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Soil Mechanics and Foundation Engineering - Engineering

Q1:

In a fow net

A flow lines and equipotential lines cross each other at right angles

B fields are rectangles whose length is twice the breadth

C smaller the dimensions of the field, smaller will be the hydraulic gradient and velocity of flow through it

D for homogeneous soil, the curves are smooth and circular.

ANS:A - flow lines and equipotential lines cross each other at right angles

  1. Flow Lines: Flow lines represent the paths that fluid particles would take as they move through the porous medium under the influence of hydraulic gradients. These lines indicate the direction of flow at any point in the medium.
  2. Equipotential Lines: Equipotential lines represent points of equal hydraulic potential within the medium. Hydraulic potential is a measure of the total energy per unit weight of fluid in the system and is composed of pressure head, elevation head, and velocity head.
When these lines intersect at right angles in a flow net, it signifies certain fundamental principles of fluid flow and potential theory:
  • Orthogonality Principle: The orthogonality principle states that flow lines and equipotential lines are perpendicular to each other at any point in a steady-state flow field. This principle arises from mathematical and physical principles governing fluid flow and potential fields.
  • Conservation of Mass: The orthogonality of flow lines and equipotential lines ensures that mass is conserved within the flow field. The flow lines represent streamlines along which fluid particles move, while the equipotential lines represent surfaces of constant hydraulic potential. The perpendicular intersection between these lines ensures that fluid flux across the lines is balanced and mass is conserved.
  • Mathematical Consequence: In two-dimensional flow, the Laplace equation governs the relationship between flow and potential fields. The solutions to the Laplace equation result in equipotential lines and flow lines crossing each other at right angles.