• id: JME-09-N06
• title: Continuity Equation for Incompressible Fluids
• tags: continuity, flow-rate, conservation-mass

For an incompressible fluid in steady flow through a pipe of varying cross-section: $A_1 v_1 = A_2 v_2 = Q$ (constant volume flow rate). This is conservation of mass — what flows in must flow out. $Q = Av$ has units m$^3$/s. If the pipe narrows ($A_2 < A_1$), velocity increases ($v_2 > v_1$) — like placing your thumb over a hose nozzle. Mass flow rate $\dot{m} = \rho A v$ (kg/s) is constant for both compressible and incompressible fluids, but volume flow rate $Av$ is constant only for incompressible fluids.