Section 4: Soil and Water Conservation Engineering
Soil Permeability, Seepage & Flow Nets
Subtopic: Properties of flow net
Question Statement:
Which of the following statements regarding orthogonal flow nets is/are TRUE?
Options:
(A) Flow lines (streamlines) and equipotential lines intersect orthogonally at $90^\circ$ everywhere in an isotropic soil
(B) The rate of seepage through each flow channel between adjacent streamlines is equal
(C) The drop in total head between any two adjacent equipotential lines is constant ($Δh = H / N_d$)
(D) In anisotropic soil where $k_x \ne k_z$, flow nets can only be drawn after transforming coordinates by $x' = x \sqrt{k_z/k_x}$
Answer Key:
A, B, C, D
Step-by-Step Solution & Explanation
All four properties define classical flow net theory for Laplace's equation $\nabla^2 h = 0$:
1. Orthogonality holds strictly for isotropic media ($k_x = k_z$).
2. By definition of flow channel, $\Delta q = k \Delta h (b/a)$; for square elements ($b/a = 1$), $\Delta q$ is identical in every channel.
3. Head loss per field is $\Delta h = H / N_d$.
4. For anisotropic permeability, coordinate transformation $x' = x \sqrt{k_z/k_x}$ restores Laplace form $\frac{\partial^2 h}{\partial x'^2} + \frac{\partial^2 h}{\partial z^2} = 0$.
All options A, B, C, D are correct.