Define the gross (total) head for turbines Gross head between headrace and tailrace is obtained by what relation between their water surface levels?

Introduction:
Before accounting for conduit and entry losses, engineers begin with the gross or total head available from a site. This head reflects the vertical energy difference driving the hydropower installation.

Given Data / Assumptions:

• Steady water levels at headrace and tailrace.
• Neglecting velocity heads for a basic definition (or considered small).

Concept / Approach:
Gross head H_gross is the elevation (energy) difference between the upstream headrace water level and the downstream tailrace water level. It is a site attribute, independent of penstock routing. The net head used for power calculations is obtained after subtracting hydraulic losses.

Step-by-Step Solution:

Verification / Alternative check:
Bernoulli’s equation between headrace and tailrace simplifies to the difference in piezometric heads when velocities are small and pressures are hydrostatic.

Why Other Options Are Wrong:

• Sum/product/ratio/average: have no physical meaning for head definition.

Common Pitfalls:
Confusing gross head with rated head at the turbine inlet; forgetting that tailrace levels rise during floods, reducing gross head.

Final Answer: