808 
PROFESSOR O. REYNOLDS ON CERTAIN DIMENSIONAL 
t -=<>.< 71 > 
And since the action of the tube is symmetrical about the plane x y, we have at this 
plane 
f=°.< 72 > 
Therefore, integrating between the limits z and 0, we have from equation (69) 
clp s dXJ . 
d, z =V^P a lh .< 73 > 
Also, since s is constant across the tube, except within the layer over which the 
influence of the surface of the tube extends, and which is not taken into account, we 
have, integrating from z to c, and putting U c for U at the surface 
i|C- s2 )=^“( U ‘- u >.< 74 > 
Jfrom equation (43) we have, since s does not vary with z 
p(u — u 0 ) =p(U — U c ).(75) 
Therefore, from equation (74) 
l+*.w 
or putting 
P- 
udz 
fi=7r-.(77) 
ch 
•'o 
so that n is the mean velocity of the gas along the tube, we have integrating (76), and 
o 
par 
putting p = 
U c _ \/ir d l dp 
a. 6 S JO dx .' ' 
The relation between s and y. 
93. The only respect in which equation (78) differs from the usual equation between 
the motion of gas and the variation of pressure in a tube is that instead of y we have 
4- 
\ / 77 a 
