± \SQRT {(\frac {u^2 + V^{2}}{a^{2}})-1}}{1 – \frac {u^{2}}{a^{2}}}\)

The term inside the SQUARE ROOT \(\frac {u^2 + v^{2}}{a^{2}}\) – 1 can be written in the form of Mach number as follows:

\(\frac {u^2 + v^{2}}{a^{2}}\) – 1 = \(\frac {V^{2}}{a^{2}}\) – 1 = M^2 – 1

When the flow is supersonic i.e. Mach number is greater than 1, two characteristics pass through a point in a flow field. Hyperbolic partial differential equation is used to define it.



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