---
title: "Discharge velocity"
subject: "Soil Mechanics"
chapter: 6
key: "semester_4/soil_mechanics:discharge-velocity-define"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/discharge-velocity-define
site: BCT Engineering
---

# Discharge velocity

Soil Mechanics · Chapter 6: Principle of Effective Stress, Capillarity and Permeability

- Asked in: 2075 Baisakh, 1 marks
- Video: [Soil Permeability - Darcy's Law](https://www.youtube.com/watch?v=-bYptlimsdI) — Elementary Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/discharge-velocity-define
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-6

## Question

What is discharge velocity?

## Short answer

Discharge velocity is the volume of water flowing per unit time per unit gross cross-sectional area of soil, v = Q/A = k i. It is an imaginary average velocity because flow occurs only through voids; the actual seepage velocity is v_s = v/n.

## Answer

**Discharge velocity** (superficial or approach velocity) is the quantity of water flowing per unit time per unit gross cross-sectional area of the soil, taken perpendicular to the flow:

$$
v = \frac{Q}{A} = k\,i
$$

It is an average, imaginary velocity, since water flows only through the voids. The actual velocity in the pores (seepage velocity) is $v_s = v/n$.

## Check yourself

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

1. Discharge velocity is the flow per unit time per unit:
   A. Void area
   B. Gross cross-sectional area normal to flow
   C. Soil volume
   D. Length of flow path
   Answer: B. v = Q/A with A the gross area. (Key point: Definition)

2. Discharge velocity equals:
   A. k/i
   B. k i
   C. k i n
   D. i/k
   Answer: B. Darcy's law: v = k i. (Key point: Relation to Darcy)

3. The actual velocity in the pores (seepage velocity) is:
   A. v n
   B. v
   C. v/n
   D. v(1-n)
   Answer: C. Water flows only through voids, so v_s = v/n, larger than v. (Key point: Seepage velocity)

## Related in Soil Mechanics

- [Discharge velocity vs seepage velocity](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Adischarge-vs-seepage-velocity) — Soil Mechanics, chapter 6, asked 2×
- [Constant head permeameter, seepage velocity](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aconstant-head-permeameter-seepage-velocity) — Soil Mechanics, chapter 6

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