Hydraulic turbines—specific speed: A turbine develops 10^4 metric horsepower at 100 rpm under a head of 40 m. Estimate the specific speed (metric) and choose the nearest option.

Introduction / Context:
Specific speed classifies turbines independent of size, relating speed, head, and power so designers can select appropriate turbine types (Pelton, Francis, Kaplan) for site conditions. Converting the given power to consistent units and applying the standard metric formula yields the selection metric.

Given Data / Assumptions:

• Power = 10^4 metric horsepower (1 mhp ≈ 0.7355 kW).
• N = 100 rpm.
• H = 40 m.
• Metric specific speed formula: Ns = N * sqrt(PkW) / H^(5/4).

Concept / Approach:

Convert horsepower to kW, compute the numerator N * sqrt(P), compute H^(5/4), and take the ratio. The result indicates the family of turbines suitable at the given head and speed.

Step-by-Step Solution:

Verification / Alternative check:

Recomputing with a calculator yields Ns ≈ 85.3. Exam options typically round to standard indicative bands; 100 is the closest choice and indicates a medium specific speed range compatible with mixed-flow designs.

Why Other Options Are Wrong:

• 314, 523, 628 are far larger and indicate low-head propeller types; inconsistent with H = 40 m and N = 100 rpm.

Common Pitfalls:

• Forgetting to convert metric horsepower to kW.
• Using H^(1/2) instead of H^(5/4) in the metric formula.

Final Answer:

100