A being the piston area, and w the weight of a c. ft. of water. Pressure Machine in Steady Motion.-When a pressure machine is moving steadily at a constant speed, the pressure in the accumulator has to overcome the useful resistance to the moving piston, the friction of the moving parts, and the hydraulic resistances to the motion of the water. These last are of great importance, and we must see what effect they produce. Fig. 367 shows a cylinder C with a piston B. The cylinder is supplied by a pipe A from the accumulator. Let Po pressure in accumulator, P=pressure resisting motion of piston, useful resistance + solid friction, V-velocity of piston, v=velocity of water in pipe. There is now between the accumu B Fig. 367. lator and the working piston a fall of pressure P。 – P, so that head equivalent to this fall of pressure must have been wasted in overcoming hydraulic resistances. Hence where all the separate wastes are referred to the one velocity v (page 489). We choose v in the first instance as the most natural velocity to refer to, but it is more convenient to use V, that being the most easily determined in most practical cases. Let D= diameter of cylinder, Hence the relation between Po, p, and v becomes now where F, is the coefficient of hydraulic resistances referred to the velocity V. From the formula last obtained we see that for a given value of P, V has a certain definite value, i.e. that there is only one particular speed at which the machine can work steadily, and this is called the speed of steady motion. When first started the speed will increase up to this, but will not go beyond so long as P and F remain unaltered. Now this property is not shared by ordinary machines ; in all ordinary cases, if the effort be more than sufficient to balance the resistance, the speed will go on increasing indefinitely, e.g. the racing of an engine, and appliances as governors or brakes must be fitted to prevent this. But a hydraulic machine cannot exceed the speed just found, and so contains automatic brakes within itself. Moreover the speed can be adjusted to any extent we please by altering F, which can be easily effected by means of a cock placed in the supply pipe (see table, page 488). Examples of Pressure Machines.-The working of these machines cannot be fully studied without considering the forces necessary to produce the accelerations of the moving water which necessarily accompany those of the piston, but this is beyond our limits; and so we can only briefly mention a few examples of this type of machine. 1. Direct acting lifts. Here a platform rests on the end of a plunger or ram which is forced out of cylinder by water supplied from a tank. The tank may be used in this instance instead of an accumulator, as the head required is not very great; and besides, since the head decreases as the plunger rises, the velocity is not increased so much as the lift rises, and it can be more easily stopped than it could be were the head constant. The simple figure (Fig. 368) shows all that is necessary for our purposes. A is the platform moving between guides, B is the ram, C the hydraulic cylinder, supplied by the pipe D from the tank at a height h. The ram does not fit the cylinder, so that the water pressure P is not exerted on an area π/4.D2 where D is the diameter of cylinder, but /4. D'2, D' being the diameter of the ram ; the diameter of the cylinder is of no consequence. We have now an actual head h, so that for P, we write wh in the preceding formulæ, and hence determine Vo, the speed of steady motion. The calculation of the effect of the variation of h as the ram rises is beyond our present powers. Fig. 368. supply 2. In a direct acting lift, the length of ram and working cylinder must be more than equal to the total lift, so much space is occupied. To avoid this the platform is in many cases lifted by blocks and tackle, used in the reverse way to that in which we originally considered them. In that case we wished to magnify the effort, but in the present case we can easily obtain any required effort simply by increasing the area of the ram, and we then apply the tackle to magnify the velocity. The working cylinder can be placed in any position, as is most convenient for space; thus for working a derrick on board ship, the cylinder has at various times been bolted to the deck, then to the mast, and in some cases to the jib of the derrick. Fig. 369 shows the application of hydraulic cylinders to a crane. A is the cylinder placed for convenience in a sloping position, B is the ram, the blocks a, b are fastened to the cylinder framing and the end of the ram respectively, and they may contain one, two, or more sheaves as required; the chain, which in the direct manner of using blocks would be acted on by the effort, is now led up through the hollow crane post and over fixed pulleys to the weight to be lifted. If now there were only one sheave in the movable block on B, the thrust of the ram would be 2W when lifting a weight W, and the motion of the ram would be only half that of the weight. For two sheaves at B the motion would be magnified four times, and so on exactly as on page 114. The crane is slewed by hydraulic cylinders, arranged as shown in plan by Fig. 369, and in elevation in Fig. 370. C and C' are equal cylinders, D and D' the rams. A chain is fastened below C, passes over a pulley on the end of D, then round the sheave E on the crane post, over the pulley on the end of D', and is then fastened to a similar point below C'. Evidently if D be thrust out the crane is rotated clockwise, and D' is pulled in, and vice versâ if D' be thrust out. There is no energy expended other than that required to overcome the friction, if the pressure on the water forced out of D′ be utilised, but if not then there is just as much energy used as if the ram C had been thrust out against the full load it could overcome. Differential Rams.-The last point we have mentioned is of great importance, and requires examination. In all cases we have a constant head, h say, producing the pressure Po If then A be the area of the ram, a load PA can be lifted at a very slow speed; if the load be less than PA, the speed must be controlled by means of the frictional resistance, but in all cases the effort is PA, and during a lift y energy PoAy must be exerted. If the load be small the greater part of this energy is necessarily wasted in overcoming the increased friction which must be applied to keep the motion steady, |