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Solved: Evaluate the three-dimensional divergence V v for
Chapter 13, Problem 13.32(choose chapter or problem)
Evaluate the three-dimensional divergence V v for each of the following vectors: (a) v = (b) v = kxx, (c) v = kyi. We know that V v represents the net outward flow associated with v. In those cases where you found V v = 0, make a simple sketch to illustrate that the outward flow is zero; in those cases where you found V v 0, make a sketch to show why and whether the outflow is positive or negative.
Questions & Answers
QUESTION:
Evaluate the three-dimensional divergence V v for each of the following vectors: (a) v = (b) v = kxx, (c) v = kyi. We know that V v represents the net outward flow associated with v. In those cases where you found V v = 0, make a simple sketch to illustrate that the outward flow is zero; in those cases where you found V v 0, make a sketch to show why and whether the outflow is positive or negative.
ANSWER:Step 1 of 3
We have to evaluate the three-dimensional divergence V v for (a), (b) and (c)
It is straightforward to calculate divergence of fields:
