80 
MR. T. E. STANTON ON THE PASSAGE OF HEAT BETWEEN 
IV., being greater than would be accounted for by the difference in the value of 
Other experiments carefully made gave similar results. 
Thus, for a pipe of given diameter these experiments indicate that the transmission 
of heat from the surface of the pipe to water flowing through it, at velocities above 
the critical value for the pipe used, is given by an expression of the form 
fZH = Vi2wr dl (To - t)f(v) F (T„) 3- (().(1), 
It is also seen that the values of F (Tq) and <I> (^) do not vary very much from unity, 
and may probably be put in the form 
F (Tq) = 1 + aTg, 
(0 = 1 + (it, 
where a and yd are constants to be determined by experiment. 
Again, from Experiments II., it is seen that the heat transmitted is nearly 
proportional to the velocity, thus iiidicating the probable form of the velocity 
function, as 
f{v) = V^ 
where n is a number a little less than unity, and to be determined by experiments at 
varying velocity. 
It may be noticed that in equation (1) the value of K may depend on the diameter 
of the pipe and the nature of the surface. 
The experiments made on the three drawn copper pipes, of diameter 1'39, 1'07, 
and ‘736 centim., did not clearly indicate what the relation between H and r was, 
beyond showing that the effect of the variation in diameter of these pipes was not 
great, the supply of hot water from the heating coils not being sufiicient to enable 
experiments to be made on pipes of larger diameter. 
It is shown in the theory that the heat transmitted is projDortional to the value of 
where n has the value 1‘84 approximately. 
This would make the heat transmitted across unit area of the surface of the 
smallest pipe (‘736 centim. diameter) about 10 per cent, greater than that trans¬ 
mitted through unit area of the surface of the largest pipe (1*39 centim. diameter) 
under the same conditions of flow and temperature. 
General Theory. 
The experiments described in this paper were originally made in order to determine, 
if possible, an expression for the rate of transmission of heat from metal surfaces to 
