§ 198.General Description of an Impulse Turbine or Turbine with Free Deviation.—Fig. 197 shows a general sectional elevation of a Girard turbine, in which the flow is axial. The water, admitted above a horizontal floor, passes down through the annular wheel containing the guide-blades G, G, and thence into the revolving wheel WW. The revolving wheel is fixed to a hollow shaft suspended from the pivot p. The solid internal shaft ss is merely a fixed column supporting the pivot. The advantage of this is that the pivot is accessible for lubrication and adjustment. B is the mortise bevel wheel by which the power of the turbine is given off. The sluices are worked by the hand wheel h, which raises them successively, in a way to be described presently. d, d are the sluice rods. Figs. 198, 199 show the sectional form of the guide-blade chamber and wheel and the curves of the wheel vanes and guide-blades, when drawn on a plane development of the cylindrical section of the wheel; a, a, a are the sluices for cutting off the water; b, b, b are apertures by which the entrance or exit of air is facilitated as the buckets empty and fill. Figs. 200, 201 show the guide-blade gear. a, a, a are the sluice rods as before. At the top of each sluice rod is a small block c, having a projecting tongue, which slides in the groove of the circular cam plate d, d. This circular plate is supported on the frame e, and revolves on it by means of the flanged rollers f. Inside, at the top, the cam plate is toothed, and gears into a spur pinion connected with the hand wheel h. At gg is an inclined groove or shunt. When the tongues of the blocks c, c arrive at g, they slide up to a second groove, or the reverse, according as the cam plate is revolved in one direction or in the other. As this operation takes place with eachsluice successively, any number of sluices can be opened or closed as desired. The turbine is of 48 horse power on 5.12 ft. fall, and the supply of water varies from 35 to 112 cub. ft. per second. The efficiency in normal working is given as 73%. The mean diameter of the wheel is 6 ft., and the speed 27.4 revolutions per minute.Fig. 200.Fig. 201.Fig. 202.As an example of a partial admission radial flow impulse turbine, a 100 h.p. turbine at Immenstadt may be taken. The fall varies from 538 to 570 ft. The external diameter of the wheel is 41⁄2ft., and its internal diameter 3 ft. 10 in. Normal speed 400 revs. per minute. Water is discharged into the wheel by a single nozzle, shown in fig. 202 with its regulating apparatus and some of the vanes. The water enters the wheel at an angle of 22° with the direction of motion, and the final angle of the wheel vanes is 20°. The efficiency on trial was from 75 to 78%.§ 199.Theory of the Impulse Turbine.—The theory of the impulse turbine does not essentially differ from that of the reaction turbine, except that there is no pressure in the wheel opposing the discharge from the guide-blades. Hence the velocity with which the water enters the wheel is simplyvi= 0.96 √2g (H − ɧ),where ɧ is the height of the top of the wheel above the tail water. If the hydropneumatic system is used, then ɧ = 0. Let Qmbe the maximum supply of water, r1, r2the internal and external radii of the wheel at the inlet surface; thenui= Qm/ {π(r22− r12)}.The value of uimay be about 0.45 √2g (H − ɧ), whence r1, r2can be determined.The guide-blade angle is then given by the equationsin γ = ui/ vi= 0.45 / 0.94 = .48;γ = 29°.The value of uishould, however, be corrected for the space occupied by the guide-blades.The tangential velocity of the entering water iswi= vicos γ = 0.82 √2g (H − ɧ).The circumferential velocity of the wheel may be (at mean radius)Vi= 0.5 √2g (H − ɧ).Hence the vane angle at inlet surface is given by the equationcot θ = (wi− Vi) / ui= (0.82 − 0.5) / 0.45 = .71;θ = 55°.The relative velocity of the water striking the vane at the inlet edge is vri= uicosec θ = 1.22ui. This relative velocity remains unchanged during the passage of the water over the vane; consequently the relative velocity at the point of discharge is vro= 1.22ui. Also in an axial flow turbine Vo= Vi.If the final velocity of the water is axial, thencos φ = Vo/ vro= Vi/ vri= 0.5 / (1.22 × 0.45) = cos 24º 23′.This should be corrected for the vane thickness. Neglecting this, uo= vrosin φ = vrisin φ = uicosec θ sin φ = 0.5ui. The discharging area of the wheel must therefore be greater than the inlet area in the ratio of at least 2 to 1. In some actual turbines the ratio is 7 to 3. This greater outlet area is obtained by splaying the wheel, as shown in the section (fig. 199).Fig. 203.§ 200.Pelton Wheel.