cos 2n[alpha] - cos 2n[theta] × ----------------------------- sin 2n[theta] Along the wall AB, cos n[theta] = 0, sin n[theta] = 1, a > u > b, (22) / Q \^n /b - a´ /a - u ch n[Omega] = i sh log ( --- ) = i / ------ / ------ (23) \ q / \/ a - a´ \/ u - b´ / Q \^n /a - b /u - a´ sh n[Omega] = i ch log ( --- ) = i / ------ / ------ (24) \ q / \/ a - a´ \/ u - b´ ds ds d[phi] m c Q -- = ------ ------ = ------ = --- -- (25) du d[phi] dt [pi]qu [pi] qu _ AB / a Q du [pi]-- = | --- -- c _/ b q u _ _ _ / | [root](a - b)[root](u - a´) + [root](b - a´)[root](a - u) |^1/n du = | | --------------------------------------------------------- | --. (26) _/ |_ [root](a - a´)[root](u - b´) _| u Along the wall Bx, cos n[theta] = 1, sin n[theta] = 0, b > u > 0 (27) / Q \^n /b - a´ /a - u ch n[Omega] = ch log ( --- ) = / ------ / ------ (28) \ q / \/ a - a´ \/ b - u´ / Q \^n /a - b /u - a´ sh n[Omega] = sh log ( --- ) = / ------ / ------. (29) \ q / \/ a - a´ \/ b - u At x where [phi] = [oo], u = 0, and q = q0, / Q \^n /b - a´ / a /a - b / -a´ ( --- ) = / ------ / --- + / ------ / ---. (30) \ q0 / \/ a - a´ \/ b \/ a - a´ \/ q In crossing to the line of flow x´A´P´J´, [psi] changes from 0 to m, so that with q = Q across JJ´, while across xx´ the velocity is q0, so that m = q0.xx´ = Q.JJ´ (31) _ _ JJ´ q0 | /b - a´ / a /a - b / -a´ |^1/n -- = --- = | / ------ / --- - / ------ / --- | , (32) xx´ Q |_ \/ a - a´ \/ b \/ a - a´ \/ q _| giving the contraction of the jet compared with the initial breadth of the stream. Along the line of flow x´A´P´J´, [psi] = m, u = a´e^(-[pi][phi]/m), and from x´ to A´, cos n[theta] = 1, sin n[theta] = 0, / Q \^n /b - a´ /a - u ch n[Omega] = ch log ( --- ) = / ------ / ------, (33) \ q / \/ a - a´ \/ b - u´ / Q \^n /a - b /u - a´ sh n[Omega] = sh log ( --- ) = / ------ / ------. (34) \ q / \/ a - a´ \/ b - u´ 0 > u > a´. (35) Along the jet surface A´J´, q = Q,