Recently I have come across a question as follows:

At the eye tip of a centrifugal impeller, blade velocity is 200 m/s while the uniform axial velocity at the inlet is 150 m/s. If the sonic velocity is 300 m/s, then the inlet Mach number of flow will be?

My answer is $\frac{150}{300} = .5$,

but the correct answer is $0.83$, with an explanation:

$M = \frac{\sqrt{(blade\ velocity)^2 + (axial\ velocity)^2}}{sonic velocity} = 0.83$

My question is: when we are considering the inlet mach why are we considering the blade velocity also why not just inlet flow velocity?

Please help me, Thanks.

  • $\begingroup$ Given your 3 questions so far, are your questions related to homework? $\endgroup$ – Solar Mike Jan 7 '20 at 10:31

There is a velocity triangle relating the velocities at the blade - this changes as the shape of the blade changes.

Both components of the fluid have to be taken into account: the velocity of the fluid at the inlet and the axial velicity to get the outlet velocity.

  • $\begingroup$ Can you please elaborate or guide me to any good reference? Thanks $\endgroup$ – Anivarth Jan 7 '20 at 10:01
  • $\begingroup$ A quick Google search for velocity triangle gives pumpsandsystems.com/… But your lecture notes should be sufficient or the book you got the question from. $\endgroup$ – Solar Mike Jan 7 '20 at 10:07

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