Continuity Equation

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Continuity equation is the moving of a quantity through a pipe in a steady flow.

 

continuity equation 1

Continuity Equation for Area formula

This formula calculates the initial cross-section area of the pipe.

\(\large{ A_1 = \frac{ \rho_2 \; A_2 \; v_2 }{ v_1 \; \rho_1 }  }\)   

Where:

\(\large{ A_1 }\) = initial area cross-section

\(\large{ A_2 }\) = final area cross-section

\(\large{ \rho_2 }\)  (Greek symbol rho) =  final cross-section density

\(\large{ \rho_1 }\)  (Greek symbol rho) =  initial cross-section density

\(\large{ v_2 }\) = final cross-section velocity

\(\large{ v_1 }\) = initial cross-section velocity

 

continuity equation 1Continuity Equation for Density formula

This formula calculates the initial density of the fluid.

\(\large{ \rho_1 = \frac{ \rho_2 \; A_2 \; v_2 }{ A_1 \; v_1 }  }\)   

Where:

\(\large{ \rho_1 }\)  (Greek symbol rho) =  initial cross-section density

\(\large{ A_2 }\) = final area cross-section

\(\large{ A_1 }\) = initial area cross-section

\(\large{ \rho_2 }\)  (Greek symbol rho) =  final cross-section density

\(\large{ v_2 }\) = final cross-section velocity

\(\large{ v_1 }\) = initial cross-section velocity

 

continuity equation mass 1Continuity Equation for Mass formula

This formula states that the mass entering a system is equal to the mass leaves the system both at the same rate.

\(\large{ A_1 \; v_1 = A_2 \; v_2  }\)   

Where:

\(\large{ A_2 }\) = final area cross-section

\(\large{ A_1 }\) = initial area cross-section

\(\large{ v_2 }\) = final cross-section velocity

\(\large{ v_1 }\) = initial cross-section velocity

 

continuity equation 1

Continuity Equation for Velocity formula

This formula calculates the initial velocity in a pipe.

\(\large{ v_1 = \frac{ \rho_2 \; A_2 \; v_2 }{ A_1 \; \rho_1 }  }\)   

Where:

\(\large{ v_1 }\) = initial cross-section velocity

\(\large{ A_2 }\) = final area cross-section

\(\large{ A_1 }\) = initial area cross-section

\(\large{ \rho_2 }\)  (Greek symbol rho) =  final cross-section density

\(\large{ \rho_1 }\)  (Greek symbol rho) =  initial cross-section density

\(\large{ \rho_1 }\)  (Greek symbol rho) =  initial cross-section density

\(\large{ v_2 }\) = final cross-section velocity

 

Tags: Equations for Velocity Equations for Flow Equations for Mass Equations for Density Equations for Area