Energy grade concepts: the Total Energy Line (TEL) for steady incompressible flow represents the sum of which heads?

Introduction / Context:
In pipeline and open-channel analysis, the Energy Grade Line (EGL or TEL) and Hydraulic Grade Line (HGL) visualize how energy varies along the flow. Correctly identifying what the Total Energy Line includes is essential for head-loss calculations and pump/turbine sizing.

Given Data / Assumptions:

• Steady, incompressible flow of a single-phase fluid.
• Bernoulli equation applies along a streamline (with pump/turbine and losses as appropriate).
• Elevation is measured from a chosen datum plane.

Concept / Approach:

The Total Energy Line (TEL) plots the total head H_total = p/(ρ g) + V^2/(2 g) + z at points along the system. The Hydraulic Grade Line (HGL) is the sum of pressure head and elevation head only, HGL = p/(ρ g) + z. The vertical distance between the TEL and HGL equals the velocity head, V^2/(2 g).

Step-by-Step Solution:

Verification / Alternative check:

Plot a simple pipeline: TEL slopes downward by h_f between sections; when pipe diameter changes, a step occurs in TEL due to velocity head change, while HGL may step differently depending on pressure change.

Why Other Options Are Wrong:

(a), (b), and (c) list individual components only; TEL is the sum of all three. (e) contradicts standard head plotting practice used in hydraulics and fluid mechanics.

Common Pitfalls:

Confusing TEL with HGL; forgetting to include pump head additions or turbine head extractions; misplacing the datum.

Final Answer:

All of the above summed (pressure + velocity + elevation)