# 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 equation

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

### Where:

 Units 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 $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$ 