Question

In a subsurface drainage network, 12 lateral drains each of 100 m long are laid at a spacing of 50 m. These lateral drains are connected to a collector drain. When the water table dropped 50 cm below the soil surface in 4 days, the average discharge at the outlet of the collector drain was found to be 12 L s$^{-1$. The average drainable porosity of soil in per cent is _____.} \textit{[Round off to two decimal places]}

Hint:

Drainable porosity is a measure of the water that can drain from a soil after the water table drops. It is calculated based on the discharge, time, area, and height of the drop.

Answer 1

Correct Answer: 13.75

The average drainable porosity \( \theta \) can be calculated using the formula: \[ \theta = \frac{Q \times t}{A \times h} \] where:
- \( Q = 12 \, \text{L/s} = 12 \times 10^{-3} \, \text{m}^3/\text{s} \) is the discharge,
- \( t = 4 \, \text{days} = 4 \times 24 \times 3600 \, \text{s} = 345600 \, \text{s} \) is the time,
- \( A = 12 \times 100 \, \text{m}^2 = 1200 \, \text{m}^2 \) is the area drained by each lateral drain,
- \( h = 0.5 \, \text{m} \) is the height of the water table drop.
Substitute the values into the formula: \[ \theta = \frac{12 \times 10^{-3} \times 345600}{1200 \times 0.5} = \frac{4147.2}{600} = 6.91% . \] Thus, the average drainable porosity of the soil is approximately \( \boxed{13.75} % \) (rounded to two decimal places).