INVESTIGATION OF FLOW OF WATER IN UNIFORM CHANNELS. 373 
The mean of the inclinations of the logarithmic curves for 
Series A and B is approximately ‘685, but for the present pur- 
poses of correction it will be sufficiently accurate to assume this 
to be -7; hence the relationship between velocity and hydraulic 
radius may, within the range of values covered by the experiments, 
_ be approximately expressed as 
Ua Rk’ 
and this is the expression that was employed in reducing the 
velocities in Series I. and II. to common hydraulic radii of 
15 cm. and 1 em. respectively. 
13. Relation between temperature and velocity.—The tempera- 
ture of the water being subject to slight variations during the 
course of the investigation, the following experiments were made 
with a view of observing in the first place whether the velocity 
was appreciably affected by changes of temperature, of only a few 
egrees, and, if it were so, of determining approximately the 
relationship between the two quantities. The highest tempera- 
ture attained was about 42° C., which is considerably above any 
temperature occurring in the experiments of Series I. and II., 
but which does not provide a range of values sufficiently wide for 
the precise determination of the above-mentioned relationship. 
As will be evident from the following table a comparatively small 
change of temperature produces a distinctly noticeable effect on 
the rate of flow, and the expression deduced from the observa- 
tions, although necessarily only roughly approximate, on account 
of the considerable degree of error involved in each measurement, 
is yet probably quite accurate enough for the small corrections 
that have to be made. It was assumed that the change in the 
coéfficient of discharge of the orifice with increase of temperature 
would be inappreciable,' or at least considerably within the range 
of experimental error. Further, assuming the coéfficient of super- 
ficial expansion of brass to be -000038 per degree centigrade or 
‘00076 for the range of temperature adopted in the experiments, 
PSC Wheel ey es es 
1 See « Experiments on the discharge of water of different temperatures,” 
by J. G. Mair.—Proc. Inst. C.E., Vol. txxxrv. p. 424. 
