The motion of a liquid in a cylindrical container of radius 1 is described by the velocity field $\mathbf { F } ( x , y , z ) = 5 \mathbf { i } + 6 \mathbf { j } - 7 \mathbf { k }$. Find $\iint _ { S } ( \operatorname { curl } \mathbf { F } ) \cdot \mathbf { N } d S$, where $S$ is the upper surface of the cylindrical container.
A) 5
B) 7
C) 2
D) 0
E) 3

Question

Quizplus · Accepted Answer

The curl of a constant vector field is zero, and the surface integral of zero over any surface is also zero.

The Motion of a Liquid in a Cylindrical Container of Radius