MHB Volume of Liquid: Proving $\overrightarrow{v}\cdot\overrightarrow{n}$

[mathmari]

Hey!

A liquid flows through a flat surface with uniform vector velocity $\overrightarrow{v}$.

Let $\overrightarrow{n}$ an unit vector perpendicular to the plane.

Show that $\overrightarrow{v} \cdot \overrightarrow{n}$ is the volume of the liquid that passes through the unit surface of the plane in the unit of time.

Could you give me some hints how we could show this?? (Wondering)

 

[mathmari]

I found the following:

Volumetric flow rate - Wikipedia, the free encyclopedia

To show that $\overrightarrow{v} \cdot \overrightarrow{n}$ is the volume of the liquid that passes through the unit surface of the plane in the unit of time, do we use the justification at the part "The reason for the dot product is as follows" of wikipedia?? (Wondering)

 

[I like Serena]

Yep. (Nod)