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

## Description

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## Variables

Δ_{E} | The fluid's mechanical energy loss per unit of fluid volume (J/m^{3}) |

ρ | Density of the fluid (kg/m^{3}) |

A_{1} | The cross-sectional area at section 1 (m^{2}) |

A_{2} | The cross-sectional area at section 2 (m^{2}) |

v_{1} | The mean flow velocity at section 1 (m/s) |