Hydraulic Gradient Line (HGL) vs Pipe Centre Line By how much does the hydraulic gradient line lie above the centre line of a flowing pipe, in terms of heads?

Introduction:
The Hydraulic Gradient Line (HGL) and Energy Grade Line (EGL) are visual tools to interpret head distribution in pipe flow. Understanding what each represents helps diagnose pressure, cavitation risk, and available energy.

Given Data / Assumptions:

• Incompressible flow in a full pipe.
• Steady conditions; elevation measured from a common datum.
• Neglecting minor losses for the conceptual definition.

Concept / Approach:
HGL represents piezometric head: p/(rhog) + z. The pipe centre line elevation is z. Therefore the vertical distance from the centre line up to HGL equals p/(rhog), which is the pressure head. The EGL is higher than the HGL by the velocity head V^2/(2g).

Step-by-Step Solution:
Write total head: H = p/(rhog) + V^2/(2g) + z.Define HGL = p/(rhog) + z.At the pipe centre line, elevation is z; distance to HGL is p/(rhog) = pressure head.

Verification / Alternative check:
Plot EGL and HGL for a uniform pipe: EGL - HGL = V^2/(2g) (velocity head). Thus HGL distance above the centre line is not velocity head but pressure head, confirming option A.

Why Other Options Are Wrong:
Velocity head corresponds to the vertical gap between EGL and HGL, not HGL and pipe centre line.
Sum or difference of heads mixes concepts incorrectly for this definition.

Common Pitfalls:
Confusing EGL-HGL separation with HGL-to-centre-line spacing; ignoring that pressure can become negative (risk of cavitation) if HGL dips below vapour head.

Final Answer:
pressure head