v = c √ α,
where c is a constant coefficient for the instrument.
The instrument as constructed had three disks which could be used at will. Their radii and leverages were in feet
| R = | b = | |
| 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 61⁄2 ft. long. Supposing α measured in degrees, we get by calculation
v = 0.335 √ α; 0.115 √ α; 0.042 √ α.
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√α,
| 1st disk, c = 0.3126 for velocities of 3 to 16 ft. 2nd disk, c = 0.1177 for velocities of 11⁄4 to 31⁄4 ft. 3rd disk, c = 0.0349 for velocities of less than 11⁄4 ft. |
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 The current meter, except in some improved forms, must be withdrawn from the water to read the result of each experiment, and the law connecting the velocity and number of rotations of a current meter is less well-determined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.