Find the points where the fluid flowing into a point equals the fluid flowing out by setting the divergence of the vector field to zero.

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Points of Zero Divergence in a Fluid Flow

Multivariable calculus warmup

For vector field \( \mathbf{v}(x, y) = \langle -xy, y \rangle \), \( y > 0 \), find all points \( P \) such that the amount of fluid flowing in to \( P \) equals the amount of fluid flowing out of \( P \).

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What you need first

The definition of the divergence of a 2D vector field
How to compute partial derivatives
The physical interpretation of divergence in fluid dynamics

What this problem tests

Tests the student's ability to connect a physical description of fluid flow to the mathematical concept of divergence, and to compute it.

This problem is typical in a multivariable or vector calculus course when introducing the physical interpretation of divergence.

Points of Zero Divergence in a Fluid Flow

What you need first

What this problem tests

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