Question

In mathematical modeling, for which option, a fluid flow can be approximated by a two-dimensional model?

(a) One of the dimensions is very small, and there is some flow along with it

(b) One of the dimensions is very long, and there is no flow along with it

(c) One of the dimensions is very long, and there is some flow along with it

(d) The velocity components in two directions vary along the third direction

The question was posed to me during an online exam.

I would like to ask this question from Governing Equations topic in section Flows of Viscous Incompressible Fluids of Finite Element Method

Answer 1

Right option is (b) One of the dimensions is very long, and there is no flow along with it

For explanation I would say: For a fluid flow, assuming that one of the dimensions say, along the z-direction (into the plane of the screen) of the domain is very long, and there is no flow along that direction. The velocity components in the other two directions (vx and vy) do not vary with the z-direction. Under these conditions, the flow can be approximated by a two-dimensional model.