The area of pipe or process vessel cut perpendicular to its axis. The cross-sectional area is the area through which material passes. For a circular cross section, the area related to diameter by $a=\frac{\pi d^2}{4}$. The volume of the pipe or vessel, V, is the cross-sectional area multiplied by the length $V=al$. The average velocity, v, of the movement of a fluid through a pipe is the volumetric flow, Q, divided by the cross-sectional area $v=\frac{Q}{a}$.