Section 4: Soil and Water Conservation Engineering
Soil Mechanics
Subtopic: Permeability and seepage analysis
Question Statement:
A flow net is constructed for a homogeneous earthen dam of length $L = 120.0\text{ m}$. The total hydraulic head acting across the dam is $H = 12.0\text{ m}$. The soil coefficient of permeability is $k = 4.5 \times 10^{-6}\text{ m/s}$. The flow net consists of $N_f = 4$ flow channels and $N_d = 16$ equipotential drops. The total seepage discharge through the dam in liters per second ($\text{L/s}$) is ________ (round off to two decimal places).
Answer Key:
1.62
Step-by-Step Solution & Explanation
1. Seepage discharge per unit width of dam ($q$):
$q = k \cdot H \cdot \frac{N_f}{N_d}$
$q = (4.5 \times 10^{-6}\text{ m/s}) \times 12.0\text{ m} \times \frac{4}{16}$
$\frac{N_f}{N_d} = \frac{4}{16} = 0.25$
$q = 4.5 \times 10^{-6} \times 12.0 \times 0.25 = 1.35 \times 10^{-5}\text{ m}^3/(\text{s}\cdot\text{m})$
2. Total seepage discharge for total dam crest length $L = 120.0\text{ m}$:
$Q = q \times L = (1.35 \times 10^{-5}) \times 120.0 = 1.62 \times 10^{-3}\text{ m}^3/\text{s}$
3. Converting to liters per second:
$Q = 1.62 \times 10^{-3} \times 1000 = 1.62\text{ L/s}$