§ 170.Energy of a Water-fall.—Let Htbe 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 portion, which can be estimated independently, is expended in overcoming the resistances of the head and tail races or the supply and discharge pipes. Let this portion of head wasted be ɧr. Then the available head to work the motor is H = Ht− ɧr. 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 utilized in three ways. (a) The GQ pounds of water may be placed on a machine at the highest level, and descending in contact with it a distance of H ft., the work done will be (neglecting losses from friction or leakage) GQH foot-pounds per second. (b) 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 p = 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. (c) Or lastly, the water may be allowed to acquire the velocity v = √2gHby its descent. The kinetic energy of Q cubic feet will then be1⁄2GQv2/g = GQH, and if the water is allowed to impinge on surfaces suitably curved which bring it finally to rest, it will impart to these the same energy as in the previous cases. Motors which receive energy mainly in the three ways described in (a), (b), (c) may be termed gravity, pressure and inertia motors respectively. Generally, if Q ft. per second of water act by weight through a distance h1, at a pressure p due to h2ft. of fall, and with a velocity v due to h3ft. of fall, so that h1+ h2+ h3= H, then, apart from energy wasted by friction or leakage or imperfection of the machine, the work done will beGQh1+ pQ + (G/g) Q (v2/2g) = GQH foot pounds,the same as if the water acted simply by its weight while descending H ft.
§ 170.Energy of a Water-fall.—Let Htbe 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 portion, which can be estimated independently, is expended in overcoming the resistances of the head and tail races or the supply and discharge pipes. Let this portion of head wasted be ɧr. Then the available head to work the motor is H = Ht− ɧr. 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 utilized in three ways. (a) The GQ pounds of water may be placed on a machine at the highest level, and descending in contact with it a distance of H ft., the work done will be (neglecting losses from friction or leakage) GQH foot-pounds per second. (b) 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 p = 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. (c) Or lastly, the water may be allowed to acquire the velocity v = √2gHby its descent. The kinetic energy of Q cubic feet will then be1⁄2GQv2/g = GQH, and if the water is allowed to impinge on surfaces suitably curved which bring it finally to rest, it will impart to these the same energy as in the previous cases. Motors which receive energy mainly in the three ways described in (a), (b), (c) may be termed gravity, pressure and inertia motors respectively. Generally, if Q ft. per second of water act by weight through a distance h1, at a pressure p due to h2ft. of fall, and with a velocity v due to h3ft. of fall, so that h1+ h2+ h3= H, then, apart from energy wasted by friction or leakage or imperfection of the machine, the work done will be
GQh1+ pQ + (G/g) Q (v2/2g) = GQH foot pounds,
the same as if the water acted simply by its weight while descending H ft.
§ 171.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 constructing 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 available 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. Streams fed from lakes which form natural reservoirs or fed from glaciers are less variable than streams depending directly on rainfall, and are therefore advantageous for water-power purposes.
§ 172.Water Power at Holyoke, U.S.A.—About 85 m. from the mouth of the Connecticut river there was a fall of about 60 ft. in a short distance, forming what were called the Grand Rapids, below which the river turned sharply, forming a kind of peninsula on which the city of Holyoke is built. In 1845 the magnitude of the water-power available attracted attention, and it was decided to build a dam across the river. The ordinary flow of the river is 6000 cub. ft. per sec., giving a gross power of 30,000 h.p. In dry seasons the power is 20,000 h.p., or occasionally less. From above the dam a system of canals takes the water to mills on three levels. The first canal starts with a width of 140 ft. and depth of 22 ft., and supplies the highest range of mills. A second canal takes the water which has driven turbines in the highest mills and supplies it to a second series of mills. There is a third canal on a still lower level supplying the lowest mills. The water then finds its way back to the river. With the grant of a mill site is also leased the right to use the water-power. A mill-power is defined as 38 cub. ft. of water per sec. during 16 hours per day on a fall of 20 ft. This gives about 60 h.p. effective. The charge for the power water is at the rate of 20s. per h.p. per annum.
§ 172.Water Power at Holyoke, U.S.A.—About 85 m. from the mouth of the Connecticut river there was a fall of about 60 ft. in a short distance, forming what were called the Grand Rapids, below which the river turned sharply, forming a kind of peninsula on which the city of Holyoke is built. In 1845 the magnitude of the water-power available attracted attention, and it was decided to build a dam across the river. The ordinary flow of the river is 6000 cub. ft. per sec., giving a gross power of 30,000 h.p. In dry seasons the power is 20,000 h.p., or occasionally less. From above the dam a system of canals takes the water to mills on three levels. The first canal starts with a width of 140 ft. and depth of 22 ft., and supplies the highest range of mills. A second canal takes the water which has driven turbines in the highest mills and supplies it to a second series of mills. There is a third canal on a still lower level supplying the lowest mills. The water then finds its way back to the river. With the grant of a mill site is also leased the right to use the water-power. A mill-power is defined as 38 cub. ft. of water per sec. during 16 hours per day on a fall of 20 ft. This gives about 60 h.p. effective. The charge for the power water is at the rate of 20s. per h.p. per annum.
§ 173.Action of Water in a Water Motor.—Water motors may be divided into water-pressure engines, water-wheels and turbines.
