TABLE VIII. Experiments on the Friction or Quantity of Water discharged by Leaden Pipes of different diameters and lengths, from a vessel kept constantly full, and at different heights. Experiments on the Quantities of Water discharged by Leaden Pipes inch bore, but of different lengths from one foot to thirty feet in length. Remarks :-The ratio of discharge by glass tubes with pipes of 30 feet long, is as 1 : 4 nearly. Ditto with brass orifices, is as 1: 3 Conclusions on Pipes of different Lengths. That the expenditures of water by pipes of equal diameters, but of unequal lengths and under different altitudes, are nearly as follow : The length being as 30 to 1, the expenditures are as 3.7 to 1 Do. . . . . . . 8 to 1 VOL. VIII. SECOND SERIES. do... . 2.6 to 1 2 N The discharges by glass and leaden tubes are nearly alike. The length of a pipe may be increased from 3 to 4 feet without diminishing the discharge as compared with the plate orifices. TABLE X. The straight pipe of an inch bore, on which the preceding experiments were made, was carefully bent into one, two, aud fourteen semicircular bends respectively, each of 7 inches in the semi-diameter, and two of th part of a circle of 34 inches radius. One end of the pipe was fixed in the wooden orifice as before, and the following are the results, Pipe 15 feet long, inch bore, with one semicircular and two 4-circle bends. Height of surface Time in discharging Time in discharging of water above the one cubic foot by a one cubic foot by a centre of orifice. pipe with 3 bends. straight pipe. Remarks: The position of the bends, whether ver- Pipe 15 feet long, inch bore, with 14 semicircular and two 4-circle bends. 1. That with one semicircular and two of a circle bends, as compared with a straight pipe of equal length and bore, the resistance varies from one-36th to one-70th part of the resistance of the straight pipe. 2. That within fourteen semicircular and two quarters of a circle bends, the resistance varies from one-19th to one-39th of the resistance of a straight pipe. 3. That the increased number of bends does not increase the resistance in the ratio of the number of bends, but merely shows an increased resistance, as compared with the four bends, of one14th to one-35th. TABLE XI. Experiments on the Discharge of Water by Leaden Pipes of an inch bore, 15 feet long, but bent in the forms of from one to twenty-four right angled elbows, each side being 63 inches From the foregoing experiments with one rectangular pipe, it would be reasonable to conclude that the diminution of discharge would be as the number of right angles; but comparing the expenditure by one right-angled pipe with the expenditure of a pipe with twenty-four right angles, the difference is only in the ratio of about two to one. General Remarks on the Expenditure of Horizontal Formulæ adapted to the different circumstances of the motion of water in pipes and conduits have been given by various authors. By some, the retardations were supposed to be in the inverse ratios of the squares of the lengths of the pipes; and by others, to be represented by a certain portion of the altitude of the reservoir above the centre of the pipe, the resistance being directly as the length and circumference of the pipe, and inversely as the area of the section. M. Girard, in his beautiful experiments,* conceived the resistance to be compounded of the first and second powers of the velocity. So that, deducing the values from Dubuat's experiments, and expressing the resistance due to cohesion by R x U, R being the quantity to be obtained by experiment, and making the resistance due to the asperities equal to R x U2, the sum of the resistance is R (U+U)2. M. PRONY, applying his profound acquirements to the solution of all the cases of preceding authors, deduced from a selection of upwards of fifty experiments the following simple formula : — U being the mean velocity of the section of the pipe; D the diameter of the pipe; Z the altitude of the water; A the leugth of the pipe: from which it appears that the velocity is directly in the compound ratio of the square roots of the diameter of the pipe and head of of water, and inversely as the square roots of the length of the pipe; that is, for any given head of water and diameter of pipe, the velocity is inversely as the square root of the length of the pipe. If we compare these results with those of Dubuat, Girard, and others, they approximate very nearly to each other. * Memoires des Scavans Etrangers. In general, if we incline a pipe to an angle of about 6 degrees, or one ninth of its legnth, the discharge will be nearly equal to the discharge by additional tubes. The charge necessary to express the mean velocity of water issuing from straight pipes is * Dr. Young makes it ; the 478 550 by some authors equal to diminution of expenditure depending upon the contraction of the fluid vein and the friction of the pipe. The change occasioned by bends and angles in the direction of the fluid vein tends to diminish the velocity in a very remarkable manner. Dubuat undertook several experiments upon this subject, but the formula proposed by him does not solve the difficulty, where V2 S2 m gives the resistance due to one bend, V being the velocity, S the sine of incidence or reflection, and m a constant quantity determined by Dubuat to be 2998.50. Now although it is reasonable to suppose that the resistance should be proportionable to the squares of the sines of the angles of incidence, yet as all the particles of the fluid vein are not reflected in the same angle, and as a considerable portion of the velocity is destoyed by the first angle or bend the fluid meets with in the pipe, M. Dubuat's theory is fundamentally erroneous, the more especially as he has rejected more than one half of the twenty-five experiments mentioned by him. Dr. Young's suppositions, of the resistance being as the angular flexure and the power of the radius, of which the index is 3, are equally erroneous, as is evinced by the foregoing experiments. In conclusion, it is evident that the subject of friction admits of an immense variety of applications. To determine the measure of the resistances experienced by vessels and floating bodies in their motion through fluids; the law of the retardations of rivers, and the cause of the obstructions presented to the waves *DUBUAT and LANGSDORFF. |