---
title: "Seepage and superficial velocity relation"
subject: "Soil Mechanics"
chapter: 6
key: "semester_4/soil_mechanics:seepage-superficial-velocity-relation"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/seepage-superficial-velocity-relation
site: BCT Engineering
---

# Seepage and superficial velocity relation

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

- Asked in: 2073 Bhadra, 3 marks
- Video: [Soil Mechanics 3.2 | Seepage Velocity | Shubham Sarathe](https://www.youtube.com/watch?v=8HOIgsQeMp8) — EIQ
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/seepage-superficial-velocity-relation
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-6

## Question

Establish the relationship between seepage velocity and superficial velocity.

## Short answer

Superficial velocity v = Q/A is based on gross area. Seepage velocity v_s is the actual average velocity in the voids: v_s = v/n, where n is porosity. Because n<1, v_s > v. In terms of void ratio, v_s = v(1+e)/e.

## Answer

Superficial (discharge) velocity $v$ is based on the total area; seepage velocity $v_s$ is the real velocity in the voids.

#### Derivation

Consider a soil of gross cross-section $A$ and length $L$. Let $A_v$ be the area of voids on the cross-section and $V_v$, $V$ the volumes of voids and total.

$$
n = \frac{V_v}{V} = \frac{A_v L}{A L} = \frac{A_v}{A}
$$

Let the discharge be $Q$. It passes through the gross area $A$ at velocity $v$ and through the void area $A_v$ at velocity $v_s$:

$$
Q = v A = v_s A_v
$$

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

Since $v = k i$:

$$
v_s = \frac{k\,i}{n}
$$

Since $n<1$, $v_s > v$. In terms of void ratio, $n = \dfrac{e}{1+e}$ so $v_s = v\,\dfrac{1+e}{e}$.

## Check yourself

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

1. Porosity n equals the ratio:
   A. A_v / A on a cross-section (same as V_v / V)
   B. A / A_v
   C. V / V_v
   D. A_v / L
   Answer: A. n = V_v/V = A_v L/(A L) = A_v/A. (Key point: Porosity as area ratio)

2. The derivation uses Q equal to:
   A. v A_v = v_s A
   B. v A = v_s A_v
   C. v n = v_s
   D. v L = v_s A
   Answer: B. The same discharge passes through gross area at v and through voids at v_s. (Key point: Continuity)

3. The relation between seepage and superficial velocity is:
   A. v_s = v n
   B. v_s = v
   C. v_s = v / n
   D. v_s = v (1 - n)
   Answer: C. v_s = v A/A_v = v/n. (Key point: Result)

4. In terms of void ratio, v_s equals:
   A. v e/(1+e)
   B. v (1+e)/e
   C. v e
   D. v/(1+e)
   Answer: B. n = e/(1+e), so v_s = v (1+e)/e, which is greater than v. (Key point: In terms of e)

## 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
- [Seepage in anisotropic soil](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aseepage-anisotropic-soil-derivation) — Soil Mechanics, chapter 7

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