(J1)11(J2)12(J3)j3ï¿½.ï¿½ jj!j2!j3!..ï¿½ where since(m1 1 m2 2 m3 3 ...) is the specification of (J1)j1(J2)j2(J3)j3..., ï¿½ l +ï¿½2+/23+ï¿½ï¿½ï¿½ =ii +j2+j3+ï¿½ï¿½ï¿½ï¿½ Comparison of the coefficients of x:14243...
Thus f (= 4-rb 2;JJ Z dY (e r) dx dy dz.
The stream lines xBAJ, xA'J' are given by = 0, m; so that if c denotes the ultimate breadth JJ' of the jet, where the velocity may be supposed uniform and equal to the skin velocity Q, m=Qc, c=m/Q.
Ja - u ?I a -a b -u' sh nS2=sh log (Q)=?a - b a - a' b - u' At x where = co, u = o, and q= go, (O n b - a ' a + a -b a' cio) - ?a-a'?b a-a' q In crossing to the line of flow x'A'P'J', b changes from o to m, so that with q = Q across JJ', while across xx the velocity is qo, so that i n = go.
Xx' = Q.JJ' (31) JJ _ g o _ lb-a' la_I a-b a' 11n xx' Q L Va - a' b Va-a' b j ' (32) giving the contraction of the jet compared with the initial breadth of the stream.