---
title: "Flow net under sheet pile, discharge"
subject: "Soil Mechanics"
chapter: 7
key: "semester_4/soil_mechanics:sheet-pile-flow-net-steps-discharge"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/sheet-pile-flow-net-steps-discharge
site: BCT Engineering
---

# Flow net under sheet pile, discharge

Soil Mechanics · Chapter 7: Seepage through Soils

- Asked in: 2076 Baisakh, 4 marks
- Video: [Soil Mechanics - 1.1 Flow Net -Sheet Pile](https://www.youtube.com/watch?v=JyHl9q20nd8) — khaled Elaswany
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/sheet-pile-flow-net-steps-discharge
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-7

## Question

Draw a flow net for the flow of water under a sheet pile wall. Write down the steps to draw this flow net and find the discharge, q, for this flow.

## Short answer

Steps: draw section to scale, identify boundaries (upstream/downstream surfaces equipotentials, pile faces and base flow lines), sketch 3-4 flow lines and equipotentials intersecting at right angles forming curvilinear squares, adjust by trial, count Nf and Nd. Discharge q = kH(Nf/Nd) per meter length, where H is net head loss.

## Answer

A sheet pile wall is driven into a pervious layer with an impervious base. The water level is higher upstream (head $h_1$) than downstream ($h_2$), so water flows under the pile tip.

```text
  upstream ▽      |P|      ▽ downstream
  ----------------|P|----------------
   flow lines ~~> |P| ~~> curve under tip
  ================================== impervious
```

#### Steps to draw the flow net

1. Draw the section to scale showing the sheet pile, soil surfaces and the impervious base.
2. Note boundary conditions: upstream and downstream soil surfaces are equipotential lines; the sheet pile faces and the impervious base are flow lines.
3. Draw 3 or 4 flow lines as smooth curves round the pile tip, perpendicular to the equipotentials.
4. Draw equipotential lines, perpendicular to flow lines, so that the fields are squares.
5. Adjust by trial and error until all fields are curvilinear squares.
6. Count $N_f$ and $N_d$.

#### Discharge

$$
q = k\,H\,\frac{N_f}{N_d}
$$

where $H = h_1 - h_2$ is the net head loss, $N_f$ the number of flow channels and $N_d$ the number of equipotential drops. $q$ is in m³/s per metre length of the wall.

## Check yourself

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

1. Which are flow lines for flow under a sheet pile wall?
   A. Upstream soil surface
   B. Downstream soil surface
   C. Sheet pile faces and impervious base
   D. None of the boundaries
   Answer: C. The pile faces and impervious base are impermeable so water runs along them. (Key point: Boundary lines)

2. How are equipotential lines drawn relative to flow lines?
   A. Parallel
   B. At 45 degrees
   C. Perpendicular, forming square fields
   D. Randomly
   Answer: C. They cross at right angles with fields as curvilinear squares. (Key point: Orthogonality)

3. What is H in q = k H N_f / N_d?
   A. Pile depth
   B. Aquifer thickness
   C. Net head loss h1 - h2
   D. Downstream head only
   Answer: C. H is the net head loss between upstream and downstream. (Key point: Head H)

4. In what units is q found?
   A. m/s
   B. m3/s per metre length of wall
   C. m2
   D. kN/m
   Answer: B. q is a discharge per unit length of the wall. (Key point: Units of q)

## Related in Soil Mechanics

- [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
- [Sheet pile seepage quantity numerical](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Asheet-pile-seepage-quantity-numerical) — Soil Mechanics, chapter 7
- [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
- [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
- [Flow net: definition, properties, uses](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aflow-net-properties-applications) — Soil Mechanics, chapter 7, asked 7×

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