Seepage Analysis MCQ with answer and solution

Concept

Flow Net and Laplace's Equation

Formula

Yes, Laplace's equation for two-dimensional steady-state flow: ∂²h/∂x² + ∂²h/∂z² = 0 For calculating total seepage quantity (q) using a flow net: q = k × H × (Nf / Nd) Where: - k = Coefficient of permeability - H = Total hydraulic head loss - Nf = Number of flow channels - Nd = Number of equipotential drops

Step-by-step solution

1. Identify that a flow net represents two-dimensional steady-state seepage through isotropic soil. 2. Recall that the governing mathematical equation for 2D steady-state groundwater flow is Laplace's equation (∂²h/∂x² + ∂²h/∂z² = 0). 3. Conclude that a flow net is the graphical solution to Laplace's equation.

Explanation

A flow net is a graphical representation of two-dimensional groundwater flow. It consists of equipotential lines and flow lines that intersect at right angles, serving as a solution to Laplace's equation for steady-state seepage through isotropic soil.

Shortcut

Remember: "Flow Net" = Laplace's Equation. Think of water flowing smoothly into a "Lap" (Laplace).

Common mistake

Students often confuse a flow net with Darcy's law or the Darcy-Weisbach equation because both relate to fluid flow through soil or pipes. They wrongly select Option B (Darcy-Weisbach equation), forgetting that Darcy's law governs basic flow velocity while Laplace's equation governs the overall 2D differential continuity equation solved by a flow net.