Water-pressure engines are machines with a cylinder and piston or ram, in principle identical with the corresponding part of a steam-engine. The water is alternately admitted to and discharged from the cylinder, causing a reciprocating action of the piston or plunger. It is admitted at a high pressure and discharged at a low one, and consequently work is done on the piston. The water in these machines never acquires a high velocity, and for the most part the kinetic energy of the water is wasted. The useful work is due to the difference of the pressure of admission and discharge, whether that pressure is due to the weight of a column of water of more or less considerable height, or is artificially produced in ways to be described presently.
Water-wheels are large vertical wheels driven by water falling from a higher to a lower level. In most water-wheels, the water acts directly by its weight loading one side of the wheel and so causing rotation. But in all water-wheels a portion, and in some a considerable portion, of the work due to gravity is first employed to generate kinetic energy in the water; during its action on the water-wheel the velocity of the water diminishes, and the wheel is therefore in part driven by the impulse due to the change of the water’s momentum. Water-wheels are therefore motors on which the water acts, partly by weight, partly by impulse.
Turbines are wheels, generally of small size compared with water wheels, driven chiefly by the impulse of the water. Before entering the moving part of the turbine, the water is allowed to acquire a considerable velocity; during its action on the turbine this velocity is diminished, and the impulse due to the change of momentum drives the turbine.
In designing or selecting a water motor it is not sufficient to consider only its efficiency in normal conditions of working. 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 adaptability to varying conditions of working.
Water-pressure Engines.
§ 174. In these the water acts by pressure either due to the height of the column in a supply pipe descending from a high-level reservoir, or created by pumping. Pressure engines were first used in mine-pumping on waterfalls of greater height than could at that time be utilized by water wheels. Usually they were single acting, the water-pressure lifting the heavy pump rods which then made the return or pumping stroke by their own weight. To avoid losses by fluid friction and shock the velocity of the water in the pipes and passages was restricted to from 3 to 10 ft. per second, and the mean speed of plunger to 1 ft. per second. The stroke was long and the number of strokes 3 to 6 per minute. The pumping lift being constant, such engines worked practically always at full load, and the efficiency was high, about 84%. But they were cumbrous machines. They are described in Weisbach’sMechanics of Engineering.
The convenience of distributing energy from a central station to scattered working-points by pressure water conveyed in pipes—a system invented by Lord Armstrong—has already been mentioned. This system has led to the development of a great variety of hydraulic pressure engines of very various types. The cost of pumping the pressure water to some extent restricts its use to intermittent operations, such as working lifts and cranes, punching, shearing and riveting machines, forging and flanging presses. To keep down the cost of the distributingmains very high pressures are adopted, generally 700 ℔ per sq. in. or 1600 ft. of head or more.
In a large number of hydraulic machines worked by water at high pressure, especially lifting machines, the motor consists of a direct, single acting ram and cylinder. In a few cases double-acting pistons and cylinders are used; but they involve a water-tight packing of the piston not easily accessible. In some cases pressure engines are used to obtain rotative movement, and then two double-acting cylinders or three single-acting cylinders are used, driving a crank shaft. Some double-acting cylinders have a piston rod half the area of the piston. The pressure water acts continuously on the annular area in front of the piston. During the forward stroke the pressure on the front of the piston balances half the pressure on the back. During the return stroke the pressure on the front is unopposed. The water in front of the piston is not exhausted, but returns to the supply pipe. As the frictional losses in a fluid are independent of the pressure, and the work done increases directly as the pressure, the percentage loss decreases for given velocities of flow as the pressure increases. Hence for high-pressure machines somewhat greater velocities are permitted in the passages than for low-pressure machines. In supply mains the velocity is from 3 to 6 ft. per second, in valve passages 5 to 10 ft. per second, or in extreme cases 20 ft. per second, where there is less object in economizing energy. As the water is incompressible, slide valves must have neither lap nor lead, and piston valves are preferable to ordinary slide valves. To prevent injurious compression from exhaust valves closing too soon in rotative engines with a fixed stroke, small self-acting relief valves are fitted to the cylinder ends, opening outwards against the pressure into the valve chest. Imprisoned water can then escape without over-straining the machines.
In direct single-acting lift machines, in which the stroke is fixed, and in rotative machines at constant speed it is obvious that the cylinder must be filled at each stroke irrespective of the amount of work to be done. The same amount of water is used whether much or little work is done, or whether great or small weights are lifted. Hence while pressure engines are very efficient at full load, their efficiency decreases as the load decreases. Various arrangements have been adopted to diminish this defect in engines working with a variable load. In lifting machinery there is sometimes a double ram, a hollow ram enclosing a solid ram. By simple arrangements the solid ram only is used for small loads, but for large loads the hollow ram is locked to the solid ram, and the two act as a ram of larger area. In rotative engines the case is more difficult. In Hastie’s and Rigg’s engines the stroke is automatically varied with the load, increasing when the load is large and decreasing when it is small. But such engines are complicated and have not achieved much success. Where pressure engines are used simplicity is generally a first consideration, and economy is of less importance.
