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A 
TURBINE STEAM YACHT WINCHESTER. 73 
velocity through a pipe would not lead to correct results, since for a variation in coefficient 
of over three times, the resistance is increased only two and one-quarter times, for the same 
mean velocity. 
“The cuts and description relative to the flow in open channels are a little crude, 
but it seemed to be an intermediate step from friction in a pipe to friction in the open, to 
consider that part of the subject; and the method of taking the total energy or total head, 
as being made up of the velocity head and what I call the position head, which has to do 
with the height of center of gravity of the moving water—this same method of treatment 
for narrowing and widening channels seems to have some possibilities in connection with 
wave formation accompanying the motion of vessels, on which we have been trying to get 
some line ever since model experiments were first started. 
“Curves showing the retardation of velocity and the width of wake under certain as- 
sumed values of coefficients of F and tan a indicate that the percentage of speed adjacent 
to the plane decreases very rapidly at first for a very small increase in length, and decreases 
very slowly for lengths above 1,000 feet. 
“The width of the wake increases fairly rapidly for the first 300 feet, and then very 
much more slowly for the longer plane. One peculiar thing is indicated by the formula 
for the width of the wake :—According to the theory, the width of the wake decreases with 
the increase of velocity, and increases with the roughness of surface. 
“Following equation (15), you will note that I draw some comparison as to how the 
width of the wake varies and how the loss of head varies. For corresponding conditions, 
the length varies inversely as the velocity, and the resistance varies directly as the velocity; 
from which, for the same fluid and the same roughness of the surface, it will be seen that for 
a constant value of the product of the velocity and the length, the resistance varies as the 
velocity. 
“This fact would seem to be apparent by the experiments made on flat planes, as you 
will notice from Fig. 10, Plate 61, that the resistance for speed of 400 feet per minute and 
a length of 40 feet will be one-half the resistance at 800 feet per minute, and a length of 20 
feet. The spots do not fall exactly on the experimental curves, but they do fall so closely as 
to indicate that this is probably a true statement of the case for the same roughness of 
surface and the same fluid. 
“T tried to enlarge this comparison by introducing the viscosity in the formula of the 
product of the length times velocity, but I was unable to get a good comparison with Rey- 
nolds’ number, as the viscosity coefficients do not seem to mean exactly the same as the 
coefficient which I have used in the paper. 
“The feature of the theory which leads me to consider that it is not complete, as I have 
noted in the fifth item of the theory, is as there stated :—‘The determination of the loss of 
head in the wake is complicated by the condition that the volume of the fluid passing the 
fixed body is not altered, although the velocity in the wake is decreased.’ Neglect of that 
condition leads to a very serious difference between the experimental curves and the theo- 
retical curves. In the experimental curve you will notice that after passing a length of 
about 30 feet the variation in resistance seems to follow almost a straight line, whereas in 
the theoretical curve the resistance tends to decrease at a fairly rapid rate for quite a dis- 
tance longer than the 50 feet of the original experiments by Mr. Froude. If this condition 
may be neglected, the coefficient of friction we are using on ships would hardly be correct 
for long vessels. It is probable, however, that the experimental data are correct, and that 
