Energy grade line (TEL) and hydraulic grade line (HGL) Which statement is correct regarding the graphical interpretation of head lines in pipe flow?

Introduction / Context:
Plotting energy lines helps visualize head distribution along pipes, nozzles, and fittings. The total energy line (TEL) and hydraulic grade line (HGL) separate dynamic and static contributions and reveal where pumps add head or friction removes it.

Given Data / Assumptions:

• Total head H = z + p/γ + V^2/(2g).
• Hydraulic grade line is z + p/γ (piezometric head).
• Steady, incompressible flow in a conduit with losses.

Concept / Approach:

The HGL expresses static energy (elevation plus pressure head). The TEL adds velocity head on top. Their vertical separation is precisely the kinetic term V^2/(2g). Friction and minor losses make both lines slope downward in the flow direction unless a pump elevates the TEL (and HGL accordingly).

Step-by-Step Solution:

Verification / Alternative check:

At a reservoir (V ≈ 0), TEL and HGL coincide. At a nozzle exit to atmosphere, HGL meets the exit elevation line (p/γ = 0), while TEL remains above by the exit velocity head.

Why Other Options Are Wrong:

(a) TEL includes elevation, pressure, and velocity heads. (c) The separation is kinetic, not static pressure. (d) HGL is always at or below TEL; it cannot lie above. (e) With friction, TEL drops; zero difference implies no losses or a frictionless, idealization-only case.

Common Pitfalls:

Confusing pressure head with piezometric head; forgetting to include minor-loss-induced TEL drops at fittings and valves.

Final Answer:

The vertical distance between the total energy line (TEL) and hydraulic grade line (HGL) equals the velocity head