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Let suppose that $\vec{F}$ is the velocity vector field of of a fluid in space, and $\vec{s}$ is a straight path of arbitrary length. Let's suppose that $\vec{F}$ and $\vec{s}$ are parallels and point in the same direction, so that $\vec{F} \cdot \vec{s} = F s$. How can we account for the total amount of fluid that moves along the path (per unit of time).

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  • $\begingroup$ I don't think you can get a non-infinitesimal answer by using a one-dimensional path $\vec s$. Don't you need some type of non-zero cross-sectional area to your path? $\endgroup$
    – BMS
    Commented Jun 27, 2014 at 22:16

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