Kinetic Power Transfer from Axial Force

if m be the indefinite but large mass flow in the wind, and actuator disk is placed
m perpendicular to the flow direction of wind, exerts a finite axial force is Dax, in this picture below no external force acts on the flow, so momentum is conserved and the flow does not expand further.



The velocity change obtained from the momentum relation is connected to the change of the kinetic power in the wind, by use this formula
at this is the formula that use to describe change of the kinetic power in the flow due to the axial force when the outer flow is included



Where :
A(delta)P is : the change of the kinetic power in the flow in the stream tube when it crosses the actuator disk
m : large mass flow in the wind
U : is velocity of wind until little past actuator boundary (see picture above)
V : is velocity of wind after fake boundary (see pincture)
Dax : Finite axial force
a : constant value from dynamic pressure function is 16/27 or 1/3
e : is fraction flows trough the stream tube