THROUGH PIPES OR PASSAGES HAVING DIVERGENT BOUNDARIES. 107 
Areas, Angle of 
F Ratio of Length. | Corresponding 
|) Areas: Straight 
Initial. Final. Taper Pipes. 
j ins. 
‘590 in. x 1°329 in. 5°315 in. x 1°329 in, ae alis-40 20° 
xe Pa f 2 eal 10°25 26° 
; = 1-329 in. x 1°329 in. 5: SLD anne! 329 in. BN all bono 22° 42’ 
: : : 4:1 | 745 30° 
o 2 be is 4:1 | 5:49 40° 
1:329 in. x 1°329 in. 2°99 in. x 1°329 in. 2-25:1 | 4°70 20° 
% 4 Pe 2°25: 1 3°10 30° 
‘50 in. diam. 1°50 in. diam. Sia 3°80 15° 
AS e se il 1:870 30° 
Circular 1°50 in. diam. 3°0 in. diam. AL 2 Jl 8-575 10° 
Pipes. 6) 4) 4:1 2°802 30° 
2-0 in. diam. 3°0 in. diam, 2°25: 1 e/a 10° 
» 55 2°25: 1 1870 30° 
| 
a length dx of a trumpet-shaped rectangular pipe, over which the mean angle is 0, the 
' “6 
loss is presumably proportional to 0(v)? ey sirarlto eee Cae . 0% where y is the 
half-breadth of the pipe and where # measures the distance of the element under con- 
sideration from some datum point on the axis of the pipe. 
But in such a pipe vecy’, 
.. loss in length v= Ss) i. bx 
For this to be constant per unit length 
14 
sr Z) = constant , 
or 
24 
(54) = constant , 
d. 
, dy _ - 
=k 1°25 
ae 'y 
Ly — fu 
ie Yeo K@—a:) : : : : ae) 
If the origin from which x is measured be taken at the small end of the pipe where 
the half-breadth is y,, «,=0, and if 7 be the length of the pipe and if y, be the half- 
breadth at the larger end, x, — a, =1, and 
ie : ' yy = yy? ® \ 
