Centrifugal pump — compute specific speed (Ns) (Given Q = 44 m^3/s, H = 36 m, N = 1450 rpm; use Ns = N * sqrt(Q) / H^(3/4).)

Introduction / Context:
Specific speed (Ns) classifies pump impellers by geometry and performance similarity. It guides selection between radial-, mixed-, and axial-flow designs and helps anticipate efficiency ranges and NPSH behavior.

Given Data / Assumptions:

• Discharge Q = 44 m^3/s (Cumecs).
• Total head H = 36 m.
• Rotational speed N = 1450 rpm.
• Formula: Ns = N * sqrt(Q) / H^(3/4) (SI-based convention typical in many texts).

Concept / Approach:
Compute sqrt(Q) and H^(3/4), then evaluate Ns. Larger Q and lower H increase Ns (tending toward axial-flow), while smaller Q and higher H reduce Ns (radial-flow).

Step-by-Step Solution:
1) Compute sqrt(Q) = sqrt(44) ≈ 6.633.2) Compute H^(3/4): 36^(0.75) = (36^(1/2)) * (36^(1/4)) ≈ 6 * 2.449 = 14.694.3) Evaluate Ns = 1450 * 6.633 / 14.694 ≈ 1450 * 0.4513 ≈ 654.4) Select option 654.

Verification / Alternative check:
Order-of-magnitude: With large Q and moderate H, Ns in the hundreds is expected, consistent with mixed/axial tendencies.

Why Other Options Are Wrong:
509 and 700 deviate from the precise calculation; 90 is far too low given the high discharge and moderate head.

Common Pitfalls:
Mistaking unit systems or using US customary definitions; misapplying exponent 3/4; rounding too early in intermediate steps.

Final Answer:
654