## 5 Results and Discussion
Suffice it to say that the pressure difference values of the ADT are higher than those of the VRT for local radii between 2.867 m and about 43 m. Even though both the actuator disk and rotating annular stream-tube theories consider the WT rotor as a disk, the pressure difference estimated using the RAST is the highest of all the three theories. It suffices to say that the RAST overestimates the pressure difference across the rotor compared to the VRT and the ADT. The low values resulting from the ADT are evident because only the flow in the axial direction is considered in its formulation. A closer look at the VRT curve reveals that for local radii between 2.867 m and 11.75 m, the values of the pressure difference are positive; for local radii between 11.75 m and 36.35 m, the pressure difference is negative; and for local radii between 36.35 m and 61.633 m, the pressure difference is positive, whereas the pressure difference is positive for all local radii in the cases of the ADT and the RAST. The negative values of pressure difference exhibited by the VRT curve for local radii between 11.75 m and 36.35 m is the upshot of back pressure resulting from the acceleration of the flow within this region of the rotor blade. Suffice it to say that the mere fact that this negative pressure difference is exhibited by the VRT curve is proof that the VRT better captures the flow physics of the WT rotor than the actuator disk and rotating annular stream-tube theories. This phenomenon of the acceleration of flow within the inner parts of the WT rotor is like the one described by [PERSON] et al. [19] in which wake rotation  
Figure 5: Normal force per unit span as a function of the local radius. accelerates the flow at the inner parts of the rotor and decelerates the flow at the outer parts of the rotor. The curves of the local power coefficient \(dC_{p}\) as a function of the local tip-speed ratio \(\lambda(r)\) for the ADT, the RAST and the VRT are shown in Figure 7a. For clarity, the plot of the local power coefficient as a function of the local tip-speed ratio is plotted for the ADT and the VRT as depicted in Figure 7b. The three curves in Figure 7a appear to coincide at local tip-speed ratios ranging from about 0.32 to 0.918 after which the RAST curve leaves the ADT and VRT curves. Even though the ADT and VRT curves appear to coincide and run parallel to the horizontal axis at local tip-speed ratios between 0.918 and 4.33 as seen in Figure 7a, the two curves do intersect at local tip-speed ratios of about 0.32 and 2.900, respectively, as seen in Figure 7b. For local tip-speed ratios between 0.320 and 2.900, the ADT curve runs above the VRT curve because the \(dC_{p}\) values of the former are higher than those of the latter within this range of local tip-speed ratios. After this range of local tip speed-ratios, the VRT curve runs above the ADT curve as depicted in Figure 7b. The three theories appear to agree for local tip-speed ratios between 0.32 and 0.918, while the ADT and the VRT agree at local tip-speed ratios of 0.32 and 2.900. The RAST curve rises from values of \(dC_{p}\) slightly above zero to about 7.908 for \(0.3\leq\lambda(r)\leq 5.6\) with an upward concavity after which it falls steeply to about 6.38 at a \(\lambda(r)\) of about 6.0 and rises thereafter. The VRT curve follows the same trend as the former within the same range of local tip-speed ratios, with a peak value of \(dC_{p}\) of about 0.21 at \(\lambda(r)\cong 5.6\) and a trough at \(dC_{p}\cong 0.159\) and \(\lambda(r)=6.0\). It then rises to another peak at \(\lambda(r)=6.3\) and drops thereafter. The ADT curve stays relatively flat for \(0.3\leq\lambda(r)\leq 5.6\), even though this portion of the curve is supposed to have an upward concavity. It then exhibits a gently sloping peak at  
Figure 6: Pressure difference as a function of the local radius: (**a**) plots of the ADT, the RAST and the VRT; and (**b**) those of the ADT and the VRT.