--- title: "HGL and TEL definition and sketch" subject: "Hydraulics" chapter: 1 key: "semester_4/hydraulics:hgl-tel-definition-sketch" source: https://www.bctengineer.com/q/semester_4/hydraulics/hgl-tel-definition-sketch site: BCT Engineering --- # HGL and TEL definition and sketch Hydraulics · Chapter 1: Pipe flow - Asked in: 2082 Kartik, 2+4 marks - Video: [Fluid Mechanics: Topic 7.3.1 - Energy grade line (EGL) & Hydraulic grade line (HGL)](https://www.youtube.com/watch?v=-oecDDrYfyY) — CPPMechEngTutorials - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/hydraulics/hgl-tel-definition-sketch - Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-1 ## Question What are HGL (Hydraulic Gradient Line) and TEL (Total Energy Line)? Draw HGL and TEL showing elevation, pressure and kinetic energy heads for uniform and non-uniform pipes with real fluid flow. ## Short answer HGL is the line joining piezometric heads (p/gamma + z). TEL joins total heads, adding V^2/2g. TEL always drops downstream; in uniform pipes HGL is parallel to TEL by the gap V^2/2g. At free outlets HGL meets the pipe axis, and minor losses cause sudden TEL drops. ## Answer #### Definitions - **Hydraulic Gradient Line (HGL)** is the line joining the levels to which water would rise in piezometer tubes along the pipe. Its height above the datum is the piezometric head $\dfrac{p}{\gamma} + z$, where $z$ is the elevation head (height of the pipe axis above the datum) and $\dfrac{p}{\gamma}$ is the pressure head. - **Total Energy Line (TEL)** (also called EGL) is the line showing the total head $\dfrac{p}{\gamma} + z + \dfrac{V^2}{2g}$. It lies above the HGL by the velocity (kinetic energy) head $\dfrac{V^2}{2g}$. #### Features for a real fluid - The TEL always falls in the direction of flow because of head losses. Its slope equals the energy gradient $S_f = h_f/L$. - In a uniform pipe $V$ is constant, so the HGL is parallel to the TEL, a fixed distance $V^2/2g$ below it. - Minor losses (entrance, expansion, valve, bend) show as sudden vertical drops of the TEL. - Where the HGL is below the pipe axis the pressure is below atmospheric (negative); where it is above, the pressure is positive. - A pump gives a sudden rise of both lines; a turbine gives a drop. - At a free outlet to the atmosphere the HGL meets the pipe axis (gauge pressure zero). At a reservoir both lines coincide with the free surface ($V = 0$). #### Uniform pipe (constant diameter) ```text TEL (reservoir surface) \__ entrance loss 0.5V²/2g `-.__ `-.__ TEL (slope = hf/L) ^ `-.__ | V²/2g (same all along) `-.__ v `-.__ HGL ......`-.__ (parallel to TEL) `-.__ `-.__ pipe axis ===========================> outlet (HGL meets axis) ^ z (elevation head) datum ------------------------------------------ ``` The TEL and HGL are two parallel sloping lines; the gap between them is constant at $V^2/2g$. The height of the HGL above the pipe axis is the pressure head $p/\gamma$, and the height of the axis above the datum is $z$. #### Non-uniform pipe (diameter changes from $D_1$ to $D_2 > D_1$) ```text TEL ---.__ `-.__ steep slope (small pipe) `-.__ ^ `-.__| | V1²/2g | drop (V1-V2)²/2g v `-.__ HGL ---.__ `-.__ TEL, flatter slope `-.__ ^ `-.__ | V2²/2g (smaller gap) `-.__ | ____ v `+--' `-.__ HGL axis ==========[ D1 ]=====|==[ D2 > D1 ]========= ``` - In the smaller pipe the velocity head is large, so the HGL is far below the TEL and the slope $h_f/L$ is steeper. - At a sudden expansion the TEL drops by $(V_1 - V_2)^2/2g$. As $V$ falls, the velocity head $V^2/2g$ falls too, so the HGL can **rise** (pressure recovery) even though energy is lost. - In the larger pipe the TEL is flatter and the gap between the two lines is smaller. - In a gradual contraction or expansion the lines change slope smoothly instead of jumping. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is the TEL positioned relative to the HGL? A. Below it by V^2/2g B. Above it by V^2/2g C. Above it by p/gamma D. They always coincide Answer: B. TEL = p/gamma + z + V^2/2g, so it lies a velocity head above the HGL (p/gamma + z). (Key point: HGL vs TEL) 2. For a real fluid, how does the TEL behave along the flow direction? A. It always falls because of head losses B. It stays horizontal C. It rises where velocity decreases D. It rises in a larger pipe Answer: A. Head losses continuously reduce total energy, so the TEL falls except where a pump adds energy. (Key point: Real fluid TEL) 3. At a sudden expansion in a real pipe, what happens to the lines? A. TEL rises and HGL falls B. Both lines rise C. TEL drops by (V1-V2)^2/2g while the HGL can rise because velocity head falls D. Neither line changes Answer: C. Energy is lost so TEL drops, but lower velocity head can give pressure recovery so the HGL may rise. 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