Supposing steady, uniform axisymmetric incompressible, and inviscid flow with a nonrotating wake, the mass conservation provides the following relation: ρU_1 A_1= ρU_2 A_d=ρU_4 A_4 (6)
As is apparent, Ad is the area of the actuator disk.
Fig 2. Actuator disk model of a wind turbine (Xiaomin Chen and Ramesh Agarwal, 2014)
The axial induction factor a, since the actuator disk induces velocity in the stream tube, can be expressed by:
a=(U_1-U_2)/U_1