Consider the motion where the liquid is coming from an infinite distance between two parallel walls at a distance xx´ (fig. 4), and issues in a jet between two edges A and A´; the wall xA being bent at a corner B, with the external angle [beta] = ½[pi]/n. The theory of conformal representation shows that the motion is given by _ _ | [root](b - a´·u - a) + [root](b - a·u - a´) |^1/n [zeta] = | ------------------------------------------- | , u = ae^(-[pi]w/m); (5) |_ [root](a - a´·u - b) _| where u = a, a´ at the edge A, A¹; u = b at a corner B; u = 0 across xx´ where [phi] = [oo]; and u = [oo], [phi] = [oo] across the end JJ´ of the jet, bounded by the curved lines APJ, A´P´J´, over which the skin velocity is Q. The stream lines xBAJ, xA´J´ are given by [psi] = 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. If there are more B corners than one, either on xA or x´A´, the expression for [zeta] is the product of corresponding factors, such as in (5). Restricting the attention to a single corner B, / Q \^n [root](b - a´·u - a) + [root](b - a·u - a´) [zeta]^n = ( --- ) (cos n[theta] + i sin n[theta] = -------------------------------------------, (6) \ q / [root](a - a´.u - b) / Q \^n / Q \^n ch n[omega] = ch log( --- ) cos n[theta] + i sh log ( --- ) sin n[theta] \ q / \ q / /b - a´ /u - a´ = ½([zeta]^n + [zeta]^(-n)) = / ------ / ------ (7) \/ a - a´ \/ u - b´ / Q \ / Q \^n sh n[Omega] = sh log ( --- ) cos n[theta] + i ch log ( --- ) sin n[theta] \ q / \ q / /b - a´ /u - a´ = ½([zeta]^n - [zeta]^(-n)) = / ------ / ------ (8) \/ a - a´ \/ u - b´ [oo] > a > b > 0 > a´ > -[oo] (9) and then d[Omega] 1 [root](b - a´·b - a´) dw m -------- = - -- ---------------------------, -- = - ------ (10) du 2n (u - b)[root](a - a·u - a´) du [pi]u´ the formulas by which the conformal representation is obtained. For the [Omega] polygon has a right angle at u = a, a´, and a zero angle at u = b, where [theta] changes from 0 to ½[pi]/n and [Omega] increases by ½i[pi]/n; so that