Section 4: Soil and Water Conservation Engineering
Soil Permeability, Seepage & Flow Nets
Subtopic: Seepage discharge under weir from flow net
Question Statement:
A flow net constructed under a diversion weir consists of $4$ flow channels and $12$ equipotential drops. The total hydraulic head across the weir is $H = 5.0\text{ m}$ and the hydraulic conductivity of the foundation soil is $k = 2.5 \times 10^{-5}\text{ m/s}$. The seepage discharge per unit length of the weir is ________ $\text{m}^3/\text{day per m}$ (round off to two decimal places).
Answer Key:
3.60
Step-by-Step Solution & Explanation
From flow net theory, the seepage discharge per unit width is:
$q = k H \frac{N_f}{N_d}$
Given $k = 2.5 \times 10^{-5}\text{ m/s}$, $H = 5.0\text{ m}$, $N_f = 4$, $N_d = 12$:
$q = (2.5 \times 10^{-5}) \times 5.0 \times \frac{4}{12} = 4.166667e-05\text{ m}^3/\text{s per m}$
Converting to $\text{m}^3/\text{day}$ ($1\text{ day} = 86400\text{ s}$):
$q = 4.166667e-05 \times 86400 = 3.600\text{ m}^3/\text{day per m}$
Rounding to two decimal places: $3.60\text{ m}^3/\text{day per m}$.