§ 175.Efficiency of Pressure Engines.—It is hardly possible to form a theoretical expression for the efficiency of pressure engines, but some general considerations are useful. Consider the case of a long stroke hydraulic ram, which has a fairly constant velocity v during the stroke, and valves which are fairly wide open during most of the stroke. Let r be the ratio of area of ram to area of valve passage, a ratio which may vary in ordinary cases from 4 to 12. Then the loss in shock of the water entering the cylinder will be (r − 1)2v2/2g in ft. of head. The friction in the supply pipe is also proportional to v2. The energy carried away in exhaust will be proportional to v2. Hence the total hydraulic losses may be taken to be approximately ζv2/2g ft., where ζ is a coefficient depending on the proportions of the machine. Let f be the friction of the ram packing and mechanism reckoned in ℔ per sq. ft. of ram area. Then if the supply-pipe pressure driving the machine is p ℔ per sq. ft., the effective working pressure will bep − Gζv2/ 2g − f ℔ per sq. ft.Let A be the area of the ram in sq. ft., v its velocity in ft. per sec. The useful work done will be(p − Gζv2/ 2g − f) Av ft. ℔ per sec.,and the efficiency of the machine will beη = (p − Gζv2/ 2g − f) / p.Fig. 171.This shows that the efficiency increases with the pressure p, and diminishes with the speed v, other things being the same. If in regulating the engine for varying load the pressure is throttled, part of the available head is destroyed at the throttle valve, and p in the bracket above is reduced. Direct-acting hydraulic lifts, without intermediate gearing, may have an efficiency of 95% during the working stroke. If a hydraulic jigger is used with ropes and sheaves to change the speed of the ram to the speed of the lift, the efficiency may be only 50%. E. B. Ellington has given the efficiency of lifts with hydraulic balance at 85% during the working stroke. Large pressure engines have an efficiency of 85%, but small rotative engines probably not more than 50% and that only when fully loaded.
§ 175.Efficiency of Pressure Engines.—It is hardly possible to form a theoretical expression for the efficiency of pressure engines, but some general considerations are useful. Consider the case of a long stroke hydraulic ram, which has a fairly constant velocity v during the stroke, and valves which are fairly wide open during most of the stroke. Let r be the ratio of area of ram to area of valve passage, a ratio which may vary in ordinary cases from 4 to 12. Then the loss in shock of the water entering the cylinder will be (r − 1)2v2/2g in ft. of head. The friction in the supply pipe is also proportional to v2. The energy carried away in exhaust will be proportional to v2. Hence the total hydraulic losses may be taken to be approximately ζv2/2g ft., where ζ is a coefficient depending on the proportions of the machine. Let f be the friction of the ram packing and mechanism reckoned in ℔ per sq. ft. of ram area. Then if the supply-pipe pressure driving the machine is p ℔ per sq. ft., the effective working pressure will be
p − Gζv2/ 2g − f ℔ per sq. ft.
Let A be the area of the ram in sq. ft., v its velocity in ft. per sec. The useful work done will be
(p − Gζv2/ 2g − f) Av ft. ℔ per sec.,
and the efficiency of the machine will be
η = (p − Gζv2/ 2g − f) / p.
This shows that the efficiency increases with the pressure p, and diminishes with the speed v, other things being the same. If in regulating the engine for varying load the pressure is throttled, part of the available head is destroyed at the throttle valve, and p in the bracket above is reduced. Direct-acting hydraulic lifts, without intermediate gearing, may have an efficiency of 95% during the working stroke. If a hydraulic jigger is used with ropes and sheaves to change the speed of the ram to the speed of the lift, the efficiency may be only 50%. E. B. Ellington has given the efficiency of lifts with hydraulic balance at 85% during the working stroke. Large pressure engines have an efficiency of 85%, but small rotative engines probably not more than 50% and that only when fully loaded.
§ 176.Direct-Acting Hydraulic Lift(fig. 171).—This is the simplest of all kinds of hydraulic motor. A cage W is lifted directly by water pressure acting in a cylinder C, the length of which is a little greater than the lift. A ram or plunger R of the same length is attached to the cage. The water-pressure admitted by a cock to the cylinder forces up the ram, and when the supply valve is closed and the discharge valve opened, the ram descends. In this case the ram is 9 in. diameter, with a stroke of 49 ft. It consists of lengths of wrought-iron pipe screwed together perfectly water-tight, the lower end being closed by a cast-iron plug. The ram works in a cylinder 11 in. diameter of 9 ft. lengths of flanged cast-iron pipe. The ram passes water-tight through the cylinder cover, which is provided with double hat leathers to prevent leakage outwards or inwards. As the weight of the ram and cage is much more than sufficient to cause a descent of the cage, part of the weight is balanced. A chain attached to the cage passes over a pulley at the top of the lift, and carries at its free end a balance weight B, working inTiron guides. Water is admitted to the cylinder from a 4-in. supply pipe through a two-way slide, worked by a rack, spindle and endless rope. The lift works under 73 ft. of head, and lifts 1350 lb at 2 ft. per second. The efficiency is from 75 to 80%.
The principal prejudicial resistance to the motion of a ram of this kind is the friction of the cup leathers, which make the joint between the cylinder and ram. Some experiments by John Hick give for the friction of these leathers the following formula. Let F = the total friction in pounds;d = diameter of ram in ft.; p = water-pressure in pounds per sq. ft.; k a coefficient.F = k p dk = 0.00393 if the leathers are new or badly lubricated;= 0.00262 if the leathers are in good condition and well lubricated.Since the total pressure on the ram is P =1⁄4πd2p, the fraction of the total pressure expended in overcoming the friction of the leathers is F/P = .005/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, Hbthe 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, Ω 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 isP1= G (H − h) Ω − R − W + B − w (S − h) + wh − F,and if the ram is descendingP2= G (Hb− h) Ω + W + R − B + w (S − h) − wh − F.If w =1⁄2GΩ, P1and P2are constant throughout the stroke; and the moving force in ascending and descending is the same, ifB = W + R + wS − GΩ (H + Hb) / 2.Using the values just found for w and B,P1= P2=1⁄2GΩ (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 = √ (2PgS / U);and the mean velocity of ascent is1⁄2v.
