Borda-Carnot Equation

Written by Jerry Ratzlaff 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 calculator

 

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 \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{s}}\)

 

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