Francis turbine speed ratio: typical range The speed ratio (runner peripheral speed / √(2 g H)) for Francis turbines generally lies in which range?

Introduction / Context:
The speed ratio is a non-dimensional parameter comparing the blade tip speed of a turbine runner with the theoretical jet speed derived from head. For reaction machines like Francis turbines, this ratio is higher than for impulse machines because part of the energy conversion occurs under pressure inside the passages.

Given Data / Assumptions:

• Speed ratio φ = u / √(2 g H).
• Francis turbine operating near best efficiency with typical design coefficients.

Concept / Approach:
Impulse turbines (Pelton) have φ around 0.43–0.5. Francis turbines, with reaction and submerged runners, have larger φ typically in the 0.6–0.9 band, depending on specific speed and blade design. This reflects higher runner peripheral speeds relative to head-based velocity.

Step-by-Step Solution:
Define φ = u / √(2 g H).Consult typical design ranges: Pelton φ ≈ 0.46; Kaplan higher; Francis in-between but closer to reaction values.Select the range 0.6–0.9 as characteristic for Francis turbines.

Verification / Alternative check:
Textbook design charts and manufacturer data show φ in this range for conventional Francis runners across moderate specific speeds.

Why Other Options Are Wrong:
0.15–0.3 is too low (would suit very different machines). 0.4–0.5 suits Pelton. Values ≥1 imply blade tips faster than theoretical jet speed, not typical for Francis.

Common Pitfalls:
Confusing speed ratio with specific speed; mixing Francis and Pelton characteristic ratios.

Final Answer:
0.6 to 0.9