438 HYDROMECHANICS A series of interesting hydraulic experiments was made at Rome in 1809 by Mallet and Vici. They found that a pipe whose gauge was five ounces French measure (or 03059 French kilolitres) furnished one-seventh more water than five pipes of one ounce, an effect arising from the velocity being diminished by friction in the ratio of the perimeters of the orifices as compared with their areas. Hachette, in the year 1816, presented to the National Institute a memoir containing the results of experiments which he had made on the spouting of fluids, and the discharge of vessels. The objects he had in view were to measure the contracted part of a fluid vein, to examine the phenomena attendant on additional tubes, and to investigate and describe the figure of the fluid vein, and the results which take place when different forms of orifices are employed. Hachette showed in the second part of his memoir that greater or lesser volumes of water will be discharged in the same time through tubes of different figures, the apertures in all having the same dimensions. He also gave several remarkable results respecting other fluids issuing out of orifices into air or a vacuum. Several very interesting experiments on the propagation of waves have been made by the brothers Weber 1 and by Bidone. Mr John Scott Russell performed a number of experiments on waves, which are described in the Edin burgh Transactions, vol. xiv., and in the British Association Report for 1837. The mathematical theory has been worked out by Green, Stokes, Rankine, and other mathe maticians, but still offers an interesting field for the inves tigator. Stokes s Report of the British Association for 1846 on Recent Researches in Hydrodynamics gives an account of the subject as it existed at that date. In 1826 Bidone, 2 besides his experiments on waves, made a series on the velocity of running water at the hydraulic establishment of the university of Turin, and he published an account of them in 1829. After giving a description of his apparatus and method of experimenting, he gives the figures obtained from fluid veins, sections of which were taken at different distances from the orifice. In the year 1827 Poncelet published a Memoirs sur les Roues Hydrauliques a Aiibes Courbes, containing his experiments on the undershot wheel with curved palettes, which he had invented in the year 1824. The best undershot previous to the introduction of the Poncelet wheel never developed more than 25 of the work of the water, whereas this utilized 60 of that work, which is nearly equivalent to the maximum effect of the breast wheel. The principle on which the Poncelet wheel acts, and that which makes it utilize so much of the work of the water, is that the water is received by the curved floats without any shock, and is discharged finally with a small velocity. This undershot wheel is much used in France. Previous to the year 1827, the wheels required in the mills and manufactories of Germany and France were generally those which worked with the axis horizontal, or the tub and spoon wheels with the axis vertical ; but in that year a young mechanician named Fourneyron introduced a wheel working with the axis vertical, yet wholly different from the latter kind. Fourneyron showed that in existing wheels with a vertical axis the water left the wheel with considerable velocity in the direction of the motion of the wheel, and thus carried away and wasted much of the energy of the fall. By the introduction of a series of fixed guide blades, which gave the water initially a backward velocity of rotation, the water left the wheel with a much smaller velocity of discharge. He thus invented the first complete turbine, a kind of water motor which has largely superseded 1 Wellenlehre auf Experimente yegrundet, Leipsic, 1825. 2 Turin Memoirs, vol. xxv. the more cumbrous water wheels previously in use. Shortly after the invention was made public, Fourneyron was awarded the prize of 6000 francs which was offered by the Society for the Encouragement of National Industry. The most extensive experiments on the discharge of water Eece; from orifices are those made under the direction of the inv f s French Government by Poncelet and Lesbros (Experiences gatl( Hydrauliques, Paris, 1851). Boileau (Traite de la mesure des eaux courantes) has discussed these results and added experiments of his own. Bornemann has re-examined all these results with great care, and has been able to express in formulae the variation of the coefficients of discharge in different conditions (Civilingenieur, 1880). Very valuable experiments leading to a modification of the usual formula for the discharge over weirs were made by Mr J. B. Francis (Loivell Hydraidic Experiments, Boston, Mass., 1855). Wiesbach also has made many experimental investigations of the discharge of fluids. The friction of water investigated originally by Coulomb at slow speeds has been measured for higher speeds by Mr W. Froude, whose researches have very great value in the theory of ship resistance (Report of Brit. Assoc., 1869). The flow of air and steam from orifices has been measured by many experimenters from Young to Saint Venant. Mr Napier in some interesting experiments first pointed out that when the ratio of the pressures on the two sides of an orifice exceeded a certain limit the measured discharge was very different from that calculated by the accepted formulae. Since then numerous experiments have been made, and the theory of the flow of elastic fluids has been discussed in numerous memoirs. The valuable investigations of Fliegner (Civilingenieur, 1878) deserve special mention. A most valuable investigation of the flow of water in pipes and channels has been carried out with exceptional accuracy and on a very large scale by the late M. Darcy, and continued by his successor the late M. Bazin, at the expense of the French Government (Rechcrches Hydrau- li^ues, Paris, 1866). The measurement of the flow in rivers has been extensively carried out, especially by German engineers. Harlacher s Beitrdge zur Hydrographie des Konigreiches Bohmen contains exceedingly valuable measure merits of this kind, and a comparison of the experimental results with all the formulas of flow which have been pro posed. Messrs Humphreys and Abbott s gaugings of the Mississippi for the United States Government, Mr Gordon s gaugings of the Irrawaddi, and Captain Cunningham s experiments on the Ganges Canal may be referred to as having materially advanced hydraulic science. The first adequate theory of turbines is that of Poncelet in the Cornptes Rendus de I Academic de Paris, 1838. Redtenbacher s Theorie und Bau der Turbinen und Ven- tilatoren (Mannheim, 1844) is the first complete treatise on the subject. Girard s turbine, which was of an entirely new type, was discussed in Le Genie industrielle, 1856-1857, and lately by Fink (Civilinyenieur, 1880). Important experiments on turbines were made by Francis (Lowell Hydraulic Experiments, Boston, Mass., 1855). GENERAL PRINCIPLES. Hydromechanics is the science of the equilibrium and motion of fluids, both elastic and non elastic. A fluid is defined to be a substance which yields continually to the slightest tangential stress; and, consequently, when the fluid has come to rest, the stress across any surface in the fluid must be normal to the surface. The stress considered in hydromechanics is always a pressure, as fluids are in general capable of sustaining only a slight tension without disruption (see CAPILLARY ACTION). The intensity of the pressure is measured, as in the subject
of elasticity, by the number of units of force per unit of area.
