Derive the energy conservation equation for a three-dimensional incompress- ible flow, in presence of gravity forces. Hint: Apply equation (1.3.18) to the momentum equation (1.4.40) and mul- tiply scalarly by v. Introducing the total energy (H=p/p+v/2+gz) where z is the vertical coordinate, proof the Bernoulli equation: a + (.V)H = v . L at 17 at (v x ) + V 7 + fe (1.3.18) av = (1.4.40)