The fluid continuity equation is based on the Law of Conservation of Mass and the principle of streamlines.
Consider a tube with a small diameter at one end and a large diameter at the other - like a wind tunnel, or like a funnel, but longer. Because there can be no flow across streamlines, within a tube of expanding diameter in steady flow (invariant with time), the mass flowing through a given cross sectional area must be equal to the mass flowing through every other cross sectional area in the same amount of time. This is known as mass flow, and can be represented as the product of density, velocity, and area - or the derivative of mass with respect to time.
Hence, the continuity equation consists of the relation:
ρ1A1V1 = ρ2A2V2
where ρ is density, A is area, and V is velocity.
For highly incompressible fluids, such as water, density is constant and need not be accounted for in the equation.
The continuity equation is used in physics classes and by aeronautical and marine engineers.