Section 4: Soil and Water Conservation Engineering
Soil Mechanics
Subtopic: Permeability and seepage analysis
Question Statement:
A flow net constructed under a concrete dam foundation indicates $4$ flow channels ($N_f = 4$) and $16$ equipotential drops ($N_d = 16$). The total hydraulic head causing seepage is $6.0\text{ m}$ and the coefficient of permeability of the foundation soil is $2.5 \times 10^{-5}\text{ m/s}$. The seepage loss per unit length of the dam in $\text{m}^3\text{/(day}\cdot\text{m)}$ is ________ (round off to 2 decimal places).
Answer Key:
3.24
Step-by-Step Solution & Explanation
Seepage discharge per unit width $q$ through a flow net is:
$q = k H \frac{N_f}{N_d}$
Given:
• $k = 2.5 \times 10^{-5}\text{ m/s}$
• $H = 6.0\text{ m}$
• $N_f = 4$
• $N_d = 16 \implies \frac{N_f}{N_d} = \frac{4}{16} = 0.25$
$q = (2.5 \times 10^{-5}) \times 6.0 \times 0.25 = 3.75 \times 10^{-5}\text{ m}^3\text{/(s}\cdot\text{m)}$
Converting to $\text{m}^3\text{/(day}\cdot\text{m)}$ ($1\text{ day} = 86,400\text{ s}$):
$q = 3.75 \times 10^{-5} \times 86400 = 3.24\text{ m}^3\text{/(day}\cdot\text{m)}$