Borda-Carnot Equation

on . Posted in Fluid Dynamics

borda carnotBorda-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

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


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