Continuity Equation for Area

on . Posted in Fluid Dynamics

Continuity equation is the moving of a quantity through a pipe in a steady flow.  This formula calculates the initial cross-section area of the pipe.   

 

continuity equation 1

Continuity Equation for Area Formula

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

\( A_1 \;=\;  \dfrac{ \rho_2 \cdot A_2 \cdot v_2 }{ v_1 \cdot \rho_1   }\)     (Continuity Equation for Area

\( \rho_2 \;=\;  \dfrac{ A_1 \cdot v_1 \cdot \rho_1 }{ A_2 \cdot v_2   }\)

\( A_2 \;=\;  \dfrac{ A_1 \cdot v_1 \cdot \rho_1 }{ \rho_2 \cdot v_2   }\)

\( v_2 \;=\;  \dfrac{ A_1 \cdot v_1 \cdot \rho_1 }{ \rho_2 \cdot A_2   }\)

\( v_1 \;=\;  \dfrac{ \rho_2 \cdot A_2 \cdot v_2 }{ A_1 \cdot \rho_1   }\)

\( \rho_1 \;=\;  \dfrac{ \rho_2 \cdot A_2 \cdot v_2 }{ A_1 \cdot v_1   }\)

Symbol English Metric
\( A_1 \) = Initial Area Cross-section \(in^2\) \(mm^2\)
\( \rho_2 \)  (Greek symbol rho) =  Final Cross-section Density \(lbm \;/\; ft^3\) \(kg \;/\; m^3\)
\( A_2 \) = Final Area Cross-section \(in^2\) \(mm^2\)
\( v_2 \) = Final Area Cross-section Velocity \(ft \;/\; sec\) \(m \;/\; s\)
\( v_1 \) = Initial Area Cross-section Velocity \(ft \;/\; sec\) \(m \;/\; s\)
\( \rho_1 \)  (Greek symbol rho) =  Initial Area Cross-section Density \(lbm \;/\; ft^3\) \(kg \;/\; m^3\)

 

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Tags: Flow Area