Flow is the transport of matter from one place to another. We define an area and see how much matter passes through it per instant.Ā
Flow must be equal at every point along the way of an incompressible fluidās volume. Since flow is Av area times velocity, (A_1)(v_1) must be equal to (A_2)(v_2), and this defines the continuity equation.Ā
The pressure is not the same at every point in a fluid as the fluid is moving.Ā
Bernoulliās principle related this with work and kinetic energy:
W = Ā½ ro(v2^2 - v1^2)dV = (P1 - P2)dV P + Ā½(ro)v1^2 = P2 + Ā½(ro)v2^2 V2 = v1A1 / A2
In short, itās a statement of conservation of mass and energy.