pumped water up to a tank on an elevation, but this is unnecessary, since the same effect can be produced by the use of an accumulator. This apparatus consists simply of a cylinder in which a piston or plunger works, this piston being loaded with heavy weights. Fig. 366 shows the arrangement, the weights being shown resting on the piston rod head; actually they are not applied in this way, but the principle is unaffected. Fig. 366. W supply Let y=greatest height of piston in feet, We can always neglect the pressure The store of energy in the accumulator would not drive the machines for any great time, but during the working it is being continually supplied by the steam engine. For example, in riveting, the engine supplying the accumulator continues working until the piston is right up, this shuts off steam; now a rivet is compressed, the piston falls, opening the steam valve, and the engine starts working again, and so on. Taking a pressure of 1500 lbs. per sq. inch. which is used for riveting, this would require a head of which it would be practically impossible to obtain. Generally, we have the head equivalent to W given by 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 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. 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. Here a platform rests on the 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 π/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 Po 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 D 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 |