Specific speed of a hydraulic turbine — parameter dependence On which parameters does the specific speed (metric) of a hydraulic turbine depend?

Introduction:
Specific speed is a dimensionless-like index (in a chosen unit system) used to characterize and select turbines. It indicates which turbine type (Pelton, Francis, Kaplan) is most suitable for a given head and power condition.

Given Data / Assumptions:

• Metric definition commonly used in textbooks: N_s = Nsqrt(P)/H^(5/4).
• N in r.p.m., P in kW, H in m (units chosen to match metric N_s).

Concept / Approach:
From the definition N_s = Nsqrt(P)/H^(5/4), it is clear that specific speed depends on rotational speed N, power P, and head H simultaneously. It does not directly depend on discharge Q in this common form, although P itself is related to Q and H via P ≈ ρgQHη.

Step-by-Step Solution:

Verification / Alternative check:
Selection charts plot turbine type versus specific speed. Pelton occupies low N_s, Francis mid, Kaplan high—consistent with dependencies on N, P, H.

Why Other Options Are Wrong:

• Speed and power only: ignores head, which is pivotal.
• Discharge + power: H is missing; the conventional formula uses H explicitly.
• Speed and head only: excludes power, which determines size and number of runners.
• Head and discharge only: not the textbook specific-speed form.

Common Pitfalls:
Confusing specific speed with unit quantities; assuming Q appears explicitly—while P encapsulates Q via P ≈ ρgQH*η.

Final Answer: