Inlet Mach No for a centrifugal pump?

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.

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

1 Answer

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.

• Can you please elaborate or guide me to any good reference? Thanks – Anivarth Jan 7 '20 at 10:01
• 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. – Solar Mike Jan 7 '20 at 10:07