Hydraulic grade line (HGL) relative to the conduit centerline In pressurized pipe flow, where can the hydraulic grade line lie relative to the pipe centerline?

Introduction / Context:
The hydraulic grade line (HGL) represents the piezometric head (pressure head plus elevation head) and is foundational in diagnosing pressurized pipeline behavior. Its position relative to the pipe centerline changes with pressure conditions along the system.

Given Data / Assumptions:

• Pressurized, steady pipe flow.
• HGL is defined as z + p/γ (neglecting velocity head).
• Elevations referenced to the pipe centerline for comparison.

Concept / Approach:

If p/γ is positive (gauge pressure), the HGL lies above the centerline; if p/γ is negative (sub-atmospheric), the HGL can drop below the centerline. Therefore, depending on local pressure conditions (e.g., high velocities, siphon crests), the HGL may be either above or below the pipe axis.

Step-by-Step Solution:

Verification / Alternative check:

Plotting HGL and the energy grade line (EGL) along a pipeline confirms that their relative positions vary; EGL always lies above HGL by v^2/(2 g).

Why Other Options Are Wrong:

(a) and (b) restrict HGL location incorrectly; (c) the HGL is not generally parallel to the pipe alignment due to friction losses and grade changes.

Common Pitfalls:

Confusing HGL with EGL; ignoring zones of low pressure at high points in siphons; forgetting that negative gauge pressure shifts HGL below the centerline.

Final Answer:

may be above or below the centre line of conduit.