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.

\(\large{ \Delta E = \epsilon \; \frac { 1 }{ 2 } \; \rho \; \left({v_1 - v_2}\right)^2 }\)       Where: \(\large{ \Delta E }\) = fluid mechanical energy loss \(\large{ \epsilon }\)  (Greek symbol epsilon) = empirical loss coefficient \(\large{ \rho }\)  (Greek symbol rho) = fluid density \(\large{ v_1 }\) = mean flow velocity before expansion \(\large{ v_2 }\) = mean flow velocity after expansion