The principal prejudicial resistance to the motion of a ram of this kind is the friction of the cup leathers, which make the joint between the cylinder and ram. Some experiments by John Hick give for the friction of these leathers the following formula. Let F = the total friction in pounds;d = diameter of ram in ft.; p = water-pressure in pounds per sq. ft.; k a coefficient.
F = k p d
k = 0.00393 if the leathers are new or badly lubricated;
= 0.00262 if the leathers are in good condition and well lubricated.
Since the total pressure on the ram is P =1⁄4πd2p, the fraction of the total pressure expended in overcoming the friction of the leathers is F/P = .005/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, Hbthe 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, Ω 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
P1= G (H − h) Ω − R − W + B − w (S − h) + wh − F,
and if the ram is descending
P2= G (Hb− h) Ω + W + R − B + w (S − h) − wh − F.
If w =1⁄2GΩ, P1and P2are constant throughout the stroke; and the moving force in ascending and descending is the same, if
B = W + R + wS − GΩ (H + Hb) / 2.
Using the values just found for w and B,
P1= P2=1⁄2GΩ (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 = √ (2PgS / U);
and the mean velocity of ascent is1⁄2v.
§ 177.Armstrong’s Hydraulic Jigger.—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.Rotative Hydraulic Engines.—Valve-gear 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.
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 η the efficiency of the engine. Then the horse-power of the engine isH.P. = ηGQH / 550.The efficiency of large slow-moving pressure engines is η = .66 to .8. In small motors of this kind probably η is not greater than .5. Let v be the mean velocity of the piston, then its diameter d is given by the relationQ = πd2v/4 in double-acting engines,= πd2v/8 in single-acting engines.If there are n cylinders put Q/n for Q in these equations.
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 η the efficiency of the engine. Then the horse-power of the engine is
H.P. = ηGQH / 550.
The efficiency of large slow-moving pressure engines is η = .66 to .8. In small motors of this kind probably η is not greater than .5. Let v be the mean velocity of the piston, then its diameter d is given by the relation
Q = πd2v/4 in double-acting engines,= πd2v/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.
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 lignum vitae in a metal recess, and the revolving valve of gun-metal. In the case of a small capstan engine the cylinders are 31⁄2in. diameter and 3 in. stroke. At 40 revs. per minute, the piston speed is 31 ft. per minute. The ports are 1 in. diameter or1⁄12of the piston area, and the mean velocity in the ports 6.4 ft. per sec. With 700 ℔ 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.Hastie’s Engine.—Fig. 173 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 C 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 communication 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, 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 automatically, in proportion to the amount of work to be done (fig. 174). The 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. 175). 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 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. When a resistance has to be overcome, the shaft N rotatesrelatively to P, compressing the springs, till their resistance balances the pressure due to the resistance to the rotation of P. The engine then commences to work, the crank pin being in the position in which the turning effort just overcomes the resistance. If the resistance diminishes, the springs force out the chains and shorten the stroke of the plungers, and vice versa. The following experiments, on an engine of this kind working a hoist, show how the automatic arrangement adjusted the water used to the work done. The lift was 22 ft. and the water pressure in the cylinders 80 ℔ per sq. in.Weight lifted, in ℔Chain only42763374585796910811193Water used, in gallons71⁄210141617202122
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 lignum vitae in a metal recess, and the revolving valve of gun-metal. In the case of a small capstan engine the cylinders are 31⁄2in. diameter and 3 in. stroke. At 40 revs. per minute, the piston speed is 31 ft. per minute. The ports are 1 in. diameter or1⁄12of the piston area, and the mean velocity in the ports 6.4 ft. per sec. With 700 ℔ 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.
Hastie’s Engine.—Fig. 173 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 C 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 communication 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, 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 automatically, in proportion to the amount of work to be done (fig. 174). The 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. 175). 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 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. When a resistance has to be overcome, the shaft N rotatesrelatively to P, compressing the springs, till their resistance balances the pressure due to the resistance to the rotation of P. The engine then commences to work, the crank pin being in the position in which the turning effort just overcomes the resistance. If the resistance diminishes, the springs force out the chains and shorten the stroke of the plungers, and vice versa. The following experiments, on an engine of this kind working a hoist, show how the automatic arrangement adjusted the water used to the work done. The lift was 22 ft. and the water pressure in the cylinders 80 ℔ per sq. in.
§ 179.Accumulator Machinery.—It has already been pointed out that it is in some cases convenient to use a steam engine to create an artificial head of water, which is afterwards employed in driving water-pressure machinery. Where power is required intermittently, for short periods, at a number of different points, as, for instance, in moving the cranes, lock gates, &c., of a dockyard, a separate steam engine and boiler at each point is very inconvenient; nor can engines worked from a common boiler be used, because of the great loss of heat and the difficulties which arise out of condensation in the pipes. If a tank, into which water is continuously pumped, can be placed at a great elevation, the water can then be used in hydraulic machinery in a very convenient way. Each hydraulic machine is put in communication with the tank by a pipe, and on opening a valve it commences work, using a quantity of water directly proportional to the work done. No attendance is required when the machine is not working.
