MACHINERY.] HYDROMECHANICS 521 Since the total pressure on the ram is d?p, the fraction of the total pressure expended in overcoming the friction of the leathers is
- Ato^, rf being in feet
d d Let II 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, H& 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, fl 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 leither and slides. Then, neglecting fluid friction, if the ram is rising the accelerating force is P! = G(H - A)0 - R - W I- B - u-(S - 7t) + wh - F , and if the ram is descending P 2 = - G( H 6 - A)0 + W + R - B + w(S - h) - wh - F . If w = i Gil , 1^ and P 2 are constant throughout the stroke ; and the moving force in ascending and descending is the same, if B = W + R + ?S - Gfi H j5 . u Using the values just found for ic and B, Pi-Pa- iGfi(H-H6)-F. Let "W + R-M S + B = U, and let P be the constant accelerating force acting on the system, then the acceleration is P IT The velocity at the end of the stroke is (assuming the friction to be constant) and the mean velocity of ascent is 1G4. Keif -Acting Hydraulic Engines. The admission and discharge valve in the lift just described is worked by hand at the required times, It is easy to see that mechanism like that used in steam engines can be applied to actuate the admission and discharge valves periodically, and the lift is then converted into a continuously acting engine. 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 TJ the efficiency of the engine. Then the horse-power of the engine is TjGQH 550 The efficiency of large slow-moving pressure engines is ij= 66 to 8. In small motors of this kind probably 77 is not greater than 5. Let v be the mean velocity of the piston, then its diameter d is given by the relation Q = .1L cPv in double-acting engines, 4 oo H.P. - cPi in single-acting engines. If o there are n cylinders put ~- for Q in these equations. n The mean velocity v is from -J- to 2 feet per second in large engines. Smaller engines working on high lifts may be run at a greater speed, but with a sacrifice of efficiency. The usual piston speed of Messrs Hastie s engines de scribed below is 100 feet per minute. For pressures of less than 200 feet of head, the speed is less. The velocity of the water in the supply pipes may be 3 to 6 feet per second. In large engines the admission and discharge valves are of very large size, and require very considerable force to move them. It is also desirable that they should open and close more rapidly than the eccentric-moved valves used in steam engines. In these engines the valves are made cylindrical, so that the water pressure causes no friction of the valve on its seating. They are moved by a weight which is released at ;the proper moment, or by a subsidiary water-pressure engine, the valves of which being Email can be actuated automatically. Tolerably full details of engines with mechanism of this kind are to be found in Weisbach s Mechanics of Engineering. Small pressure engines form extremely convenient motors for hoists, capstans, or winches, and for driving small machinery. They are usually rotative engines, and may be single or double acting. 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. Mr Brotherhood s well-known three-cylinder steam engine has been modified so as to be used as a water-pressure engine. The three cylinders are formed in one casting. The valve is a circular revolving disc with segmental ports> which pass over corresponding apertures in the valve seating during rotation. The valve seating is of lignum vitae. | Fig. 175 shows a similar engine made by Messrs Hastie of Greenock. G, G, G are the three plungers which pass out of the cylinders through cup leathers, and act on the same crank pin. A is the inlet pipe which 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 G is in its extreme positions and as a brake when in its middle position. With the handle in its middle position, the ports of the cylinders are in com munication with 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 end as shown at E. The oscillation of the cylinders puts them alternately in communication with each of these passages, and thus the water is alternately admitted and exhausted. In any ordinary rotative engine the length of stroke is invariable. Consequently the consumption of water depends simply on the speed of the engine, irre spective of the effort overcome. If the power of the engine must be varied with out altering the number of rotations, then the stroke must be made variable. Messrs Hastie have contrived an exceed ingly ingenious method of varyi proportion to the amount of work to be done (fig. 176). Tim crank pin I is carried in a slide H moving in a disk M. In this is a double cam K acting on two small steel rollers J, L attached to the slide H. If the cam rotates it moves the slide and increases or decreases the radius of the circle in which the crank pin I rotates. The disk M is keyed on a hollow shaft surrounding the driving .shaft P, to which the cams are attached. The hollow shaft N has two snugs to which the chains RR are attached (fig. 177). The shaft P carries the spring case SS to which also are attached the other ends of the chains. When the engine is at rest the springs extend them selves, 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. When- XII. 66 Fig. 170.
the stroke automatically, in
