Fluid mechanics – hydraulic gradient line (HGL) relative to pipe centerline Consider steady internal flow in a pressurized pipeline. Can the hydraulic gradient line lie above or below the pipe’s centerline, depending on pressure distribution and datum?

Introduction / Context:
The hydraulic gradient line (HGL) represents the piezometric head line: z + p/(γ). For closed, pressurized pipes, its position relative to the physical pipe can vary with local pressure and elevation. Understanding HGL and the energy grade line (EGL) is essential for analyzing head losses and pump/siphon behavior.

Given Data / Assumptions:

• Incompressible liquid (e.g., water), steady flow.
• HGL is defined as z + p/γ (velocity head excluded).
• Centerline elevation is a convenient datum for reference.

Concept / Approach:
At any pipe section, the piezometric head can be higher or lower than the pipe centerline elevation. If pressure is sufficiently high, p/γ raises HGL above the centerline; if the local absolute pressure approaches or drops below atmospheric, the computed HGL can fall to the centerline or below (e.g., siphons or high points where pressure decreases).

Step-by-Step Solution:

Verification / Alternative check:
Typical system profiles show HGL descending along flow due to head loss; at siphon summits, HGL may drop near or below the pipe crown, illustrating positions both above and below the centerline.

Why Other Options Are Wrong:

• False / “only above” / “only below” contradict practical cases such as pumped lines and siphons.

Common Pitfalls:
Confusing HGL with EGL. HGL excludes velocity head; EGL = HGL + v^2/(2g), and always lies above HGL by the velocity head amount.

Final Answer:
True