# Borda–Carnot equation

## 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 loss coefficient ξ can be influenced by streamlining. For example in case of a pipe expansion, the use of a gradual expanding diffuser can reduce the mechanical energy losses.

## Variables

δ_{E} | mechanical energy loss of the fluid per unit of fluid volume (J/m^{3}) |

ξ | empirical loss coefficient , 0 ≤ ξ ≤ 1 (dimensionless) |

ρ | fluid density (kg/m^{3}) |

u1 | mean flow velocity before expansion (m/s) |

u2 | mean flow velocity after expansion (m/s) |