Angle between streamlines and equipotential lines

The angle between streamlines and equipotential lines in a flow net depends on the type of flow and the boundary conditions of the problem. In general, the angle between these lines can vary, but at the point of intersection, the angle is always 90°.

Flow net

A flow net is a graphical representation of the flow field in a two-dimensional problem. It consists of a network of streamlines and equipotential lines that intersect each other at right angles. Streamlines represent the path followed by fluid particles, while equipotential lines represent lines of equal hydraulic head.

Explanation

When streamlines and equipotential lines intersect at a point, it means that the fluid particles at that point are moving along the same path and have the same hydraulic head. Since streamlines and equipotential lines are perpendicular to each other at this point, the angle between them is 90°.

At the point of intersection, the fluid particles are moving in a direction perpendicular to the equipotential lines, which means that the pressure gradient is perpendicular to the equipotential lines. This condition is satisfied when the flow is governed by Darcy's law and the flow is steady and incompressible.

In such cases, the flow net represents a flow field that satisfies the governing equations of fluid flow. The flow net is a useful tool in solving problems related to seepage, groundwater flow, and flow through porous media.

To summarize, at the point of intersection in a flow net, the angle between streamlines and equipotential lines is always 90°. This condition is satisfied when the flow is steady, incompressible, and governed by Darcy's law.