Centrifugal pump casing – nature of flow leaving the impeller In a typical volute or diffuser casing of a centrifugal pump, the flow of water leaving the impeller is best idealized as which motion?

Introduction / Context:
Understanding the swirl characteristics downstream of a centrifugal impeller is crucial for estimating head rise, diffuser performance, and hydraulic losses. The classification into free or forced vortex guides how tangential velocity varies with radius.

Given Data / Assumptions:

• Single-stage centrifugal pump with volute/diffuser casing.
• Impeller imparts swirl; pressure recovery occurs in casing.
• Viscous effects and secondary flows are ignored for the basic idealization.

Concept / Approach:

A free vortex has constant angular momentum per unit mass (Vθ * r = constant), implying Vθ ∝ 1/r. A forced vortex (solid-body rotation) has Vθ ∝ r. After leaving the impeller blade tips, the casing area increases, static pressure rises, and swirl weakens approximately as a free vortex rather than maintaining solid-body rotation.

Step-by-Step Solution:

Verification / Alternative check:

Experimental velocity profiles typically show swirl decay consistent with Vθ ∝ 1/r downstream of the impeller in well-designed casings.

Why Other Options Are Wrong:

(a) Rectilinear flow ignores swirl. (b) Pure radial flow is not accurate at exit; there is significant tangential component. (d) Forced vortex requires external torque to maintain solid-body rotation, which a casing does not provide. (e) Same issue as (d).

Common Pitfalls:

Assuming zero whirl at exit for maximum efficiency—this applies at an ideal design point at the impeller outlet relative velocity, not the absolute casing flow pattern which still exhibits vortex-like decay.

Final Answer:

free vortex motion