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d=diameter of ram in ft.; p=water-pressure in pounds per sq. ft.; k a coefficient. F=kpd k=O~OO393 if the leathers are new or badly lubricated; =o-00262 if the leathers are in good condition and well lubricated. Since the total pressure on the ram is P==i1rd2p, the fraction of the total pressure expended in overcoming the friction of the leathers is F/P= -oo5/d to -0033/d, d being in feet. Let H be the height of the pressure column measured from the free surface of the supply reservoir to the bottom of the ram in its lowest position, Hy, the height from the discharge reservoir to the same point, h the height of the ram above its lowest point at any moment, S the length of stroke, S2 the area of the ram, W the weight of cage, R the weight of ram, B the weight of balance weight, 'w the weight of balance chain per foot run, F the friction of the cup leather and slides. Then, neglecting fluid friction, if the ram is rising the accelerating force is P, =G(H-h)SZ-R-W+B-'w(S-h) -I-wh-F, and if the ram is descending P2= -G(H;, -h)SZ+W-I-R-B+'w(S-h)-wh-F. If ~w=% GS), P1 and P2 are constant throughout the stroke; and the moving force in ascending and descending is the same, if B =W-I-R+wS-Gf2(l-I-l-Hb)/2. Using the values just found for 'w and B, P1 = P2 = § G§ Z(H-Hb) -F. Let W+R+wS+B=U, and let P be the constant accelerating force acting on the system, then the acceleration is (P/U)g The velocity at the end of the stroke is (assuming the friction to be constant) v=~J (2P€5/U): and the mean velocity of ascent is év. § 177. Armstrong? Hydraulic J igger.-This is simply a single acting hydraulic cylinder and ram, provided with sheaves so as to give motion to a wire rope or chain. It is used in various forms of lift and crane. Fig. 172 shows the arrangement. A hydraulic ram or plunger B works in a stationary cylinder A. Ram and cylinder ®< carry sets of sheaves over which passes a chain or rope, fixed at one end to the / cylinder, and at the other connected over @ ”

(°/ guide pulleys to a lift or crane. For each pair of pulleys, one on the cylinder and one on the ram, the movement of the free end of the rope is doubled compared with that of the ram. With three pairs of pulleys the free end of the rope has a movement equal to six times the stroke of the ram, the force exerted being in the inverse proportion. - § 178. Rotalive Hydraulic Engines.-Valvegear mechanism similar in principle to that of steam engines can be applied to actuate the admission and discharge valves, and the pressure engine is then converted into a continuously-acting motor.

k, Let H be the available fall to work the engine after deducting the loss of head in the supply and discharge pipes, Q the supply of water in cubic feet per second, and 1; the efficiency of the engine. Then the horse-power of the en me is 3 H.P.=1;GQH/550. The efficiency of large slow-moving pressure engines is 17= '66 to -8. In small motors of this kind probably 17 IS not greater than -5. Let 'U be the mean velocity of the piston, then its diameter d is given by the relation Q= vrdzv/4 in double-acting engines, =1rd2'v/8 in single-acting engines. If there are n cylinders put Q/n for Q in these equations. Small rotative pressure engines form extremely convenient motors for hoists, capstans or Winches, and for driving small machinery. The single-acting engine has the advantage that the pressure of the piston on the crank pin is always in one direction; there is then no knocking as the dead centres are passed. Generally three single-acting cylinders are used, so that the engine will readily start in all positions, and the driving effort on the crank pin is very uniform. K/ FIG. 172. Brotherhood Hydraulic Engine.-Three cylinders at angles of 120° with each other are formed in one casting with the frame. The plungers are hollow = trunks, and the connecting rods abut in cylindrical recesses in them and are connected to a common crank pin. A circular valve disk with concentric segmental ports revolves at the same rate as the crank over ports in the valve face common to the three cylinders. Each cylinder is always in communication with either an admission or exhaust port. The blank parts of the circular valve close the admission and exhaust ports alternately. The fixed valve face is of li num vitae in a metal recess, and the revolving valye of gun-meta? In the case of a small capstan engine the the piston speed is 31 ft. per minute. The ports are I in. diameter orilg of the piston area, and the mean velocity in the ports 6-4 ft. per sec. With 700 Tb per sq. in. water pressure and an efficiency of 50%, the engine is about 3 h.p. A common arrangement is to have three parallel cylinders acting on a three-throw crank shaft, the cylinders oscillating on trunnions. Hasliels Engine.-Fig. 173 shows a similar engine made by Messrs Hastie of Greenock. G, G, G are the three cylinders are 3% in. diameter and 3 in. stroke. At 40 revs. per minute. E A s G7-'W /, aw J“ it If,) " ' W 'ann // ° '%(/M Fig. 173. plungers which pass out 7 of the cylmderstlirough cup leathers, and act on the same crank pin A is the 1nl t l ' ° e pipe wiich communicates with the cock B. This cock controls the action of the engine, being so constructed that it acts as a reversing valve when the handle C is in its extreme ositions and as a brake when 111 its middle position. ¢Vith the fiandle in its m}dd1¢ IJ0S1U0I1, the ports of the cylinders are in communication w1th the exhaust. Two passages are formed in the framing 'leading from the cock B to the ends of the cylinders, one being in communication with the supply pipe A, the other with the discharge pipe Q. These passages cylinders puts them end as shown at E. The oscillation of the alternately in communication with each of @ , these passages, and thus 5 the water IS alternately -', / 1 K admitted and exhausted @ 3 In any ordinary rota- ', tive engine the length of 'G ff stroke is invariable. Z6 — Consequentlty the con- sumption o water depends simply on the speed of the engine, irrespective of the effort overcome. If the power of the engine must be varied without altering the number of rotations, then the stroke must be made variable. Messrs Hastie have contrived an exceedingly ingenious method of varying the stroke FIG. 174. 174). The crank(pin is carried in a sli e H automatically, in proportion to the amount of work to be done (fig. f""' ~ ' r moving in a disk M., fag, In this IS a double 1 § cam K acting on two E* »'O'; 3 g small steel rollers ], 3, .' '. -', L attached to the 4 5 slide H. If the Cam ., r~»<° T Q rotates it moves the 8 E slide and increases or 5 N 2 H»~ N ¢ E decreases the radius of Q il (7/'Ly S the circle in which the ' ll, QQ) gg crank pin I rotates. § 1', W »< The disk M is keyed T s if, on a hollow shaft sur- T 11, T . H rounding the driving 7' 'E .j - R 'Q shaft P, to which the ' '§ i »cams are attached. f i 13 €7 Elie hollow shaft N § § °" I as two snugs to ~ . § . ., .» which the chains RR "'a;>r g A/fs" are attached (fig. 175). The shaft Pcarries the A F G springcaseSStowhich I ' 175 also are attached the other ends of the chains. When the engine is at rest the springs extend themselves, rotating the hollow shaft N and the frame M, so as to place the crank pin I at its nearest position to the axis of

rotation. W'hen a resistance has to be overcome, the shaft N rotates