Figure 137 — Flow past a plane lamina ata = 90 degrees. 



It may seen strange that the lift should remain perpendicular to U at oblique angles, 

 although the pressure on the lamina is everywhere perpendicular to its faces. The expla- 

 nation lies in the occurrence of infinite velocities at the edges. In such cases erroneous 

 results may be obtained if the forces are calculated from an integration of the pressures. 

 In the present case, study of the behavior of the pressure distribution over the ellipsoid as 

 it becomes progressively flattened into a lamina indicates that finite forces must be supposed 

 to act on the edges of the lamina; see Morton, Reference 106. Mathematically, the limit of 

 the integral giving the lift on the ellipsoid is not the same as the integral of the limit of the 

 integrand, which represents pressure on the lamina. That the limit of the force must be the 

 correct value for the lamina, on the other hand, is physically obvious, since no discontinuous 

 change occurs in the motion of the neighboring fluid as the ellipsoid is flattened. 



(For notation and method; see Section 34; Reference 1, Article 71.) 



86. PLANE LAMINA IN TRANSLATION. 



If the plane lamina described in the last section moves in translation through fluid at 

 rest at infinity, only its perpendicular component of motion is significant, since motion 

 parallel to its plane does not disturb the fluid. Let the lamina lie parallel to the a;-axis and 



206 



