then taking eq. (77) leads to:
where . Dividing through by and rearranging terms then gives:
where is just the Bernoulli energy for this incompressible system given by:
It is easy to prove that is conserved in steady flow by taking the scalar product of the transformed momentum equation (76) with to give:
and since
then, after some rearrangement :
implying (for the 2D flow considered here) that .