84 
MR. T. E. STANTOiSr ON THE PASSAGE OF HEAT BETWEEN 
Now for smooth metal pipes the value of B" may be assumed nearly constant, so 
for a pipe of given length and diameter in which the surface temperature is constant, 
(2?’)^”" log jh 
/.T _ _^0 — ^2 
F-(l+«To)(i+y3y.. 
where k is a constant depending on the nature of the surface of the pipe. 
For the ranges of temperature obtained in these experiments no sensible error is 
introduced by taking the mean value of 
and t 
for the experiment and substituting them in equation (6). 
When the variation in t is considerable, equation (5) must be integrated more 
exactly. 
Applying equation (6) to the results of the experiments on the three copper pipes 
used, the values of h are found to be ;— 
1 
I 
1 
j Pipe. 
Diameter. 
Lengtli. 
Value of 4-. 
Number of 
Maximum. 
Minimum. 
Mean. 
experiments. 
I. 
centims. 
1-39 
centims. 
47-0 
•0108 
•0104 
•0106 
22 
II. 
1-07 
44-5 
•0104 
•0100 
•0102 
18 
III. 
•736 
46-0 
•0108 
•0099 
•0100 
15 
If W = weight of water flowing through the pipe in grammes per second, 
equation (5) may be written 
W 
IV’‘ ^ (Tq — ^) (1 + aT,)) (1 + /3t) 
in 
which gives for the transmission of heat from metal to ivater per square centlin. 
of the surface of the pipe 
( 2 ,.)!-^ (To - ') (1 + “T„) (1 + /3d) do* ' 
( 8 ). 
gramme-degrees per second. 
