Question

What is laplacian equation?

(a) d^2φ / dx^2 + d^2Φ/dz^2

(b) d^2Φ / dx^2 + d^2Φ/dz^2

(c) dΦ / dx + d^2Φ/dy^2

(d) d^2φ / dx^2 + d^2Φ/dz

This question was addressed to me in an online quiz.

This is a very interesting question from Seepage Theories in portion Seepage Theories and Weirs and Barrages Design of Irrigation Engineering

Answer 1

Right option is (b) d^2Φ / dx^2 + d^2Φ/dz^2

The explanation is: The laplacian equation is based on Φ(flow potential) which is a combination of flow potential Kh, where K is coefficient of permeability of soil and h is residual head at any point. The equation is represented as d^2Φ/dx^2 + d^2Φ/dz^2.