A site for such an elevated tank is, however, seldom available, and in place of it a beautiful arrangement termed an accumulator, invented by Lord Armstrong, is used. This consists of a tall vertical cylinder; into this works a solid ram through cup leathers or hemp packing, and the ram is loaded by fixed weights, so that the pressure in the cylinder is 700 ℔ or 800 ℔ per sq. in. In some cases the ram is fixed and the cylinder moves on it. The pumping engines which supply the energy that is stored in the accumulator should be a pair coupled at right angles, so as to start in any position. The engines pump into the accumulator cylinder till the ram is at the top of its stroke, when by a catch arrangement acting on the engine throttle valve the engines are stopped. If the accumulator ram descends, in consequence of water being taken to work machinery, the engines immediately recommence working. Pipes lead from the accumulator to each of the machines requiring to be driven, and do not require to be of large size, as the pressure is so great.
Fig. 176 shows a diagrammatic way the scheme of a system of accumulator machinery. A is the accumulator, with its ram carrying a cylindrical wrought-iron tank W, in which weights are placed to load the accumulator. At R is one of the pressure engines or jiggers, worked from the accumulator, discharging the water after use into the tank T. In this case the pressure engine is shown working a set of blocks, the fixed block being on the ram cylinder, the running block on the ram. The chain running over these blocks works a lift cage C, the speed of which is as many times greater than that of the ram as there are plies of chain on the block tackle. B is the balance weight of the cage.Fig. 177.In the use of accumulators on shipboard for working gun gear or steering gear, the accumulator ram is loaded by springs, or by steam pressure acting on a piston much larger than the ram.R. H. Tweddell has used accumulators with a pressure of 2000 ℔ per sq. in. to work hydraulic riveting machinery.The amount of energy stored in the accumulator, having a ram d in. in diameter, a stroke of S ft., and delivering at p ℔ pressure per sq. in., isπ/4 p d2S foot-pounds.Thus, if the ram is 9 in., the stroke 20 ft., and the pressure 800 ℔ per sq. in., the work stored in the accumulator when the ram is at the top of the stroke is 1,017,600 foot-pounds, that is, enough to drive a machine requiring one horse power for about half an hour. As, however, the pumping engine replaces water as soon as it is drawn off, the working capacity of the accumulator is very much greater than this. Tweddell found that an accumulator charged at 1250 ℔ discharged at 1225 ℔ per sq. in. Hence the friction was equivalent to 121⁄2℔ per sq. in. and the efficiency 98%.When a very great pressure is required a differential accumulator (fig. 177) is convenient. The ram is fixed and passes through both ends of the cylinder, but is of different diameters at the two ends, A and B. Hence if d1, d2are the diameters of the ram in inches and p the required pressure in ℔ per sq. in., the load required is1⁄4pπ(d12− d22). An accumulator of this kind used with riveting machines has d1= 51⁄2in., d2= 43⁄4in. The pressure is 2000 ℔ per sq. in. and the load 5.4 tons.Fig. 178.Sometimes an accumulator is loaded by water or steam pressure instead of by a dead weight. Fig. 178 shows the arrangement. A piston A is connected to a plunger B of much smaller area. Water pressure, say from town mains, is admitted below A, and the high pressure water is pumped into and discharged from the cylinder C in which B works. If r is the ratio of the areas of A and B, then, neglecting friction, the pressure in the upper cylinder is r times that under the piston A. With a variable rate of supply and demand from the upper cylinder, the piston A rises and falls, maintaining always a constant pressure in the upper cylinder.
Fig. 176 shows a diagrammatic way the scheme of a system of accumulator machinery. A is the accumulator, with its ram carrying a cylindrical wrought-iron tank W, in which weights are placed to load the accumulator. At R is one of the pressure engines or jiggers, worked from the accumulator, discharging the water after use into the tank T. In this case the pressure engine is shown working a set of blocks, the fixed block being on the ram cylinder, the running block on the ram. The chain running over these blocks works a lift cage C, the speed of which is as many times greater than that of the ram as there are plies of chain on the block tackle. B is the balance weight of the cage.
In the use of accumulators on shipboard for working gun gear or steering gear, the accumulator ram is loaded by springs, or by steam pressure acting on a piston much larger than the ram.
R. H. Tweddell has used accumulators with a pressure of 2000 ℔ per sq. in. to work hydraulic riveting machinery.
The amount of energy stored in the accumulator, having a ram d in. in diameter, a stroke of S ft., and delivering at p ℔ pressure per sq. in., is
π/4 p d2S foot-pounds.
Thus, if the ram is 9 in., the stroke 20 ft., and the pressure 800 ℔ per sq. in., the work stored in the accumulator when the ram is at the top of the stroke is 1,017,600 foot-pounds, that is, enough to drive a machine requiring one horse power for about half an hour. As, however, the pumping engine replaces water as soon as it is drawn off, the working capacity of the accumulator is very much greater than this. Tweddell found that an accumulator charged at 1250 ℔ discharged at 1225 ℔ per sq. in. Hence the friction was equivalent to 121⁄2℔ per sq. in. and the efficiency 98%.
When a very great pressure is required a differential accumulator (fig. 177) is convenient. The ram is fixed and passes through both ends of the cylinder, but is of different diameters at the two ends, A and B. Hence if d1, d2are the diameters of the ram in inches and p the required pressure in ℔ per sq. in., the load required is1⁄4pπ(d12− d22). An accumulator of this kind used with riveting machines has d1= 51⁄2in., d2= 43⁄4in. The pressure is 2000 ℔ per sq. in. and the load 5.4 tons.
