814 
PROFESSOR O. REYNOLDS ON CERTAIN DIMENSIONAL 
Integrating equation (94) between the limits c and 2 we have 
SOi -C .— — . Is - As LOfJ 
■—=(u—u c )= ---r+ a r 
r v ' 2 dx 1 
c 2 -z 2 dp 
2 c c—z C + Z 
1 + e _ “i* 
__ __V. / o 
2 c 2c 
1—e n ‘ s 1 —e 
~ \ 
hs J 
pa da 
1 S ^2irdx ' ^ 94a ^ 
c "it 3^ 
Integrating again between the limits 0 and c and putting fl —h—A we have, substi¬ 
tuting for u c from equation (91), 
^n=-(^+«»cx)| 
2c 
, / 1+C “ xS «i 2 S 2 , \, , , rfa 
+ 1 «.*-£ - ~- 5A P I" 5 4r * 
\ 1 —e “V 7 
(95) 
100. Equation (95) is the equation of transpiration in a flat tube on the assumption 
that 
c—z c+z 
e °i s —e 
s,—S,= 
¥ 1-8 *) 
1 —e "■ 
A slight modification however is all that is necessary to render the equation perfectly 
general. 
The only way in which the shape of the tube enters into the equation is in the co- 
3p 
efficient of the first time on the right-hand side, i.e., the coefficient of —, and whatever 
may be the shape of the tube this coefficient will be of the same form as far as the 
linear dimensions of the tube are involved, the only possible difference being in the 
numerical coefficients of cr and sc\. Therefore if c 3 be multiplied by a coefficient A, 
which depends on the shape of the tube, since m also varies with the shape of the tube, 
dp 
we have for the general coefficient of — 
0 ox 
sci^Ar^mk] 
As regards the coefficient of this is affected by the assumption as to the par¬ 
ticular form of (.q— s. 2 ) ; and if we assume a general form for * s 2 , such as 
V 
f c-(g)-c-CAT 1 
t ■ 1 -«-(£)” J 
(L-A) 
(96) 
tire coefficient of the last term would still be of the form 
