On the equatorial or ys-plane, /i = 0, ar= ky/^'^ + 1, q = \u\ and 



u^q ^ -g^U - ' -sin~^ — ]; [I38k'] 



in particular, on the circumference of the ellipsoid itself, 



<^ = ^Q, w = ^V^Q + 1 =k/e and 



u-= -Q^U I ^ -sin~^ e] [1381 



For a figure, see Figure 234 as explained a little later. 



The kinetic energy of the fluid, found by the method that was employed in obtaining 

 Equation [137f'], is 



T =— 7Tpc^g^U'^[e-^/l-e'^ sin"^ ej [I38m'] 



(e-yi^ 



Circular Disk 



If ^. = 0, e = 1, a = and the ellipsoid becomes a circular disk of radius c - k moving 



2 



perpendicularly to its surface. Then g = 2/77. On the disk rar = c(l-fi^)^^^ and ip - -Vts^ fi 



Also, on its front face, q>--u=U and 



2V I T 2V 



9~= -9„ = Vl-/^' = -— . [I38n1 



til V -^ r 



f^ nfi n /■^2_~2xl/2 



Here /i increases inward, ^T outward, hence the negative sign. At the edge 5~-»~. On the 

 rear face /i = -(l-To'^/c-^)^^'^ and the velocity is reversed. 



The kinetic energy of the fluid is, from Equation [138m '], 



4 



T= — pc^U^. [138o'] 



3 



Some lines of flow near a moving circular disk, drawn for equidistant values of 0, are 

 shown in Figure 234. 



361 



