Question Bank • QB_SWCE_ADV_103 MSQ • 2 Marks

Section 4: Soil and Water Conservation Engineering

Soil Mechanics

Subtopic: Permeability and seepage analysis

Question Statement:

Which of the following geometric and hydraulic properties of a flow net drawn for two-dimensional steady seepage through an isotropic earthen dam are correct? ``` Upstream Water Level ───┐ │ Flow Line Ψ1 ──────────────────────┐ ├─── Flow Line Ψ2 ──────────────┐ │ Impermeable Core │ │ Equipotential Φ1 │ │ │ │ │ │ │ ───────────────────────┴──────┴──────┴─────────────────┴─────┴── Impermeable Stratum ```

Options:

  • (A) Flow lines (streamlines $\Psi$) and equipotential lines ($\Phi$) intersect orthogonally at right angles ($90^\circ$)
  • (B) The basic flow fields formed between adjacent streamlines and equipotentials are curvilinear squares
  • (C) The seepage discharge through each individual flow channel is identical ($\Delta q = k H / N_d$)
  • (D) The total seepage quantity increases linearly with the number of potential drops $N_d$

Answer Key:

A, B, C

Step-by-Step Solution & Explanation

- Statements A, B, and C are correct: 1. In isotropic media ($k_x = k_y$), the Cauchy-Riemann conditions mandate that potential and stream functions are orthogonal. 2. For a square flow net, the aspect ratio of each curvilinear cell is unity ($b/l \approx 1$). 3. Each flow channel carries $\Delta q = k \Delta h = k \frac{H}{N_d}$. - Statement D is incorrect: Total seepage is $q = k H \frac{N_f}{N_d}$; seepage is inversely proportional to the number of potential drops $N_d$, not directly proportional.
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