Control volume

A control volume is a portion of space on which a set of equations is applied. In a control volume, all quantities are conserved, which means that in a dynamic case, the geometry of the control volume is a function of time.

In fluid Mechanics

In fluid mechanics the constitutive equations (Navier-Stokes equations) are by nature integral. They therefore apply on volumes. Finding forms of the equation that are independent of the control volumes allows simplification of the integral signs.