Question

What will be the ratio of quantity of seepage per meter length in sand to clay layer, if the potential drops and flow lines are equal for the same thickness, if ksand­ = 3 × 10-3 cm/sec and kclay = 9 × 10-7 cm/sec
1. 10⁴/3
2. 3
3. 1/9
4. 9

Answer 1

Correct Answer - Option 1 : 10⁴/3

Concept:

Determination of seepage discharge when the medium is isotropic:

Seepage discharge per meter length is given by, \(q = kh\frac{{{N_f}}}{{{N_d}}}\)

Where, h = Hydraulic head or head difference between upstream and downstream level or head loss through the soil

Nf = Total number of flow channels

Nd = Total number of equipotential drops

k = Coefficient of permeability

Calculation:

Permeability of sand, Ksand = 3 × 10^-3 cm/sec

Permeability of clay, Kclay = 9 × 10^-7 cm/sec

h, N_f and N_d are same for both the soil (given in the question)

∵ \(q = kh\frac{{{N_f}}}{{{N_d}}}\)

⇒ q ∝ K

\(\frac{{{q_{sand}}}}{{{q_{clay}}}} = \frac{{{K_{sand}}}}{{{K_{clay}}}}\)

⇒ \(\frac{{{q_{sand}}}}{{{q_{clay}}}} = \frac{{3 \times {{10}^{ - 3}}}}{{9 \times {{10}^{ - 7}}}} = \frac{1}{3} \times {10^4}\)