Question

Which equation is obtained when Mach number is equated to zero in area-velocity relation?

(a) Momentum equation

(b) Continuity equation

(c) Energy equation

(d) Bernoulli’s equation

I got this question in semester exam.

My doubt stems from Area-Velocity Relation in chapter Quasi-One-Dimensional Flow of Aerodynamics

Answer 1

Right option is (b) Continuity equation

For explanation: The area-velocity relation is given by:

\(\frac {dA}{A}\)=(M^2-1)\(\frac {du}{u}\)

In the above equation if we substitute M=0 we get,

\(\frac {dA}{A}=-\frac {du}{u}\)

On integrating this equation we get:

Au=constant

This is the continuity equation for incompressible flow in a duct