Pelton Wheel Design — Empirical Rule for Number of Buckets For a Pelton wheel of pitch-circle diameter D supplied by a jet of diameter d, the empirical relation used to select the number of buckets around the periphery is:

Introduction:
Bucket count influences jet interference, discharge smoothness, and mechanical balance in Pelton turbines. An empirical guideline is commonly used at preliminary design to ensure proper spacing and acceptance of the jet by successive buckets.

Given Data / Assumptions:

• Single- or multi-jet Pelton wheel.
• Pitch-circle diameter = D, jet diameter = d.
• Standard splitter geometry and deflection angles.

Concept / Approach:
Empirical practice suggests keeping roughly one bucket pitch between the jet and the bucket leaving the jet to avoid interference, leading to the well-known rule: z ≈ 15 + D / (2 d) This gives adequate bucket count for smooth torque with minimal overlap.

Step-by-Step Solution:
Compute D / (2 d) from geometry.Add baseline count (≈15) to account for spacing and starting buckets.Select nearest integer to obtain the final bucket number.

Verification / Alternative check:
Design handbooks and many worked examples apply z = 15 + D/(2 d), yielding practical bucket counts for common jet ratios (D/d) between 10 and 16.

Why Other Options Are Wrong:

• Other formulas either overshoot or undershoot the count and are not standard.

Common Pitfalls:
Confusing pitch diameter with outer diameter or using jet nozzle diameter after contraction instead of the effective jet diameter.

Final Answer:
z = 15 + D / (2 d)