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Full text of "Scientific Papers - Vi"

334         HYDKODYNAMICAL PKOBLEMS  SUGGESTED BY PITOT'S TUBES         [396
The second tan"1 thus passes from 0 to TT, thereby completing its course, while | is still small.
When ^ = 0 absolutely, either | or 17, or both, must vanish, but we must still have regard to the relative values of -ty and f. Thus when  is small enough, ID = 0, and this part of the stream-line coincides with the axis of symmetry. But while f is still small, * changes from 0 to IT, the new value representing the inner face of the wall. The transition occurs when  = 2i^, 7 = 1, making in (11)'y=  oo . The point 0' at the edge of the wall (x = TT, y = 0) corresponds to  = 0, 77 = 0.
For the free part of the stream-line we may put 77 = 0, so that
2       TT
.(12)
.(13)
.(14)
where tan"1  is to be taken between 0 and \ir.    Also When  is very great,
&=+-|-7r3       2
and the curve approximates to a parabola. When  is small,
1    J1                                      1   "9                                                                                 / T CT v
0-7r = J,         y = tr, ........................(15)
so that the ratio (# - ?r)/?/ starts from zero, as was to be expected.
The upward movement of y is of but short duration.    It may be observed that, while dxjdt; is always positive,
which is positive only so long as  < 1. at -^ = 1-^ = 0-2146,
And when  = 1, 2/ = - J + log 2 = 0'097.
Some values of a; and y calculated from (12), (13) are given in Table II and the corresponding curve is shown in fig. 3.
TABLE II.   = 0.
f	X	y	*	X	y
o-o	3-142	0	2-5	4-451	- 0-571
0-5	3-178	+ 0-050	3-0	4-892	-  1-098
1-0	3-356	+ 0-097	4-0	5-816	-   2-583
1-5	3-659	+ 0-027	5-0	6-768	-  4-62
2-0	4-034	-0-195	20-0	21-621	1   -97-00
			V