STEADY FLOW OF WATER IN UNIFORM PIPES AND CHANNELS. 317 
in a pipe of elliptical section may be readily found, if the flow be 
as just described, i.¢., if the motion of all particles be parallel to 
the axis of the pipe. The following expression for mean velocity, 
or rather its equivalent, was deduced from Navier’s equations! and 
justified in my paper before referred to.” 
page HBC. a) 
in which g is the acceleration of gravity, p the density of the fluid, 
by means of a column of which, of the height H, the difference 
of the pressures, at two sections of a horizontal tube, the distance 
L apart, is measured, Band C are the semiaxes of the ellipse, 
and is the viscosity of the fluid. 
If the units are 0.G.S. throughout, the viscosity factor—a fune- 
tion of the temperature—is fairly well represented for water, by 
the formula 
= = 55°89 (14+ 0:03257+0-0005 r?)............ (2) 
7 
from 0 to 8° C.; and by 
= 55°89 (1 +0:03395 r + 0000235 7?)......... (3) 
from 0° to 40° G.: +r being the temperature in Celsius degrees. 
Instead of pg H, its equivalent P may be written, P being the 
difference of pressure in dynes per square centimetre, at the two . 
sections. For more accurate results the value of 1/n may be 
taken from the table hereinafter. (Table I.) 
For pipes of circular section the final factor B?C?/} (B? + C?) 
becomes of course R?. The ratio per unit of length of the fall in 
pressure, measured by a column of the same temperature as the 
fluid in motion, i.e, H/L, will be denoted hereinafter by J. This 
aay is often called the seca ae or ee gradient. 
1 Eons. de l’Académie, t. 6, pp. 389 - 440, ‘1823. 
2 Loe. cit., pp. 110 = 118. 
3 The factor 0-0325 is wrongly written 0°0225 in the “Note on recent — 
_ determinations &c.” previously quoted, see p. 191. The Aieee quantity — 
was however used throughout in the calculations. 
