Clogged drainage pipe soil volume

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.