Continuity Equation

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 for Area formula
\(\large{ A_1 = \frac{ \rho_2 \; A_2 \; v_2 }{ v_1 \; \rho_1 }  }\)
Symbol	English	Metric
\(\large{ A_1 }\) = initial area cross-section	\(\large{in^2}\)	\(\large{mm^2}\)
\(\large{ A_2 }\) = final area cross-section	\(\large{in^2}\)	\(\large{mm^2}\)
\(\large{ \rho_2 }\)  (Greek symbol rho) =  final cross-section density	\(\large{\frac{lbm}{ft^3}}\)	\(\large{\frac{kg}{m^3}}\)
\(\large{ \rho_1 }\)  (Greek symbol rho) =  initial cross-section density	\(\large{\frac{lbm}{ft^3}}\)	\(\large{\frac{kg}{m^3}}\)
\(\large{ v_2 }\) = final cross-section velocity	\(\large{\frac{ft}{sec}}\)	\(\large{\frac{m}{s}}\)
\(\large{ v_1 }\) = initial cross-section velocity	\(\large{\frac{ft}{sec}}\)	\(\large{\frac{m}{s}}\)

 

This formula calculates the initial density of the fluid.

Continuity Equation for Density formula
\(\large{ \rho_1 = \frac{ \rho_2 \; A_2 \; v_2 }{ A_1 \; v_1 }  }\)
Symbol	English	Metric
\(\large{ \rho_1 }\)  (Greek symbol rho) =  initial cross-section density	\(\large{\frac{lbm}{ft^3}}\)	\(\large{\frac{kg}{m^3}}\)
\(\large{ A_2 }\) = final area cross-section	\(\large{in^2}\)	\(\large{mm^2}\)
\(\large{ A_1 }\) = initial area cross-section	\(\large{in^2}\)	\(\large{mm^2}\)
\(\large{ \rho_2 }\)  (Greek symbol rho) =  final cross-section density	\(\large{\frac{lbm}{ft^3}}\)	\(\large{\frac{kg}{m^3}}\)
\(\large{ v_2 }\) = final cross-section velocity	\(\large{\frac{ft}{sec}}\)	\(\large{\frac{m}{s}}\)
\(\large{ v_1 }\) = initial cross-section velocity	\(\large{\frac{ft}{sec}}\)	\(\large{\frac{m}{s}}\)

 

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

Continuity Equation for Mass formula
\(\large{ A_1 \; v_1 = A_2 \; v_2  }\)
Symbol	English	Metric
\(\large{ A_2 }\) = final area cross-section	\(\large{in^2}\)	\(\large{mm^2}\)
\(\large{ A_1 }\) = initial area cross-section	\(\large{in^2}\)	\(\large{mm^2}\)
\(\large{ v_2 }\) = final cross-section velocity	\(\large{\frac{ft}{sec}}\)	\(\large{\frac{m}{s}}\)
\(\large{ v_1 }\) = initial cross-section velocity	\(\large{\frac{ft}{sec}}\)	\(\large{\frac{m}{s}}\)

 

This formula calculates the initial velocity in a pipe.

Continuity Equation for Velocity formula
\(\large{ v_1 = \frac{ \rho_2 \; A_2 \; v_2 }{ A_1 \; \rho_1 }  }\)
Symbol	English	Metric
\(\large{ v_1 }\) = initial cross-section velocity	\(\large{\frac{ft}{sec}}\)	\(\large{\frac{m}{s}}\)
\(\large{ A_1 }\) = initial area cross-section	\(\large{in^2}\)	\(\large{mm^2}\)
\(\large{ A_2 }\) = final area cross-section	\(\large{in^2}\)	\(\large{mm^2}\)
\(\large{ \rho_2 }\)  (Greek symbol rho) =  final cross-section density	\(\large{\frac{lbm}{ft^3}}\)	\(\large{\frac{kg}{m^3}}\)
\(\large{ \rho_1 }\)  (Greek symbol rho) =  initial cross-section density	\(\large{\frac{lbm}{ft^3}}\)	\(\large{\frac{kg}{m^3}}\)
\(\large{ v_2 }\) = final cross-section velocity	\(\large{\frac{ft}{sec}}\)	\(\large{\frac{m}{s}}\)