Flow net fundamentals in seepage analysis: Identify the correct statement regarding the geometry and properties of flow lines and equipotential lines in a flow net for homogeneous soil.
-
AFlow lines and equipotential lines intersect each other at right angles
-
BFields are rectangles whose length is exactly twice the breadth
-
CSmaller field dimensions imply smaller hydraulic gradient and smaller velocity
-
DIn homogeneous soil, the curves are smooth and generally circular
-
EFields are approximately curvilinear squares (equal aspect ratio)
Answer
Correct Answer: Flow lines and equipotential lines intersect each other at right angles
Explanation
Introduction / Context:Flow nets provide a graphical solution to two-dimensional steady seepage governed by Laplace’s equation. Correct interpretation of their geometry underpins estimates of seepage quantity and uplift pressures below hydraulic structures such as weirs and cutoffs.
Given Data / Assumptions:
- Homogeneous, isotropic soil.
- Steady-state two-dimensional flow.
- Properly constructed flow net with flow lines and equipotential lines.
Concept / Approach:
By definition, flow lines represent streamlines and equipotential lines represent loci of equal total head. Laplace’s equation requires these two families of orthogonal curves. The net is ideally composed of approximately curvilinear squares, not rectangles with prescribed 2:1 ratios. Smaller field dimensions do not reduce hydraulic gradient; rather, for a given potential drop per square, shorter path lengths imply larger local gradients.
Step-by-Step Solution:
Orthogonality property → flow and equipotential lines cross at 90°.Field shape → approximate squares (not necessarily 2:1 rectangles).Gradient intuition → smaller path length for same head loss → larger gradient and velocity.Verification / Alternative check:
Classic texts show flow nets with nearly square curvilinear fields; orthogonality is a direct consequence of harmonic functions for head.
Why Other Options Are Wrong:
(b) Imposes an arbitrary 2:1 geometry; (c) reverses the gradient behavior; (d) lines are smooth, not “generally circular.” (e) is close to a correct description but does not directly answer the stated property as clearly as (a).
Common Pitfalls:
Ignoring isotropy; poor net drawing that violates orthogonality and square field requirement.
Final Answer:
Flow lines and equipotential lines intersect each other at right angles