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 $H = 4.0\text{ m}$ 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:
2.88
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 $k = 2.5 \times 10^{-5}\text{ m/s}$, $H = 4.0\text{ m}$, $N_f = 4$, $N_d = 12$:
$q = (2.5 \times 10^{-5}) \times 4.0 \times \frac{4}{12} = 3.333333e-05\text{ m}^3/\text{s per m}$
Converting to $\text{m}^3/\text{day}$ ($1\text{ day} = 86400\text{ s}$):
$q = 3.333333e-05 \times 86400 = 2.880\text{ m}^3/\text{day per m}$
Rounding to two decimal places: $2.88\text{ m}^3/\text{day per m}$.