Velocity field classification in two-dimensional flow: for u = a x and v = b y, what is the point called where the local velocity becomes zero?

Introduction / Context:
In fluid kinematics, understanding the velocity field helps identify special locations such as stagnation points, saddle points, and vortical centers. These points control streamlines and pressure distributions and are fundamental in potential-flow theory and CFD post-processing.

Given Data / Assumptions:

• Two-dimensional velocity components u = a x and v = b y in Cartesian coordinates.
• a and b are constants; incompressibility is not assumed unless a + b = 0.
• Steady flow field; no body forces considered for this kinematic classification.

Concept / Approach:

A stagnation point is defined as a point in the flow where the local fluid velocity vector is zero. For the given linear field, the velocity components vanish when x = 0 and y = 0 simultaneously, i.e., at the origin. The term “stationary point” is a general mathematical phrase; in fluid mechanics, the precise term for zero velocity is “stagnation point.”

Step-by-Step Solution:

Verification / Alternative check:

Compute speed V = √(u^2 + v^2) = √((a x)^2 + (b y)^2). This is zero only when x = 0 and y = 0, confirming the classification.

Why Other Options Are Wrong:

(a) “Critical point” is ambiguous without additional context; (b) “neutral point” is not standard velocity-field terminology; (d) “stationary point” is mathematical jargon but lacks the specific fluid meaning; (e) incorrect because a precise standard term exists.

Common Pitfalls:

Confusing stagnation with separation points; forgetting that pressure is typically maximum at stagnation in inviscid steady flow due to Bernoulli’s principle along streamlines.

Final Answer:

stagnation point