Contiuity Equation for Fluid Dynamics

Linking the Speed, Density and Pipe Width

The continuity equation is an important link between the speed of a fluid flow, its density and the width of the pipe it is flowing through.

The volume flux, Q, of an incompressible fluid flowing in a pipe is constant.

Q=u.nA

where u is the fluid velocity and n is the unit vector perpendicular to the pipe's cross section.

In the more general case of a compressible fluid flowing in three dimensions, in the absence of sinks or sources of fluid:

div(ρ.u) = 0