Equation of Continuity

The volume of fluid flowing through a point in an area in unit time gives the volume flow rate.

On substituting volume with area times distance, and using the relation between velocity and distance, volume flow rate equals area times velocity of the fluid.

Consider an incompressible fluid with the same density at all points flowing steadily through an irregular cross-sectional pipe. For a steady flow, the velocity and density of the fluid at a point remain constant with time.

The mass of the fluid passing through a point per unit time is termed as mass flow rate, and it equals density times the volume flow rate.

Since the pipe does not have any other source or sink, the mass flowing into the pipe must equal the mass leaving the pipe. This gives the general equation of continuity for fluids.

For incompressible fluids, density cancels out. Hence, the volume flow rate into the pipe equals the volume flow rate out of the pipe.