Question

Stream function is defined for

• A. 2-D flows
• B. 3-D flows
• C. Complex plane
• D. Irrotational flows

Hint:

Contours of constant stream function represent streamlines in 2-D flow.

Answer 1

The Correct Option is A

The concept of a stream function is predominantly used in fluid dynamics for analyzing flow patterns in two-dimensional flows. This function is particularly valuable for visualizing and solving problems involving incompressible flows, where the velocity field can be derived from the stream function. For a two-dimensional incompressible flow in the (x, y) plane, the stream function, ψ, is defined such that:

• The velocity component in the x-direction, u, is given by the partial derivative of ψ with respect to y: \(u = \frac{\partial \psi}{\partial y}\).
• The velocity component in the y-direction, v, is given by the negative partial derivative of ψ with respect to x: \(v = -\frac{\partial \psi}{\partial x}\).

These relationships ensure that the continuity equation for incompressible flow is automatically satisfied, as the divergence of the velocity field is zero. Therefore, the correct context for the stream function is 2-D flows.