Borda–Carnot equation (sudden expansion of a horizontal pipe)


In fluid dynamics the Borda–Carnot equation is an empirical description of the mechanical energy losses of the fluid due to a (sudden) flow expansion. The Borda–Carnot loss equation is only valid for decreasing velocity, v1 > v2, otherwise the loss ΔE is zero – without mechanical work by additional external forces there cannot be a gain in mechanical energy of the fluid. The Borda–Carnot equation is applied to the flow through a sudden expansion of a horizontal pipe. At cross section 1, the mean flow velocity is equal to v1, the pressure is p1 and the cross-sectional area is A1. The corresponding flow quantities at cross section 2 – well behind the expansion (and regions of separated flow) – are v2, p2 and A2, respectively. At the expansion, the flow separates and there are turbulent recirculating flow zones with mechanical energy losses. The loss coefficient ξ for this sudden expansion is approximately equal to one: ξ ≈ 1.0. The mechanical energy loss in this sudden expansion is depended on the both cross section areas and the mean flow velocity v1.

Related formulas


ΔEThe fluid's mechanical energy loss per unit of fluid volume (J/m3)
ρDensity of the fluid (kg/m3)
A1The cross-sectional area at section 1 (m2)
A2The cross-sectional area at section 2 (m2)
v1The mean flow velocity at section 1 (m/s)