1st disk 0.052 0.16
2nd " 0.105 0.32
3rd " 0.210 0.66
For a thin circular plate, the coefficient k = 1.12. In the actual
instrument the torsion rod was a brass wire 0.06 in. diameter and 6½
ft. long. Supposing [alpha] measured in degrees, we get by calculation
v = 0.335 [root][alpha]; 0.115 [root][alpha]; 0.042 [root][alpha].
Very careful experiments were made with the instrument. It was fixed
to a wooden turning bridge, revolving over a circular channel of 2 ft.
width, and about 76 ft. circumferential length. An allowance was made
for the slight current produced in the channel. These experiments gave
for the coefficient c, in the formula v = c [root][alpha],
1st disk, c = 0.3126 for velocities of 3 to 16 ft.
2nd " 0.1177 " " 1¼ to 3¼ "
3rd " 0.0349 " " less than 1¼ "
The instrument is preferable to the current meter in giving the
velocity in terms of a single observed quantity, the angle of torsion,
while the current meter involves the observation of two quantities,
the number of rotations and the time. The current meter, except in
some improved forms, must be withdrawn from the water to read the
result of each experiment, and the law connecting the velocity and
number of rotations of a current meter is less well-determined than
that connecting the pressure on a disk and the torsion of the wire of
a hydrodynamometer.
The Pitot tube, like the hydrodynamometer, does not require a time
observation. But, where the velocity is a varying one, and
consequently the columns of water in the Pitot tube are oscillating,
there is room for doubt as to whether, at any given moment of closing
the cock, the difference of level exactly measures the impulse of the
stream at the moment. The Pitot tube also fails to give measurable
indications of very low velocities.