A streamline and an equipotential line in a flow field - (a) Are parallel to each other (b) Are perpendicular to each other (c) Intersect at an acute angle (d) Are identical

By Ritesh|Updated : November 1st, 2022

A streamline and an equipotential line in a flow field are perpendicular to each other. It is a hypothetical curve created in space whose tangent at any location will reveal the fluid particle's velocity at any given instant in time. A streamline is a line where the stream function (ψ) is constant.

Streamline and Equipotential Line

There are no turbulent velocity fluctuations in this situation at low fluid speeds, and the fluid tends to flow without lateral mixing. Here, the fluid's particle motion occurs in a specific order with respect to the particles traveling parallel to the pipe wall, causing the neighboring layers to slide past one another like playing cards.

Properties:

• An equipotential surface is always perpendicular to the electric field.
• Never can two equipotential surfaces meet.
• The equipotential surfaces for a point charge are spherical shells with concentric radii.
• The equipotential surfaces for a homogeneous electric field are planes perpendicular to the x-axis.
• Equipotential surfaces run in the high potential to low potential direction.

(dy/dx)ϕ x (dy/dx)ψ = -1

The slope of equipotential Line × Slope of stream function = -1

They are at right angles to one another.

Other Method -

For a streamline, ψ (x, y) = constant and the differential of ψ is zero.

dψ = dψ/dx dx + dψ/dy dy

dψ = -vdx + udy

(dy/dx)ψ = constant = v/u

For an equipotential line, ϕ (x, y) = constant and the differential of ϕ is zero.

dϕ = dϕ/dx dx + dϕ/dy dy

dϕ = udx + vdy

(dy/dx)ϕ = constant = -u/v

(dy/dx)ψ = constant = -1/ (dy/dx)ϕ = constant

Summary:

A streamline and an equipotential line in a flow field - (a) Are parallel to each other (b) Are perpendicular to each other (c) Intersect at an acute angle (d) Are identical

In a flow field, an equipotential line and a streamline are perpendicular to one another. The equipotential line is a line where the velocity potential function is constant.