202 
MESSES. T. E. STANTON AND J. R. PANNELL ON SIMILARITY OF 
have been made on pipes whose surfaces were smooth or artificially roughened so that 
the amount of the friction was more than doubled. By making observations on the 
same pipe first with air flowing through it and then with water at identical values of 
vd/v it was found that the corresponding values of R /pv 2 were also identical both for 
the smooth pipe and for the rough one.* 
Comparisons have also been made between the resistances of models of dirigible 
balloons made to different scales, in one case when exposed to a current of air and in 
the other case when towed in an experimental water tank, and results confirmatory of 
the theory have been obtained. 
The experiments described in the present paper form a continuation of the investiga¬ 
tion with reference to surface friction, so as to include the highest range in the 
velocities of flow, the dimensions of the surfaces, and in the nature of the fluids used, 
as could be conveniently obtained. It will be realised that in order to vary the 
conditions to the extent desired, and to measure the resistances with the requisite 
accuracy, the research was practically limited to observations on the resistance to the 
flow of fluids in pipes. Adopting this method of working, the velocities of flow which 
have been obtained have ranged from 30 to 6000 cm. per second in pipes varying from 
0'3 to 10‘0 cm. in diameter. The fluids used in the majority of the experiments have 
been air and water. The physical properties of these are so widely different that 
observations on others are hardly necessary, but as a matter of interest some 
experiments on thick oils are included. 
For very accurate comparison the surfaces of the tubes should have been precisely 
geometrically similar, as regards roughness, but as this condition could not be fulfilled, 
the experiments were all made on commercially smooth-drawn brass pipes. From the 
general agreement of the results of different pipes it does not appear that slight 
irregularities in this respect have a marked effect on the resistance within the range of 
diameters here used. 
Nature of the Observations in the Experiments. 
To set up the state of motion required the experimental pipe was, in the majority 
of cases, connected to a centrifugal fan or pump, driven by an electric motor and 
provided with speed-regulating devices by means of which the flow of the fluid could 
be maintained constant throughout the duration of any particular experiment. The 
length of “ leading in pipe, of the same diameter as the experimental portion, through 
which the fluid passed before any observations of its velocity or pressure were made, 
varied from 90 to 140 diameters, as it was considered that this length was sufficient 
both to enable any irregularities in the distribution of velocity to die away, or any 
stream-line motion at the inlet to break up, before the measurements were taken. 
* ‘ Roy. Soc. Proc.,’ A, vol. 85, p. 366. 
