Borda-Carnot Equation

Borda-Carnot equation is a empirical description of the mechanical loss energy losses of the fluid due to a sudden flow expansion.  It describes how the total head losses due to the expansion.  This equation is only valid for expansion, in the case of a contraction, the Borda-Carnot Equation cannot be used as it would indicate that energy is created.   The empirical loss coefficient, \(\large{\epsilon}\), is a number between 0 and 1.  For an abrupt and wide expansion, \(\large{\epsilon}\) is equal to 1.  For other instances, the value should be determined through empirical means.

 

Borda-Carnot equation
\(\large{ \Delta E = \epsilon \; \frac { 1 }{ 2 } \; \rho \; \left({v_1 - v_2}\right)^2 }\)
Symbol	English	Metric
\(\large{ \Delta E }\) = fluid mechanical energy loss	\(\large{ lbf-ft }\)	\(\large{J}\)
\(\large{ \epsilon }\)  (Greek symbol epsilon) = empirical loss coefficient	\(\large{ dimensionless }\)
\(\large{ \rho }\)  (Greek symbol rho) = density of fluid	\(\large{\frac{lbm}{ft^3}}\)	\(\large{\frac{kg}{m^3}}\)
\(\large{ v_1 }\) = mean flow velocity before expansion	\(\large{\frac{ft}{sec}}\)	\(\large{\frac{m}{s}}\)
\(\large{ v_2 }\) = mean flow velocity after expansion	\(\large{\frac{ft}{sec}}\)	\(\large{\frac{m}{s}}\)

 

Borda-Carnot calculator