---
title: "HGL and EGL for pipes in series"
subject: "Hydraulics"
chapter: 1
key: "semester_4/hydraulics:hgl-egl-three-pipes-series"
source: https://www.bctengineer.com/q/semester_4/hydraulics/hgl-egl-three-pipes-series
site: BCT Engineering
---

# HGL and EGL for pipes in series

Hydraulics · Chapter 1: Pipe flow

- Asked in: 2071 Bhadra, 1.5+1.5 marks
- Video: [Flow Through Pipes: Hydraulic Grade Line (HGL) & Energy Grade Line (EGL)  Bangla Lecture Fluid-05](https://www.youtube.com/watch?v=R0sD0VewDn0) — Engineers Cafe
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/hydraulics/hgl-egl-three-pipes-series
- Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-1

## Question

Draw HGL and EGL diagram for the flow system shown in the figure considering all major and minor losses. [Figure: Reservoir A connected to Reservoir B by three pipes in series of diameters d1, d2 and d3, with d1 < d3 < d2]

## Short answer

With d1 < d3 < d2, EGL is steepest in d1, flattest in d2. HGL lies below EGL by V^2/2g, so gap largest in d1, smallest in d2. At expansion to d2, EGL drops and HGL rises; at contraction to d3, EGL drops and HGL falls. Both lines end at the downstream reservoir surface.

## Answer

Reservoir A (higher) feeds reservoir B through three pipes in series, with $d_1 < d_3 < d_2$. Both reservoir surfaces are at rest, so HGL and EGL start at the water surface of A and end at the water surface of B.

**Rules used**
- EGL falls in the direction of flow: slope $= f V^2/(2gd)$, so it is steepest in the smallest pipe 1 and flattest in pipe 2.
- HGL is below the EGL by $V^2/2g$; the gap is largest in pipe 1 (highest velocity) and smallest in pipe 2.
- Sudden drops of the EGL: entrance loss $0.5V_1^2/2g$; expansion from $d_1$ to $d_2$: $(V_1 - V_2)^2/2g$; contraction from $d_2$ to $d_3$: $0.5\left(1-\dfrac{A_3}{A_2}\right)V_3^2/2g$ (approximately); exit loss into B: $V_3^2/2g$.
- At the exit, the whole velocity head is lost, so the EGL falls to the surface of B and both lines end at the water level of B.

```text
 A __                                           
    |\ entrance                 
    | \___ EGL                              
    |     `-.__ (steep, d1)                  
    |  HGL     `-.   | expansion drop        
    |  (gap     `-.__|`-.__ (flat, d2)     
    |   V1²/2g)         |  `-.__|contraction
    |                    HGL     |`-.__ (d3)
    |==[d1]=======[d2 big]=======[d3]=====> 
                                       exit drop
                                          \__ B
```
- The HGL rises after the expansion (velocity falls) and falls again after the contraction (velocity rises).
- Total of all drops (friction + minor losses) equals the difference of the two reservoir levels, $H = h_{f1} + h_{f2} + h_{f3} + h_{entry} + h_{exp} + h_{contr} + h_{exit}$.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. In which pipe is the EGL steepest?
   A. Pipe 2, the largest diameter
   B. Pipe 3
   C. Pipe 1, the smallest diameter
   D. All equal
   Answer: C. The slope f V^2/(2gd) is largest where V is highest and d is smallest, i.e. pipe 1. (Key point: Slope of EGL)

2. Where do the HGL and EGL end at the exit into reservoir B?
   A. At the pipe axis
   B. At the water surface of B, as the whole velocity head is lost at exit
   C. V3^2/2g above the surface of B
   D. At the surface of A
   Answer: B. Exit loss equals V3^2/2g, so EGL falls to B's surface and both lines end there. (Key point: Ends of the lines)

3. What do all drops of the EGL (friction plus minor losses) add up to?
   A. Zero
   B. The velocity head in pipe 1
   C. The difference of the two reservoir levels
   D. Twice the level difference
   Answer: C. H = hf1 + hf2 + hf3 + entry + expansion + contraction + exit. (Key point: Energy balance)

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