Flow Kinematics – Can Two-Dimensional Flow Curves Bend? In two-dimensional flow (velocity components in two orthogonal directions, with no variation in the third), the particle paths and streamlines can be curved; two-dimensional does not imply straight-line motion.

Introduction:“Two-dimensional” describes how velocity varies in space, not the geometric shape of streamlines. Many classic 2D flows (flow around a cylinder, potential vortices) have strongly curved paths while remaining two-dimensional in description.

Given Data / Assumptions:

• Velocity depends on two coordinates (e.g., u(x,y), v(x,y)), and is uniform in the third.
• No restriction on streamline curvature is implied by dimensionality.
• Fluid may be viscous or inviscid; rotational or irrotational.

Concept / Approach:

Streamlines are tangent to the velocity vector field at every point. If the velocity direction changes with position in a plane, streamlines bend accordingly, yet the flow remains two-dimensional so long as there is no dependence on the third coordinate and the velocity component in that direction is zero.

Step-by-Step Solution:

Verification / Alternative check:

Potential flow past a cylinder is exactly two-dimensional and exhibits highly curved streamlines; laboratory dye studies confirm this.

Why Other Options Are Wrong:

Conditioning truth on irrotationality or uniformity is irrelevant; curvature occurs in both rotational/irrotational and uniform/non-uniform cases. Viscosity does not determine 2D streamline curvature.

Common Pitfalls:

Equating two-dimensional with straight channels; confusing spatial dimensionality with path geometry.

Final Answer:

False