Specific speed of a centrifugal pump – compute from rated data A pump develops head H = 75 m at discharge Q = 0.464 m³/s when running at N = 1440 rpm. Estimate its specific speed Ns (use Ns = N * sqrt(Q) / H^(3/4); SI units).

Introduction:
Specific speed relates a pump’s geometry/type to its operating point, allowing rapid classification and preliminary selection. Lower Ns values typically indicate radial-flow designs; higher values indicate mixed/axial types. This problem exercises the standard SI form based on speed, discharge, and head at the best-efficiency or rated condition.

Given Data / Assumptions:

• N = 1440 rpm, Q = 0.464 m³/s, H = 75 m.
• Use Ns = N * sqrt(Q) / H^(3/4).
• Assume rated point close to best efficiency region.

Concept / Approach:

The SI specific speed (with rpm, m³/s, m) is dimensional but widely used in practice. It normalizes pump performance to allow comparison across sizes: pumps with similar Ns are dynamically similar and share geometric form.

Step-by-Step Solution:

Verification / Alternative check:

An Ns around 38 indicates a radial-flow centrifugal pump, consistent with the relatively high head (75 m) at moderate discharge.

Why Other Options Are Wrong:

4 and 26 are far below the computed value; 1440 is the rpm, not specific speed; 58 is high for the given data.

Common Pitfalls:

Using head in feet or discharge in L/s without unit consistency; accidentally computing H^(1/2) instead of H^(3/4).

Final Answer:

38