Francis turbine: definition of flow ratio The flow ratio for a Francis turbine is defined as the ratio of which velocities?

Introduction / Context:
The flow ratio is a non-dimensional parameter used in the design and analysis of reaction turbines, particularly the Francis turbine. It links the meridional (axial/radial) component of velocity at entry to a head-based reference speed and helps set guide vane openings and runner passage areas.

Given Data / Assumptions:

• Inlet head H after accounting for losses relevant to √(2 g H).
• Velocity of flow (meridional component) at inlet denoted V_f1.

Concept / Approach:
By definition, flow ratio φ_f = V_f1 / √(2 g H). It differs from speed ratio (runner peripheral ratio) and from the whirl coefficient that involves the tangential component of velocity.

Step-by-Step Solution:
Compute theoretical jet speed from head: V_th = √(2 g H).Measure or design for inlet flow component: V_f1.Form ratio: φ_f = V_f1 / V_th.Use φ_f in preliminary sizing of guide vane settings and blade heights.

Verification / Alternative check:
Typical φ_f values for Francis designs fall in standard ranges used by manufacturers; comparing with case studies confirms the definition.

Why Other Options Are Wrong:
Inverting the ratio changes the non-dimensional group meaning. The runner peripheral ratio concerns blade speed, not meridional flow. “None of the above” is incorrect because option (a) is the standard definition.

Common Pitfalls:
Confusing flow ratio with speed ratio or with whirl velocity fraction; mixing inlet and outlet symbols.

Final Answer:
Velocity of flow at inlet to the theoretical jet velocity (√(2 g H))