# Borda-Carnot Equation

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

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

Symbol English Metric
$$\Delta E$$ = Fluid Mechanical Energy Loss $$lbf-ft$$ $$J$$
$$\epsilon$$  (Greek symbol epsilon) = Empirical Loss Coefficient $$dimensionless$$ $$dimensionless$$
$$\rho$$  (Greek symbol rho) = Fluid Density $$lbm\;/\;ft^3$$ $$kg\;/\;m^3$$
$$v_1$$ = Mean Flow Velocity before Expansion $$ft\;/\;sec$$ $$m\;/\;s$$
$$v_2$$ = Mean Flow Velocity after Expansion $$ft\;/\;sec$$ $$m\;/\;s$$

Tags: Pipe Flow Energy Fluid