Hydropower turbine selection: to generate 10,000 hp (≈7.46 MW) under a net head of 81 m at a rotational speed of 500 rpm, which turbine type is most appropriate for this medium-head, medium-specific-speed application in water resources/civil engineering?

Introduction / Context:
Choosing a hydraulic turbine involves matching the site head, discharge, and desired rotational speed to a turbine with suitable specific speed and efficiency. Medium heads typically call for reaction turbines with mixed flow characteristics. This question tests recognition of the correct turbine for an 81 m head with significant power and 500 rpm speed requirements.

Given Data / Assumptions:

• Power P ≈ 10,000 hp ≈ 7.46 MW.
• Net head H ≈ 81 m (medium head).
• Shaft speed N ≈ 500 rpm.
• Standard turbine families considered: Pelton (impulse, high head), Francis (mixed-flow reaction, medium head), Kaplan/Bulb (axial-flow reaction, low head), Crossflow (small/medium power niche).

Concept / Approach:
Specific speed Ns (qualitative here) increases with lower head and higher discharge. Pelton turbines suit very high heads and low flow; Kaplan/Bulb suit low heads (typically under ~30 m) with high flow. Francis turbines bridge the medium-head range (~30–250 m), offering good efficiency and compatibility with moderate to high rotational speeds using appropriate runner diameters and gear ratios if needed.

Step-by-Step Solution:
Identify head regime: 81 m → medium head.Map turbine families to head: Pelton (too high-head oriented), Kaplan/Bulb (too low-head oriented), Francis (ideal for medium head).Check speed reasonableness: 500 rpm is compatible with Francis designs for this power and head using feasible runner size.Select Francis turbine.

Verification / Alternative check:
Selection charts (head vs. specific speed) place Francis squarely in the 30–250 m range, covering 81 m comfortably. Numerous medium-head plants of this rating use Francis runners.

Why Other Options Are Wrong:

• Kaplan/Bulb: optimized for low head, high discharge; 81 m is outside their economic sweet spot.
• Pelton: best for high head (>200 m) and would spin too fast or become impractically small here.
• Crossflow: serviceable for small plants but not the most efficient choice at multi-MW scale and this head.

Common Pitfalls:
Confusing power level with head regime; overlooking that Kaplan is not appropriate for medium-to-high heads.

Final Answer:
Francis