text: To derive an energy equation, note that the advective acceleration term  may be decomposed as:where  is the vorticity of the flow and  is the Euclidean norm. This leads to a form of the momentum equation, ignoring the external forces term, given by:Taking the dot product of  with this equation leads to:This equation was arrived at using the scalar triple product .  Define  to be the energy density:Noting that  is time-independent, we arrive at the equation:Assuming that the energy density is time-independent and the flow is one-dimensional leads to the simplification:with  being a constant; this is equivalent to Bernoulli's principle. Of particular interest in open-channel flow is the specific energy , which is used to compute the hydraulic head  that is defined as:with  being the specific weight. However, realistic systems require the addition of a head loss term  to account for energy dissipation due to friction and turbulence that was ignored by discounting the external forces term in the momentum equation.