--- title: "Total energy line and hydraulic gradient line" subject: "Hydro Power" chapter: 1 key: "semester_6/hydro_power:tel-hgl-piping" source: https://www.bctengineer.com/q/semester_6/hydro_power/tel-hgl-piping site: BCT Engineering --- # Total energy line and hydraulic gradient line Hydro Power · Chapter 1: Introduction to Basic Fluid Mechanics and Hydraulics - Asked in: 2075 Baisakh, 4 marks - Video: [Hydraulic and Energy Grade Line ? with animation [ HGL and EGL ]](https://www.youtube.com/watch?v=moI4DQNirAw) — NiLTime - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/hydro_power/tel-hgl-piping - Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1 ## Question Explain the total energy line and the hydraulic gradient line for fluid flow through a piping system with neat sketch. ## Short answer TEL joins total heads (p/ρg + V²/2g + z), always falls in flow direction except at pumps. HGL joins piezometric heads (p/ρg + z), lies below TEL by V²/2g. In uniform pipe parallel to TEL; rises at expansions. Sketch shows losses at entrance, friction, sudden enlargement, exit. ## Answer #### Total energy line (TEL or EGL) The **total energy line** is the line joining the total heads $\left(\frac{p}{\rho g} + \frac{V^2}{2g} + z\right)$ at points along the pipe, plotted above the datum. - It always falls in the direction of flow (due to friction and minor losses), except where a pump adds energy. - It has sudden drops at entry, sudden expansion, contraction, valves and bends. #### Hydraulic gradient line (HGL) The **hydraulic gradient line** joins the piezometric heads $\left(\frac{p}{\rho g} + z\right)$, i.e. the levels to which water would rise in piezometers fitted along the pipe. - It lies below the TEL by the velocity head $V^2/2g$. - It is parallel to the TEL in a uniform pipe; it can rise where the pipe enlarges (velocity falls). - Where the pipe rises above the HGL, the pressure is negative (siphon or cavitation risk). #### Sketch: two reservoirs joined by a pipe with a sudden enlargement ```text ===== reservoir 1 \__ entry loss 0.5 V1^2/2g \___ TEL (steep in small pipe) HGL \_ \___ (V1^2/2g) \_| drop (V1-V2)^2/2g \___ |____ TEL (flatter) \__ ^ \______ \| HGL rises \___ exit loss V2^2/2g |\____ HGL ______\_| | ===== reservoir 2 small pipe d1 | large pipe d2 ===============+================== ``` - At the entrance, the TEL drops by the entry loss $0.5V_1^2/2g$ and the HGL drops further by $V_1^2/2g$. - Along each pipe both lines slope down by $h_f = fLV^2/2gD$; the slope is steeper in the small pipe. - At the sudden enlargement, the TEL drops by $(V_1 - V_2)^2/2g$ but the HGL rises, since velocity head falls. - At the exit, the whole velocity head $V_2^2/2g$ is lost; the HGL meets the lower reservoir surface. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which heads does the total energy line join? A. p/rho g + V^2/2g + z B. V^2/2g only C. p/rho g + z D. z only Answer: A. TEL plots total head above the datum. (Key point: Definition of TEL) 2. What does the hydraulic gradient line represent? A. Velocity head B. Piezometric head p/rho g + z, the level reached in piezometers C. Total head D. Friction loss only Answer: B. HGL joins levels to which water rises in piezometers. (Key point: Definition of HGL) 3. How are HGL and TEL related? A. They are always equal B. HGL is below by h_f C. HGL lies below TEL by V^2/2g D. HGL lies above TEL by V^2/2g Answer: C. TEL = HGL + V^2/2g. (Key point: Relation) 4. What happens at a sudden enlargement? A. HGL drops with TEL B. TEL drops by (V1 - V2)^2/2g but HGL rises C. Both rise D. TEL rises Answer: B. Velocity falls so the HGL rises, but the shock loss makes the TEL drop. 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