Gradelines in pipe flow – Is the hydraulic gradient line (HGL) parallel to the pipe centreline? Consider steady flow in a pipeline with frictional losses. The statement “The hydraulic gradient line (HGL) is always parallel to the centreline of the pipe” is:

Introduction:
The hydraulic gradient line (HGL) traces piezometric head p/(ρ * g) + z along a pipe. Understanding how HGL relates to the physical pipeline is essential for locating high points, avoiding cavitation, and placing air valves and reservoirs appropriately.

Given Data / Assumptions:

• Steady, single-phase flow with frictional losses.
• Pipe may be horizontal, inclined, or undulating in elevation.
• Diameter may be constant or varying through fittings and appurtenances.

Concept / Approach:

The HGL represents energy grade excluding kinetic head; it is not constrained to be parallel to the physical pipe. In a horizontal, constant-diameter pipe with uniform flow, the HGL is a straight line sloping downward due to losses, while the pipe centreline is horizontal—clearly not parallel. In sloped or varying-diameter systems, the relative slopes further differ. Only the energy grade line (EGL) and HGL maintain fixed spacing v^2/(2 * g) where v is uniform; neither is guaranteed to be parallel to the centreline.

Step-by-Step Solution:

Verification / Alternative check:

System head-loss and profile diagrams in handbooks routinely show HGL intersecting or diverging from the centreline depending on elevations and local losses, confirming that “always parallel” is false.

Why Other Options Are Wrong:

“Correct only …” qualifiers: Parallelism is not a general rule even under those restricted conditions; e.g., in horizontal pipes the HGL slopes while the pipe does not.

Common Pitfalls:

Confusing HGL with the physical pipeline profile; HGL is an energy representation, not a geometric constraint.

Final Answer:

Incorrect