---
title: "Clogged drainage pipe soil volume"
subject: "Soil Mechanics"
chapter: 6
key: "semester_4/soil_mechanics:clogged-drainage-pipe-soil-volume"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/clogged-drainage-pipe-soil-volume
site: BCT Engineering
---

# Clogged drainage pipe soil volume

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

- Asked in: 2078 Poush, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/clogged-drainage-pipe-soil-volume
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-6

## Question

A drainage pipe is clogged with soil having coefficient of permeability 10 m/day. Due to clogging, the water level in the tank is raised to 20 m and the discharge is reduced to 0.15 m³/day. If the cross section of the pipe is 200 cm², what is the volume of soil in the pipe?

## Short answer

Apply Darcy's law to find the soil plug length: L = k h A / Q = (10 × 20 × 0.02) / 0.15 = 26.67 m. Volume = A × L = 0.02 × 26.67 = 0.533 m³.

## Answer

The soil plug in the pipe is a short column through which the tank water flows. Apply Darcy's law $Q = k\,\dfrac{h}{L}\,A$ to find its length $L$.

#### Given

$k = 10$ m/day, head $h = 20$ m, $Q = 0.15$ m³/day, $A = 200$ cm² $= 0.02$ m².

#### Length of soil plug

$$
L = \frac{k\,h\,A}{Q} = \frac{10 \times 20 \times 0.02}{0.15} = 26.67\ \text{m}
$$

#### Volume of soil

$$
V = A \times L = 0.02 \times 26.67 = 0.533\ \text{m}^3
$$

**Answer: The clogging soil is 26.67 m long, so its volume is about $0.533$ m³ ($\approx 533$ litres).**

The head is assumed to be fully lost through the plug.

## Check yourself

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

1. The soil plug in the pipe is treated as:
   A. A well with radial flow
   B. A soil column through which Darcy's law Q = k (h/L) A applies
   C. A flow net
   D. An unconfined aquifer
   Answer: B. Flow through the plug follows Darcy's law with the full head lost over its length L. (Key point: Model)

2. Rearranging Darcy's law, the plug length is:
   A. L = Q/(k h A)
   B. L = k h A / Q
   C. L = Q h/(k A)
   D. L = k A/(Q h)
   Answer: B. Q = k h A/L gives L = k h A/Q. (Key point: Length formula)

3. The pipe area 200 cm2 in m2 is:
   A. 0.2
   B. 0.002
   C. 0.02
   D. 2.0
   Answer: C. 200 cm2 = 200 x 10^-4 = 0.02 m2. (Key point: Unit conversion)

4. With L = 26.67 m, the volume of soil is about:
   A. 5.33 m3
   B. 0.533 m3
   C. 53.3 m3
   D. 0.0533 m3
   Answer: B. V = A L = 0.02 x 26.67 = 0.533 m3. (Key point: Volume)

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