In crossing to the line of flow x′A′P′J′, ψ 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 | , |
| xx′ | Q | a − a′ | b | a − a′ | b |
(32)
giving the contraction of the jet compared with the initial breadth of the stream.
Along the line of flow x′A′P′J′, ψ = m, u = a′e−πφ/m, and from x′ to A′, cos nθ = 1, sin nθ = 0,
| ch nΩ = ch log ( | Q | ) | n | = √ | b − a′ | √ | a − u | , |
| q | a − a′ | b − u |
(33)
| sh nΩ = sh log ( | Q | ) | n | = √ | a − b | √ | u − a′ | . |
| q | a − a′ | b − u |