Flow nets and seepage direction: During steady seepage through porous soil, the direction of seepage flow is always related to equipotential lines how?

Introduction / Context:
Flow nets are graphical solutions to Laplace’s equation for groundwater flow. They consist of two families of orthogonal curves: equipotential lines and streamlines. Knowing the relationship between them is vital for interpreting seepage directions and hydraulic gradients under dams, sheet piles, and retaining structures.

Given Data / Assumptions:

• Steady, two-dimensional seepage in a homogeneous, isotropic soil.
• No sources or sinks within the domain besides boundaries.

Concept / Approach:
Equipotential lines connect points of equal total head. Streamlines represent the path of seepage flow. In isotropic media solving Laplace’s equation, these families intersect at right angles. Therefore, the seepage velocity vector is normal to equipotential lines and tangent to streamlines.

Step-by-Step Solution:

Verification / Alternative check:
Finite difference/finite element groundwater models yield velocity vectors perpendicular to equipotential contours in isotropic zones; anisotropy skews angles in transformed space but remains perpendicular in transformed coordinates.

Why Other Options Are Wrong:

• Parallel to equipotentials: incorrect; no head drop along equipotential.
• Perpendicular to streamlines contradicts definition.
• Independence from equipotential pattern is false; both are linked solutions to Laplace’s equation.
• Parallel to both is impossible unless trivial uniform flow without head change.

Common Pitfalls:
Misreading flow nets; forgetting anisotropy effects (use transformed scales).

Final Answer:
Perpendicular to equipotential lines (i.e., along streamlines)