Sometimes an accumulator is loaded by water or steam pressure instead of by a dead weight. Fig. 178 shows the arrangement. A piston A is connected to a plunger B of much smaller area. Water pressure, say from town mains, is admitted below A, and the high pressure water is pumped into and discharged from the cylinder C in which B works. If r is the ratio of the areas of A and B, then, neglecting friction, the pressure in the upper cylinder is r times that under the piston A. With a variable rate of supply and demand from the upper cylinder, the piston A rises and falls, maintaining always a constant pressure in the upper cylinder.
Water Wheels.
§ 180.Overshot and High Breast Wheels.—When a water fall ranges between 10 and 70 ft. and the water supply is from 3 to 25 cub. ft. per second, it is possible to construct a bucket wheel on which the water acts chiefly by its weight. If the variation of the head-water level does not exceed 2 ft., an overshot wheel may be used (fig. 179). The water is then projected over the summit of the wheel, and falls in a parabolic path into the buckets. With greater variation of head-water level, a pitch-back or high breast wheel is better. The water falls over the top of a sliding sluice into the wheel, on the same side as the head race channel. By adjusting the height of the sluice, the requisite supply is given to the wheel in all positions of the head-water level.
The wheel consists of a cast-iron or wrought-iron axle C supporting the weight of the wheel. To this are attached twosets of arms A of wood or iron, which support circular segmental plates, B, termed shrouds. A cylindrical sole plate dd extends between the shrouds on the inner side. The buckets are formed by wood planks or curved wrought-iron plates extending from shroud to shroud, the back of the buckets being formed by the sole plate.
The efficiency may be taken at 0.75. Hence, if h.p. is the effective horse power, H the available fall, and Q the available water supply per second,h.p. = 0.75 (GQH/550) = 0.085 QH.If the peripheral velocity of the water wheel is too great, water is thrown out of the buckets before reaching the bottom of the fall. In practice, the circumferential velocity of water wheels of the kind now described is from 41⁄2to 10 ft. per second, about 6 ft. being the usual velocity of good iron wheels not of very small size. In order that the water may enter the buckets easily, it must have a greater velocity than the wheel. Usually the velocity of the water at the point where it enters the wheel is from 9 to 12 ft. per second, and to produce this it must enter the wheel at a point 16 to 27 in. below the head-water level. Hence the diameter of an overshot wheel may beD = H − 11⁄3to H − 21⁄4ft.Overshot and high breast wheels work badly in backwater, and hence if the tail-water level varies, it is better to reduce the diameter of the wheel so that its greatest immersion in flood is not more than 1 ft. The depth d of the shrouds is about 10 to 16 in. The number of buckets may be aboutN = πD / d.Let v be the peripheral velocity of the wheel. Then the capacity of that portion of the wheel which passes the sluice in one second isQ1= vb (Dd − d2) / D= v b d nearly,b being the breadth of the wheel between the shrouds. If, however, this quantity of water were allowed to pass on to the wheel the buckets would begin to spill their contents almost at the top of the fall. To diminish the loss from spilling, it is not only necessary to give the buckets a suitable form, but to restrict the water supply to one-fourth or one-third of the gross bucket capacity. Let m be the value of this ratio; then, Q being the supply of water per second,Q = mQ1= mb dv.This gives the breadth of the wheel if the water supply is known. The form of the buckets should be determined thus. The outer element of the bucket should be in the direction of motion of the water entering relatively to the wheel, so that the water may enter without splashing or shock. The buckets should retain the water as long as possible, and the width of opening of the buckets should be 2 or 3 in. greater than the thickness of the sheet of water entering.Fig. 180.For a wooden bucket (fig. 180, A), take ab = distance between two buckets on periphery of wheel. Make ed =1⁄2eb and bc =6⁄5to5⁄4ab. Join cd. For an iron bucket (fig. 180, B), take ed =1⁄3eb; bc =6⁄5ab. Draw cO making an angle of 10° to 15° with the radius at c. On Oc take a centre giving a circular arc passing near d, and round the curve into the radial part of the bucket de.
The efficiency may be taken at 0.75. Hence, if h.p. is the effective horse power, H the available fall, and Q the available water supply per second,
h.p. = 0.75 (GQH/550) = 0.085 QH.
If the peripheral velocity of the water wheel is too great, water is thrown out of the buckets before reaching the bottom of the fall. In practice, the circumferential velocity of water wheels of the kind now described is from 41⁄2to 10 ft. per second, about 6 ft. being the usual velocity of good iron wheels not of very small size. In order that the water may enter the buckets easily, it must have a greater velocity than the wheel. Usually the velocity of the water at the point where it enters the wheel is from 9 to 12 ft. per second, and to produce this it must enter the wheel at a point 16 to 27 in. below the head-water level. Hence the diameter of an overshot wheel may be
D = H − 11⁄3to H − 21⁄4ft.
Overshot and high breast wheels work badly in backwater, and hence if the tail-water level varies, it is better to reduce the diameter of the wheel so that its greatest immersion in flood is not more than 1 ft. The depth d of the shrouds is about 10 to 16 in. The number of buckets may be about
N = πD / d.
Let v be the peripheral velocity of the wheel. Then the capacity of that portion of the wheel which passes the sluice in one second is
Q1= vb (Dd − d2) / D= v b d nearly,
b being the breadth of the wheel between the shrouds. If, however, this quantity of water were allowed to pass on to the wheel the buckets would begin to spill their contents almost at the top of the fall. To diminish the loss from spilling, it is not only necessary to give the buckets a suitable form, but to restrict the water supply to one-fourth or one-third of the gross bucket capacity. Let m be the value of this ratio; then, Q being the supply of water per second,
Q = mQ1= mb dv.
