Flow dimensionality – interpretation of streamlines A flow whose streamlines form a curve in a plane (i.e., velocity components vary in two spatial directions) is best described as:

Introduction:
Flow dimensionality classifies how many spatial coordinates are needed to describe variations in the velocity field. This question probes the distinction between one-dimensional, two-dimensional, and three-dimensional flow descriptions using streamlines.

Given Data / Assumptions:

• Steady visualization of streamlines in a plane.
• Streamlines are curves rather than straight, indicating lateral variation.
• Out-of-plane variations are negligible (typical textbook 2D idealization).

Concept / Approach:
In one-dimensional flow, properties vary along only one coordinate and are uniform across cross-sections; streamlines are effectively parallel lines. In two-dimensional flow, velocity components depend on two coordinates (e.g., x and y), producing curved streamlines within a plane. Three-dimensional flow would require variations in all three spatial directions.

Step-by-Step Solution:
1) Observe that streamlines bend within a plane → lateral gradients exist.2) Lateral gradients imply dependence on two coordinates (say x and y).3) Therefore, the appropriate idealization is two-dimensional flow.

Verification / Alternative check:
Potential-flow solutions around cylinders or airfoils in a 2D section produce curved streamlines but ignore spanwise (z) variations, matching the 2D definition.

Why Other Options Are Wrong:

• One-dimensional flow: would have straight, non-bending streamlines in the plane.
• Three-dimensional flow: requires out-of-plane variation not stated here.
• Four-dimensional flow: not a standard fluid-mechanics classification.

Common Pitfalls:
Assuming any curve means 3D; curvature in a single plane is a hallmark of 2D modeling.

Final Answer:
two-dimensional flow