320. We next place the barrel upon the axis already experimented upon
and shown in Fig. 46 at B. The circumference of the wheel is 88"·5;
the circumference of the barrel is 14"·9. The proper mode of finding
the circumference of the barrel is to suspend a weight from the rope,
then raise this weight by making one revolution of the wheel, and
the distance through which the weight is raised is the effective
circumference of the barrel. The velocity ratio of the wheel and barrel
is then found, by dividing 14·9 into 88·5, to be 5·94.
321. The mechanical efficiency of this machine is determined by
experiment. I suspend a weight of 56 lbs. from the hook, and apply
power to the wheel. I find that 10·1 lbs. is just sufficient to raise
the load.
322. The mechanical efficiency is to be found by dividing 10·1 into 56;
the quotient thus obtained is 5·54. The mechanical efficiency does not
differ much from 5·94, the velocity ratio; and consequently in this
machine but little power is expended upon friction.
323. We can ascertain the loss by computing the percentage of applied
energy which is utilized. Let us suppose a weight of 100 lbs. has to
be raised one foot: for this purpose a force of 100 ÷ 5·54 = 18·1
lbs. must be applied. This is evident from the definition of the
mechanical efficiency; but since the load has to be raised one foot,
it is clear from the meaning of the velocity ratio that the power must
move over 5'·94: hence the number of units of work to be applied is
to be measured by the product of 5·94 and 18·1, that is, by 107·5;
in order therefore to accomplish 100 units of work 107·5 units of
work must be applied. The percentage of energy usefully employed
is 100 ÷ 107·5 × 100 = 93. This is far more than 70, which is the
percentage utilized when the axle was used without the barrel (Art.
309).
324. A series of experiments made with care upon the wheel and barrel
are recorded in Table XIX.