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

# Discharge velocity vs seepage velocity

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

- Asked in: 2076 Baisakh, 2 marks; 2074 Bhadra, 2 marks (asked 2 times)
- Video: [Difference between Seepage velocity and Discharge velocity || Derivation for seepage velocity ||](https://www.youtube.com/watch?v=LcvPHRm45fc) — 𝗖𝗶𝘃𝗶𝗹 𝗡𝗲𝘅𝘂𝘀 𝗯𝘆 𝗘𝗿 𝗡𝗮𝗱𝗲𝗲𝗺
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/discharge-vs-seepage-velocity
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-6

## Question

Differentiate between discharge velocity and seepage velocity when water flows through the soil.

## Short answer

Discharge velocity is Q divided by total cross-sectional area, a fictitious average velocity; seepage velocity is Q divided by void area, the actual pore velocity. Seepage velocity equals discharge velocity divided by porosity and is always larger.

## Answer

**Discharge velocity** $v$ is the quantity of water flowing per unit time through a unit gross cross-sectional area of the soil (solids plus voids). **Seepage velocity** $v_s$ is the actual velocity of water through the void space, which is only a part of the area.

$$
v = \frac{Q}{A}, \qquad v_s = \frac{Q}{A_v} = \frac{v}{n}
$$

where $A_v = nA$ is the area of voids and $n$ is porosity.

| Point | Discharge velocity | Seepage velocity |
|---|---|---|
| Area used | Gross area $A$ | Void area $A_v$ |
| Formula | $v = ki$ | $v_s = v/n = ki/n$ |
| Nature | Fictitious (average) velocity | Actual velocity in pores |
| Magnitude | Smaller | Larger, since $n<1$ |
| Use | Computing discharge $Q = vA$ | Time of travel of water or contaminant |

## Check yourself

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

1. Discharge velocity uses:
   A. Void area
   B. Gross cross-sectional area
   C. Perimeter
   D. Solid area
   Answer: B. v = Q/A. (Key point: Discharge velocity)

2. Seepage velocity in terms of v and n:
   A. v*n
   B. v/n
   C. v/(1+n)
   D. v(1-n)
   Answer: B. vs = Q/(nA) = v/n. (Key point: Seepage velocity)

3. Seepage velocity is larger because:
   A. n > 1
   B. n < 1
   C. water accelerates
   D. k is large
   Answer: B. Water flows through only the void area. (Key point: Magnitude)

## Related in Soil Mechanics

- [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
- [Seepage in anisotropic soil](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aseepage-anisotropic-soil-derivation) — Soil Mechanics, chapter 7
- [Impervious dam seepage discharge](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aimpervious-dam-seepage-discharge-numerical) — Soil Mechanics, chapter 7
- [Seepage and superficial velocity relation](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aseepage-superficial-velocity-relation) — Soil Mechanics, chapter 6
- [Discharge velocity](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Adischarge-velocity-define) — Soil Mechanics, chapter 6
- [Normally vs over consolidated soil](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Anormally-vs-over-consolidated) — Soil Mechanics, chapter 9, asked 2×

## Related in other subjects

- [Seepage discharge through dam body (k = 1×10⁻⁶ m/s)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Aearthen-dam-seepage-gradient-figure-2072k) — Hydropower Engineering, chapter 4
- [Seepage through dam with central core (45 m dam)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Aearthen-dam-impervious-core-seepage-2075c) — Hydropower Engineering, chapter 4
- [Velocity, head loss, discharge in loop pipes BC, CD, BF, FD](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Aloop-a76) — Water Supply Engineering, chapter 7
- [Seepage through dam with central core (33 m dam)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Aearthen-dam-impervious-core-seepage-2070c) — Hydropower Engineering, chapter 4