The axial force induced on a duct (duct thrust) which surrounds a propulsor is, by means of an energy conservation argument, expressed in terms of the thrust and power of the propulsor and the kinetic energy losses per unit of time of the propulsor and the duct. Emphasis is put on the linear theory of an axisymmetric ducted actuator disk, where it is shown that the work done by the duct thrust is equal to the extra work done by the actuator disk when it is surrounded by the duct. This simplified model gives more insight into the interaction between the propeller and the duct and on the limits of linearization.