Borda-Carnot Equation

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

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 formula

\(\large{ \Delta E = \epsilon \frac { 1 } { 2 } \rho \left({v_1-v_2}\right)^2 }\)      


\(\large{ \Delta E }\) = 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



Tags: Equations for Energy Equations for Pipe