---
title: "Flow net: definition, properties, uses"
subject: "Soil Mechanics"
chapter: 7
key: "semester_4/soil_mechanics:flow-net-properties-applications"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/flow-net-properties-applications
site: BCT Engineering
---

# Flow net: definition, properties, uses

Soil Mechanics · Chapter 7: Seepage through Soils

- Asked in: 2079 Asoj, 1+2 marks; 2078 Baisakh, 1+2 marks; 2079 Jestha, 2 marks; 2075 Baisakh, 1 marks; 2076 Baisakh, 2 marks; 2074 Bhadra, 2 marks; 2078 Poush, 2 marks (asked 7 times)
- Video: [Flow Net , Flow lines and Equipotential lines - Soil Mechanics - Geotechnical Engineering  (Part-1)](https://www.youtube.com/watch?v=HFw-0yeOkPI) — Vital Vibes
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/flow-net-properties-applications
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-7

## Question

What is a flow net? Define flow lines and equipotential lines. Write its properties and applications (uses).

## Short answer

A flow net is a graphical representation of 2D steady seepage with orthogonal flow lines and equipotential lines. Properties: fields are squares, equal flow per channel, equal head drop per drop. Applications: seepage discharge (q = k h Nf/Nd), pore pressure, exit gradient, and design of filters and sheet piles.

## Answer

A **flow net** is a graphical representation of two-dimensional steady seepage, made of two families of curves that cross at right angles: flow lines and equipotential lines. It gives the discharge, pore pressures and exit gradients directly.

- **Flow line (stream line):** the path followed by a water particle through the soil from upstream to downstream. No water crosses a flow line.
- **Equipotential line:** a line joining points having the same total head. Water level in a piezometer is the same at all points of the line.

```text
     ==========  upstream
     |  |  |  |    flow lines  ----->
  ---+--+--+--+---  equipotentials  |
```

#### Properties

1. Flow lines and equipotential lines intersect at right angles.
2. The fields (elements) are approximately squares, so that a circle can be drawn touching the four sides of each.
3. The same quantity of flow takes place in each flow channel ($\Delta q$ is equal).
4. The head drop between two adjacent equipotential lines is the same ($\Delta h = h/N_d$).
5. Flow lines never cross each other; equipotential lines never cross each other.
6. The smaller the field, the greater the velocity and gradient.
7. Boundaries: an impervious surface is a flow line; the upstream and downstream ground surfaces under water are equipotentials.

#### Applications

- Seepage discharge: $q = k\,h\,\dfrac{N_f}{N_d}$
- Pore water pressure at any point (for stability and uplift on dams, weirs)
- Exit gradient and check against piping
- Seepage force and uplift pressure under hydraulic structures
- Design of the length of sheet piles, filters and drains
- Location of the phreatic line in an earth dam.

## Check yourself

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

1. A flow net consists of:
   A. Flow lines and equipotential lines crossing at right angles
   B. Only equipotential lines
   C. Parallel flow lines
   D. Pressure contours only
   Answer: A. It is two orthogonal families of curves for 2-D steady seepage. (Key point: Definition)

2. An equipotential line joins points having:
   A. The same velocity
   B. The same total head
   C. The same elevation
   D. The same pore pressure and elevation
   Answer: B. Piezometer level is the same at all points on an equipotential. (Key point: Equipotential line)

3. Which property is correct?
   A. Head drop varies between adjacent equipotentials
   B. Same flow in each channel and same head drop between adjacent equipotentials (h/Nd)
   C. Flow lines cross at nodes
   D. Smaller fields have lower velocity
   Answer: B. Each flow channel carries equal Delta q and each drop is h/N_d; smaller fields mean higher gradient and velocity. (Key point: Equal head drop)

4. Seepage discharge from a flow net is:
   A. q = k h Nd/Nf
   B. q = k h Nf/Nd
   C. q = k Nf Nd / h
   D. q = h Nf/(k Nd)
   Answer: B. q = k h N_f/N_d. (Key point: Discharge formula)

## Related in Soil Mechanics

- [Flow net discharge, 200 cc/day](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aflow-net-discharge-numerical-200cc) — Soil Mechanics, chapter 7
- [Flow lines cut equipotentials at right angles](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aprove-flow-equipotential-orthogonal) — Soil Mechanics, chapter 7, asked 3×
- [Sheet pile flow net; graded filter](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Asheet-pile-flow-net-graded-filter) — Soil Mechanics, chapter 7
- [Flow net under sheet pile, discharge](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Asheet-pile-flow-net-steps-discharge) — Soil Mechanics, chapter 7
- [Earth dam flow net and discharge](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aearth-dam-flow-net-compare-discharge) — Soil Mechanics, chapter 7

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