A centrifugal pump with smooth radial vanes rotates in the horizontal plane with

Question

A centrifugal pump with smooth radial vanes rotates in the horizontal plane with a constant angular velocity,  w.  Find the magnitude of the force exerted by a vane on a particle of mass m as it moves out along the vane.  The particle is introduced at r = r0  with no angular velocity.  Assume there is no shear (i.e., friction) force between the particle and the vane.

A centrifugal pump with smooth radial vanes rotates in the horizontal plane with a constant angular velocity, w. Find the magnitude of the force exerted by a vane on a particle of mass m as it moves out along the vane. The particle is introduced at r = r0 with no angular velocity. Assume there is no shear (i.e., friction) force between the particle and the vane.

Explanation / Answer

F=m*dv/dt

=m*a

now assuming a varies linearly so taking average we have

a=w^2*(r+r0)/2

so F=m*w^2*(r+r0)/2 ans

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