This gives the breadth of the wheel if the water supply is known. The form of the buckets should be determined thus. The outer element of the bucket should be in the direction of motion of the water entering relatively to the wheel, so that the water may enter without splashing or shock. The buckets should retain the water as long as possible, and the width of opening of the buckets should be 2 or 3 in. greater than the thickness of the sheet of water entering.
For a wooden bucket (fig. 180, A), take ab = distance between two buckets on periphery of wheel. Make ed =1⁄2eb and bc =6⁄5to5⁄4ab. Join cd. For an iron bucket (fig. 180, B), take ed =1⁄3eb; bc =6⁄5ab. Draw cO making an angle of 10° to 15° with the radius at c. On Oc take a centre giving a circular arc passing near d, and round the curve into the radial part of the bucket de.
There are two ways in which the power of a water wheel is given off to the machinery driven. In wooden wheels and wheels with rigid arms, a spur or bevil wheel keyed on the axle of the turbine will transmit the power to the shafting. It is obvious that the whole turning moment due to the weight of the water is then transmitted through the arms and axle of the water wheel. When the water wheel is an iron one, it usually has light iron suspension arms incapable of resisting the bending action due to the transmission of the turning effort to the axle. In that case spur segments are bolted to one of the shrouds, and the pinion to which the power is transmitted is placed so that the teeth in gear are, as nearly as may be, on the line of action of the resultant of the weight of the water in the loaded arc of the wheel.
The largest high breast wheels ever constructed were probably the four wheels, each 50 ft. in diameter, and of 125 h.p., erected by Sir W. Fairbairn in 1825 at Catrine in Ayrshire. These wheels are still working.
§ 181.Poncelet Water Wheel.—When the fall does not exceed 6 ft., the best water motor to adopt in many cases is the Poncelet undershot water wheel. In this the water acts very nearly in the same way as in a turbine, and the Poncelet wheel, although slightly less efficient than the best turbines, in normal conditions of working, is superior to most of them when working with a reduced supply of water. A general notion of the action of the water on a Poncelet wheel has already been given in § 159. Fig. 181 shows its construction. The water penned back between the side walls of the wheel pit is allowed to flow to the wheel under a movable sluice, at a velocity nearly equal to the velocity due to the whole fall. The water is guided down a slope of 1 in 10, or a curved race, and enters the wheel without shock. Gliding up the curved floats it comes to rest, falls back, and acquires at the point of discharge a backward velocity relative to the wheel nearly equal to the forward velocity of the wheel. Consequently it leaves the wheel deprived of nearly the whole of its original kinetic energy.
Taking the efficiency at 0.60, and putting H for the available fall, h.p. for the horse-power, and Q for the water supply per second,h.p. = 0.068 QH.The diameter D of the wheel may be taken arbitrarily. It should not be less than twice the fall and is more often four times the fall. For ordinary cases the smallest convenient diameter is 14 ft. with a straight, or 10 ft. with a curved, approach channel. The radialdepth of bucket should be at least half the fall, and radius of curvature of buckets about half the radius of the wheel. The shrouds are usually of cast iron with flanges to receive the buckets. The buckets may be of iron1⁄8in. thick bolted to the flanges with5⁄16in. bolts.Let H′ be the fall measured from the free surface of the head-water to the point F where the mean layer enters the wheel; then the velocity at which the water enters is v = √ (2gH′), and the best circumferential velocity of the wheel is V = 0.55f to 0.6v. The number of rotations of the wheel per second is N = V/πD. The thickness of the sheet of water entering the wheel is very important. The best thickness according to experiment is 8 to 10 in. The maximum thickness should not exceed 12 to 15 in., when there is a surplus water supply. Let e be the thickness of the sheet of water entering the wheel, and b its width; thenbev = Q; or b = Q/ev.Grashof takes e =1⁄6H, and thenb = 6Q/H √ (2gH).Allowing for the contraction of the stream, the area of opening through the sluice may be 1.25 be to 1.3 be. The inside width of the wheel is made about 4 in. greater than b.Several constructions have been given for the floats of Poncelet wheels. One of the simplest is that shown in figs. 181, 182.Let OA (fig. 181) be the vertical radius of the wheel. Set off OB, OD making angles of 15° with OA. Then BD may be the length of the close breasting fitted to the wheel. Draw the bottom of the head face BC at a slope of 1 in 10. Parallel to this, at distances1⁄2e and e, draw EF and GH. Then EF is the mean layer and GH the surface layer entering the wheel. Join OF, and make OFK = 23°. Take FK = 0.5 to 0.7 H. Then K is the centre from which the bucket curve is struck and KF is the radius. The depth of the shrouds must be sufficient to prevent the water from rising over the top of the float. It is1⁄2H to2⁄3H. The number of buckets is not very important. They are usually 1 ft. apart on the circumference of the wheel.The efficiency of a Poncelet wheel has been found in experiments to reach 0.68. It is better to take it at 0.6 in estimating the power of the wheel, so as to allow some margin.Fig. 182.In fig. 182 viis the initial and vothe final velocity of the water, vrparallel to the vane the relative velocity of the water and wheel, and V the velocity of the wheel.
Taking the efficiency at 0.60, and putting H for the available fall, h.p. for the horse-power, and Q for the water supply per second,
h.p. = 0.068 QH.
