Question

What is the pressure exerted by the incoming stream of particles on an inclined flat plate based on Newton’s theory?

(a) \(\frac {F}{A}\) = ρV\(_∞^2\)sin^2θ

(b) \(\frac {F}{A}\) = ρV∞sin^2θ

(c) \(\frac {F}{A}\) = ρV\(_∞^2\)cos^2θ

(d) \(\frac {F}{A}\) = ρV\(_∞^2\)sinθ

This question was addressed to me in exam.

My question is from Time-Marching Technique in division Time-Marching Technique of Aerodynamics

Answer 1

Correct option is (a) \(\frac {F}{A}\) = ρV\(_∞^2\)sin^2θ

The explanation is: For an incoming stream of particles over the inclined surface, the particles move along the surface after the collision and hence the normal velocity is V∞sinθ. Where, θ is the angle formed between the incoming free stream velocity and the flat plate.

The rate of mass flow of the particles over the flat inclined plate with an area A is given by ρAV∞sinθ.

Thus the force is given by product of mass flux and velocity change.

(ρAV∞sinθ)(V∞sinθ) = ρAV\(_∞^2\)sin^2θ = F

And since pressure is equal to force upon area, therefore it is \(\frac {F}{A}\) = ρV\(_∞^2\)sin^2θ