Continuity Equation

The continuity equation is used to relate a fluid’s velocity to a change in the pipe’s cross-sectional area. There are two versions of the continuity equation, one version is for a compressible fluid (equation 1) since the density could change as the pressure changes, while the other is for an incompressible fluid (equation 2). When using these equations there is an assumption that the flow rate is constant.

(Eq 1)  $ρ_1A_1v_1=ρ_2A_2v_2 $

ρ = Density

A = Cross-Sectional Area

v = Velocity

(Eq 2)   $A_1v_1=A_2v_2~or~Q_1=Q_2$

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