METAL SURFACES AND LIQUIDS IN CONTACT WITH THEM. 
69 
Fig. I. 
4 11 
c 
T, 
; 
AB M 
walls of the pipe to the cold water, and if tlie iiuantities of water he the same in 
each case, the fall of temperature of the jacket water will be equal to 
the rise of temperature of the water flowing through the pipe, if means 
are taken to prevent the escape of heat from the jacket water to the 
outer walls. 
In this way, although the range of temperature from water to water is 
diminishing, yet the mean value of (T + t) is the same at all cross 
sections. 
Now the temperature of the w'all of the pipe at any cross section will 
not necessarily be a mean between the values of T and t at that section, 
but if the total fall of temperature from one end of the pipe to the other 
is small, say not more than 6° C., then under certain conditions oj flow 
which vjill he stated, we may fairly assume that the ratio of the differences 
of temjjerature between (jacket water and wall) and between (wall and 
water flowing through pipe) is constant for the whole length of the 
pipe, and hence that the temperature of the pipe is constant throughout 
its length. 
As regards the conditions of flow it is necessary to point out that if 
the motion in the pipe or the jacket is “steady,” i.e., the water flows in 
stream-lines parallel to the axis of the pipe, then the temperature of the water cannot 
be considered as uniform across any section of the pipe, and might vary considerably. 
In order to avoid this condition of flow, all the experiments were made at velocities 
considerably higher than the critical velocity of water for the pipe in question ; this 
“critical” velocity, as determined by Professor Reynolds’ experiments,* being given 
by the expression 
U 
v.= 
1 p 
278 D 
( 2 ), 
where 
I) = diameter of pipe in metres, 
T = tempei'ature of the water, 
P = (I 4- -0336 T + -000221 
V;,. = critical velocity in metres per second. 
Equation (2) gives the critical velocity for the smooth lead pipes used in those 
experiments, and it may be assumed that the critical value of the velocity for smooth 
copper pipes does not vary greatly from this. 
Under these conditions, and using an apparatus as described above, it seemed 
possible to study experimentally the transmission of heat from metal to water, and 
water to metal, at varying velocities and ranges of temperature, by careful observa¬ 
tions of the initial and final temperatures of the water and the temperatures of 
the surface. 
* ‘ Phil. Trans.,’ 1883, p. 976. 
