MACHINERY,] HYDROMECHANICS 519 known. Mr Froiule has, however, indicated a way in which experi ments, on comparatively small models, may be made so as to furnish very useful data as to the resistance of ships. In order that experi ments on models may be serviceable, it is necessary that their resistance should be measured at speeds for which the different resistances bear the same proportion to each other as in the actual ship. Let d be the ratio of the dimensions of the model to that of the ship. Let Rj, R 2 , R 3 . . . be the resistances of the model at speeds i, r. 2 , v 3 . . . Then it may be expected that the actual ship at speeds t/d, v. 2 /d, v.^d . . . will have resistances (PR,, rf 3 R 2 , (PR.,. This law, however, is not strictly applicable to that part of the resistance which is due to friction, because of the diminution of the coefficient of friction for a given surface as the length increases. Hence, when the resistance of the model has been ascertained, a correction must be made to allow for the different coefficient of friction of the ship. The factional resistances of the model and of the ship are calculated from their immersed surfaces, using the co efficients of friction suitable for their respective lengths. Deduct ing the former and adding the latter to the observed resistance at the corresponding speeds, the total resistance of the ship is ascer tained. XIII. HYDRAULIC MACHINERY. 159. Hydraulic machinery may be broadly divided into hydraulic motor machines and pumps. In the former class, a quantity of water descending from a higher to a lower level, or from a higher to a lower pressure, drives a machine which receives energy from the water, and applies it to overcoming the resistances of other machines doing useful work. In the latter class, work done on the machine by a steam engine or other source of energy is employed in lifting water from a lower to a higher level. A few machines such as the ram and jet pump combine the functions of motors and pumps. WATER MOTORS. In every system of machinery deriving energy from a natural water fall there exist the following parts : (1) A supply channel or head race, leading the water from the highest accessible level to the site of the machine. This may be an open channel of earth, masonry, or wood, laid at as small a slope as is consistent with the delivery of the necessary supply of water, or it may be a closed cast or wrought-iron pipe, laid at the natural slope of the ground, and about 3 feet below the surface. In some cases part of the head race is an open channel, part a closed pipe. The channel often starts from a small storage reservoir, constructed near the stream supplying the water motor, in which the water accumulates when the motor is not working. There are sluices or penstocks by which the supply can be cut off when necessary. (2) Leading from the motor there is a tail race, culvert, or discharge pipe delivering the water after it has done its work at the lowest convenient level. (3) A waste channel, weir, or bye-wash is placed on or at the origin of the head race, by which surplus water, in floods, escapes. (4) The motor itself, of one of the kinds to be described presently, which either overcomes a useful resistance directly, as in the case of a ram acting on a lift or crane chain, or indirectly by actuating transmissive machinery, as when a turbine drives the shafting, belting, and gearing of a mill. With the motor is usually combined regulating machinery for adjusting the power and speed to the work done. This may be controlled in some cases by automatic governing machinery. Water Motors with Artificial Sources of Energy. The great convenience and simplicity of water motors has led to their adoption in certain cases, where no natural source of water power is available. In these cases, an artificial source of w itcr power is created by using a steam engine to pnmp water to a reservoir at a great elevation, or to pump water into a closed reservoir in which there is great pressure, The water flowing from the reservoir through hydraulic engines gives back the energy expended, less so much as has been wasted in friction. Such arrangements are most useful where a continuously acting steam engine stores up energy by pumping the water, while the work done by the hydraulic engines, is done intermittently. 160. Energy of a Water Fall. Let H, be the total fall of level from the point where the water is taken from a natural stream to the point where it is discharged into it again. Of this total fall a por tion, which can be estimated independently, is expended in overcom ing the resistances of the head and tail races or the supply and dis charge pipes. Let this portion of head wasted be fy. Then the available head to work the motor is H = H - ) r . It is this available head which should be used in all calculations of the proportions of the motor. Let Q be the supply of water per second. Then GQH foot-pounds per second is the gross available work of the fall. The power of the fall may be rendered available in three ways. The GQ pounds of water may be placed on a machine at the highest level, and descending in con tact with it a distance of H feet, the work done will be (neglecting losses from friction or leakage) GQH foot-pounds per second. Or the water may descend in a closed pipe from the higher to the lower level, in which case, with the same reservation as before, the pressure at the foot of the pipe will be^? = GH pounds per square foot. If the water with this pressure acts on a movable piston like that of a steam engine, it will drive the piston so that the volume described is Q cubic feet per second. Then the work done will be _pQ = GHQ foot-pounds per second as before. Or lastly, the water may be allowed to acquire the velocity v= V^H by its descent. The kinetic energy of Q cubic G i; 2 feet will then be Q - =GQH, and if the water is allowed to im- 9 * pinge on surfaces suitably curved which bring it finally to rest, it will impart to these the same energy as in the previous cases. Generally, if Q feet per second of water act by weight through a distance h lt at a pressure^ due to h 2 feet of fall, and with a velocity v due to h 3 feet of fall, so that then, apart from energy wasted by friction or leakage or imperfction of the machine, the work done will be G GQh 1 +pQ + - 9 foot pounds, the same as if the water acted simply by its weight while descend ing H feet. 161. Site for Water Motor. Wherever a stream flows from a higher to a lower level it is possible to erect a water motor. The amount of power obtainable depends on the available head and the supply of water. In choosing a site the engineer will select a portion of the stream where there is an abrupt natural fall, or at least a considerable slope of the bed. He will have regard to the facility of construct ing the channels which are to convey the water, and will take advantage of any bend in the river which enables him to shorten them. He will have accurate measurements made of the quantity of water flowing in the stream, and he will endeavour to ascertain the average quantity avail able throughout the year, the minimum quantity in dry seasons, and the maximum for which bye-wash channels must be provided. In many cases the natural fall can be increased by a dam or weir thrown across the stream. The engineer will also examine to what extent the head will vary in different seasons, and whether it is necessary to sacrifice part of the fall and give a steep slope to the tail race to prevent the motor being drowned by backwater in floods. In designing or selecting a water motor it is not sufficient to consider only its efficiency in normal conditions of work ing. It is generally quite as important to know how it will act with a scanty water supply or a diminished head. The greatest difference in water motors is in their adapta
bility to varying conditions of working.
