Efficiency increases may be the result of engineering of the wind capture devices, such as the configuration and dynamics of wind turbines, that may increase the power generation from these systems within the Betz limit. System efficiency increases in power application, transmission or storage may also contribute to a lower cost of power per unit. The Betz Limit is the maximum possible energy that may be derived by means of an infinitely thin rotor from a fluid flowing at a certain speed. In order to calculate the maximum theoretical efficiency of a thin rotor (of, for example, a windmill) one imagines it to be replaced by a disc that withdraws energy from the fluid passing through it. At a certain distance behind this disc the fluid that has passed through flows with a reduced velocity. Applying conservation of mass to this control volume, the mass flow rate (the mass of fluid flowing per unit time) is given by  where "v"1 is the speed in the front of the rotor, "v"2 is the speed downstream of the rotor, "v" is the speed at the fluid power device, "ρ" is the fluid density, the area of the turbine is given by "S", and formula_2 and formula_3 are the areas of the fluid before and after reaching the turbine. So the density times the area and speed should be equal in each of the three regions: before, while going through the turbine and afterward. The force exerted on the wind by the rotor is the mass of air multiplied by its acceleration. In terms of the density, surface area and velocities, this can be written as  The work done by the force may be written incrementally as  and the power (rate of work done) of the wind is  Now substituting the force "F" computed above into the power equation will yield the power extracted from the wind:  However, power can be computed another way, by using the kinetic energy. Applying the conservation of energy equation to the control volume yields  Looking back at the continuity equation, a substitution for the mass flow rate yields  Both of these expressions for power are completely valid, one was derived by examining the incremental work done, and the other by the conservation of energy. Equating these two expressions yields  For all "v" and "S" the density cannot be 0. Examining the two equated expressions yields an interesting result, namely  or  Therefore, the wind velocity at the rotor may be taken as the average of the upstream and downstream velocities.