Specific speed – interpretative statements about the formula Which statement is correct regarding the commonly used pump specific speed expression Ns = N * sqrt(Q) / H^(3/4) (SI practice)?

Introduction:
Specific speed organizes pump designs by relating speed, discharge, and head at a reference operating point. Interpreting what the formula does and does not include prevents common misunderstandings in preliminary selection and similarity scaling.

Given Data / Assumptions:

• SI usage: Ns = N * sqrt(Q) / H^(3/4), with N in rpm, Q in m³/s, H in m.
• Comparison across radial, mixed, and axial flow pumps.
• Impeller diameter D and power P are considered separately in similarity laws.

Concept / Approach:

The Ns expression depends only on N, Q, and H. It does not contain impeller diameter explicitly—designs with similar Ns tend to be geometrically similar after appropriate scaling. In SI practice, Ns has units (is not strictly non-dimensional). A dimensionless variant exists if one uses angular speed and normalizes with g appropriately, but that is a different definition. Radial pumps usually have lower Ns than axial pumps; including power is unnecessary for Ns.

Step-by-Step Solution:

Verification / Alternative check:

Manufacturers catalogues group pump models by Ns bands independent of D, confirming the exclusion of diameter from the expression.

Why Other Options Are Wrong:

B suggests the wrong trend; C is incorrect because SI Ns is dimensional; D is false since power is not in the formula; E is wrong—SI form uses metres, not feet.

Common Pitfalls:

Confusing SI Ns with the US customary definition; mixing up dimensional and dimensionless versions; assuming Ns alone fixes efficiency without considering specific diameter and Reynolds effects.

Final Answer:

does not include the diameter of the impeller