PROPERTIES OF MATTER IN' THE GASEOUS STATE. 
811 
For the sake of distinctness it will for the present be assumed that jq — s. 2 has the 
values given by equation (83). 
The velocity of the <jas at the solid sat face. 
97. Putting q for the tangential force on the solid surfaces z=^zc, we have 
q=cr : (Muj . 
and by equations (53a) and (54a) 
pa. . s'i — s' a da 
2=2T? ( “ 1_ “ 2) —STUS 
(84) 
(85) 
dp . 
Also since ~ is constant over the section, we have for the equilibrium of the fluid 
between two perpendicular sections of the tube at distance clx 
dp 
(]— —mc-r~ 
dx 
( 86 ) 
where me is the hydraulic mean depth of the tube (in the case of a fiat tube m— 1); 
therefore 
P“_ 
7T 
i U \ 
da. dp 
pet- —me— 
' dx dx 
(87) 
Then if u c is the velocity along the solid surface, we have 
2 a 0 —u\-\- a. 2 
( 88 ) 
And since u. 2 is the mean velocity after encounter at the surface of the tube, we 
may put 
u\=fu \ .(89) 
where f is a factor depending on the nature of the impact at the surface. Hence 
2a v — V ^{u\ —a d) . (90) 
or putting 
.(90a) 
2a,.=\^u\ — u'. : ) .......... (90b) 
