Loss of Energy due to Sudden Enlargement

For a horizontal pipe, z₁=z₂ , so that

                                                                      (2)

Using Eq. (1) in (2), we get

                                                                                             (3)

Using continuity equation, Eq. (3) may be alternatively expressed as,

                                                              (4)

Eqs. (3) and (4) is the expression for head loss due to sudden enlargement and was first obtained by J.C. Borda (1753-1799) and L. Carnot (1738-1823). Sometimes, it is known as Borda-Carnot equation.