For, the velocity normal to the disk is that of the disk itself or ^ = Q. z; hence writing 



y = oTcos w, z = oTsin co, and dS - TodTodco, Equation [17c] gives, integrated over both faces. 



^—pLq/S^pj — n2^3(p2_ ^2^1/2^—/ gjjjS 



The pressure can be found from Equation [lie] or Equation [lid]. 



In the last three cases there is no axis of symmetry, hence no stream function exists. 



(See Reference 1, Article 107, 109; Reference 2, Section 15.54, 15.55; Zahm.i°2,i74) 



139. CIRCULAR APERTURE 



The oblate-spheroidal coordinates described in the last section may be used also to 

 obtain the flow through a circular aperture in an infinite plane. 



For this purpose k is taken equal to c, the radius of the aperture, so that from 

 Equations [I38a, b] 



= c^C S'=c(C' + l)^/^ {1-ti'Y''; 



[139a, b] 



and the ranges, -oo<^<oo, = /x = l are used, so that, as in Figure 238, /i = 1 on the entire 



;r-axis. 



Axis of Symmetry 



Figure 238 — Flow through a circular aperture in an infinite 

 plane using oblate-spheroidal coordinates. 



369 



