Bernoulli’s equation
The Euler equation, when gravity forces and viscosity are neglected. The Bernoulli Equation can be considered to be a statement of the conservation of energy principle appropriate for flowing fluids. The qualitative behavior that is usually labeled with the term "Bernoulli effect" is the lowering of fluid pressure in regions where the flow velocity is increased. This lowering of pressure in a constriction of a flow path may seem counter intuitive, but seems less so when you consider pressure to be energy density. In the high velocity flow through the constriction, kinetic energy must increase at the expense of pressure energy.
Actuator disk efficiency: Now let’s look at the power and the efficiency of the actuator disk. The power input is equal to the change in kinetic energy of the air per unit time.
Enthalpy: The enthalpy h is defined as follows:
h = e + RT = e + pν
To differentiate that, the chain rule must be applied, since neither p or v are constant. So:
dh = de + pdv + vdp
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