The diameter D of the wheel may be taken arbitrarily. It should not be less than twice the fall and is more often four times the fall. For ordinary cases the smallest convenient diameter is 14 ft. with a straight, or 10 ft. with a curved, approach channel. The radialdepth of bucket should be at least half the fall, and radius of curvature of buckets about half the radius of the wheel. The shrouds are usually of cast iron with flanges to receive the buckets. The buckets may be of iron1⁄8in. thick bolted to the flanges with5⁄16in. bolts.
Let H′ be the fall measured from the free surface of the head-water to the point F where the mean layer enters the wheel; then the velocity at which the water enters is v = √ (2gH′), and the best circumferential velocity of the wheel is V = 0.55f to 0.6v. The number of rotations of the wheel per second is N = V/πD. The thickness of the sheet of water entering the wheel is very important. The best thickness according to experiment is 8 to 10 in. The maximum thickness should not exceed 12 to 15 in., when there is a surplus water supply. Let e be the thickness of the sheet of water entering the wheel, and b its width; then
bev = Q; or b = Q/ev.
Grashof takes e =1⁄6H, and then
b = 6Q/H √ (2gH).
Allowing for the contraction of the stream, the area of opening through the sluice may be 1.25 be to 1.3 be. The inside width of the wheel is made about 4 in. greater than b.
Several constructions have been given for the floats of Poncelet wheels. One of the simplest is that shown in figs. 181, 182.
Let OA (fig. 181) be the vertical radius of the wheel. Set off OB, OD making angles of 15° with OA. Then BD may be the length of the close breasting fitted to the wheel. Draw the bottom of the head face BC at a slope of 1 in 10. Parallel to this, at distances1⁄2e and e, draw EF and GH. Then EF is the mean layer and GH the surface layer entering the wheel. Join OF, and make OFK = 23°. Take FK = 0.5 to 0.7 H. Then K is the centre from which the bucket curve is struck and KF is the radius. The depth of the shrouds must be sufficient to prevent the water from rising over the top of the float. It is1⁄2H to2⁄3H. The number of buckets is not very important. They are usually 1 ft. apart on the circumference of the wheel.
The efficiency of a Poncelet wheel has been found in experiments to reach 0.68. It is better to take it at 0.6 in estimating the power of the wheel, so as to allow some margin.
In fig. 182 viis the initial and vothe final velocity of the water, vrparallel to the vane the relative velocity of the water and wheel, and V the velocity of the wheel.
Turbines.
§ 182. The name turbine was originally given in France to any water motor which revolved in a horizontal plane, the axis being vertical. The rapid development of this class of motors dates from 1827, when a prize was offered by the Société d’Encouragement for a motor of this kind, which should be an improvement on certain wheels then in use. The prize was ultimately awarded to Benoît Fourneyron (1802-1867), whose turbine, but little modified, is still constructed.
Classification of Turbines.—In some turbines the whole available energy of the water is converted into kinetic energy before the water acts on the moving part of the turbine. Such turbines are termedImpulse or Action Turbines, and they are distinguished by this that the wheel passages are never entirely filled by the water. To ensure this condition they must be placed a little above the tail water and discharge into free air. Turbines in which part only of the available energy is converted into kinetic energy before the water enters the wheel are termedPressure or Reaction Turbines. In these there is a pressure which in some cases amounts to half the head in the clearance space between the guide vanes and wheel vanes. The velocity with which the water enters the wheel is due to the difference between the pressure due to the head and the pressure in the clearance space. In pressure turbines the wheel passages must be continuously filled with water for good efficiency, and the wheel may be and generally is placed below the tail water level.
Some turbines are designed to act normally as impulse turbines discharging above the tail water level. But the passages are so designed that they are just filled by the water. If the tail water rises and drowns the turbine they become pressure turbines with a small clearance pressure, but the efficiency is not much affected. Such turbines are termedLimit turbines.
Next there is a difference of constructive arrangement of turbines, which does not very essentially alter the mode of action of the water. In axial flow or so-called parallel flow turbines, the water enters and leaves the turbine in a direction parallel to the axis of rotation, and the paths of the molecules lie on cylindrical surfaces concentric with that axis. In radial outward and inward flow turbines, the water enters and leaves the turbine in directions normal to the axis of rotation, and the paths of the molecules lie exactly or nearly in planes normal to the axis of rotation. In outward flow turbines the general direction of flow is away from the axis, and in inward flow turbines towards the axis. There are also mixed flow turbines in which the water enters normally and is discharged parallel to the axis of rotation.
Another difference of construction is this, that the water may be admitted equally to every part of the circumference of the turbine wheel or to a portion of the circumference only. In the former case, the condition of the wheel passages is always the same; they receive water equally in all positions during rotation. In the latter case, they receive water during a part of the rotation only. The former may be termed turbines with complete admission, the latter turbines with partial admission. A reaction turbine should always have complete admission. An impulse turbine may have complete or partial admission.
When two turbine wheels similarly constructed are placed on the same axis, in order to balance the pressures and diminish journal friction, the arrangement may be termed a twin turbine.
If the water, having acted on one turbine wheel, is then passed through a second on the same axis, the arrangement may be termed a compound turbine. The object of such an arrangement would be to diminish the speed of rotation.
Many forms of reaction turbine may be placed at any height not exceeding 30 ft. above the tail water. They then discharge into an air-tight suction pipe. The weight of the column of water in this pipe balances part of the atmospheric pressure, and the difference of pressure, producing the flow through the turbine, is the same as if the turbine were placed at the bottom of the fall.