—In the mining district of California about 1860 simple impulse wheels were used, termed hurdy-gurdy wheels. The wheels rotated in a vertical plane, being supported on a horizontal axis. Round the circumference were fixed flat vanes which were struck normally by a jet from a nozzle of size varying with the head and quantity of water. Such wheels have in fact long been used. They are not efficient, but they are very simply constructed. Then attempts were made to improve the efficiency, first by using hemispherical cup vanes, and then by using a double cup vane with a central dividing ridge, an arrangement invented by Pelton. In this last form the water from the nozzle passes half to each side of the wheel, just escaping clear of the backs of the advancing buckets. Fig. 203 shows a Pelton vane. Some small modifications have been made by other makers, but they are not of any great importance. Fig. 204 shows a complete Pelton wheel with frame and casing, supply pipe and nozzle. Pelton wheels have been very largely used in America and to some extent in Europe. They are extremely simple and easy to construct or repair and on falls of 100 ft. or more are very efficient. The jet strikes tangentially to the mean radius of the buckets, and the face of the buckets is not quite radial but at right angles to the direction of the jet at the point of first impact. For greatest efficiency the peripheral velocity of the wheel at the mean radius of the buckets should be a little less than half the velocity of the jet. As the radius of the wheel can be taken arbitrarily, the number of revolutions per minute can be accommodated to that of the machinery to be driven. Pelton wheels have been made as small as 4 in. diameter, for driving sewing machines, and as large as 24 ft. The efficiency on high falls is about 80%. When large power is required two or three nozzles are used delivering on one wheel. The width of the buckets should be not less than seven times the diameter of the jet.Fig. 204.At the Comstock mines, Nevada, there is a 36-in. Pelton wheel made of a solid steel disk with phosphor bronze buckets riveted to the rim. The head is 2100 ft. and the wheel makes 1150 revolutions per minute, the peripheral velocity being 180 ft. per sec. With a1⁄2-in. nozzle the wheel uses 32 cub. ft. of water per minute and develops 100 h.p. At the Chollarshaft, Nevada, there are six Pelton wheels on a fall of 1680 ft. driving electrical generators. With5⁄8-in. nozzles each develops 125 h.p.Fig. 205§ 201.Theory of the Pelton Wheel.—Suppose a jet with a velocity v strikes tangentially a curved vane AB (fig. 205) moving in the same direction with the velocity u. The water will flow over the vane with the relative velocity v − u and at B will have the tangentialrelative velocity v − u making an angle α with the direction of the vane’s motion. Combining this with the velocity u of the vane, the absolute velocity of the water leaving the vane will be w = Bc. The component of w in the direction of motion of the vane is Ba = Bb − ab = u − (v − u) cos α. Hence if Q is the quantity of water reaching the vane per second the change of momentum per second in the direction of the vane’s motion is (GQ/g) [v − {u − (v − u) cos α}] = (GQ/g) (v − u) (1 + cos α). If a = 0°, cos α = 1, and the change of momentum per second, which is equal to the effort driving the vane, is P = 2(GQ/g) (v − u). The work done on the vane is Pu = 2(GQ/g) (v − u)u. If a series of vanes are interposed in succession, the quantity of water impinging on the vanes per second is the total discharge of the nozzle, and the energy expended at the nozzle is GQv2/2g. Hence the efficiency of the arrangement is, when α = 0°, neglecting friction,η = 2Pu / GQv2= 4 (v − u) u/v2,which is a maximum and equal to unity if u =1⁄2v. In that case the whole energy of the jet is usefully expended in driving the series of vanes. In practice α cannot be quite zero or the water leaving one vane would strike the back of the next advancing vane. Fig. 203 shows a Pelton vane. The water divides each way, and leaves the vane on each side in a direction nearly parallel to the direction of motion of the vane. The best velocity of the vane is very approximately half the velocity of the jet.§ 202.Regulation of the Pelton Wheel.—At first Pelton wheels were adjusted to varying loads merely by throttling the supply. This method involves a total loss of part of the head at the sluice or throttle valve. In addition as the working head is reduced, the relation between wheel velocity and jet velocity is no longer that of greatest efficiency. Next a plan was adopted of deflecting the jet so that only part of the water reached the wheel when the load was reduced, the rest going to waste. This involved the use of an equal quantity of water for large and small loads, but it had, what in some cases is an advantage, the effect of preventing any water hammer in the supply pipe due to the action of the regulator. In most cases now regulation is effected by varying the section of the jet. A conical needle in the nozzle can be advanced or withdrawn so as to occupy more or less of the aperture of the nozzle. Such a needle can be controlled by an ordinary governor.
§ 198.General Description of an Impulse Turbine or Turbine with Free Deviation.—Fig. 197 shows a general sectional elevation of a Girard turbine, in which the flow is axial. The water, admitted above a horizontal floor, passes down through the annular wheel containing the guide-blades G, G, and thence into the revolving wheel WW. The revolving wheel is fixed to a hollow shaft suspended from the pivot p. The solid internal shaft ss is merely a fixed column supporting the pivot. The advantage of this is that the pivot is accessible for lubrication and adjustment. B is the mortise bevel wheel by which the power of the turbine is given off. The sluices are worked by the hand wheel h, which raises them successively, in a way to be described presently. d, d are the sluice rods. Figs. 198, 199 show the sectional form of the guide-blade chamber and wheel and the curves of the wheel vanes and guide-blades, when drawn on a plane development of the cylindrical section of the wheel; a, a, a are the sluices for cutting off the water; b, b, b are apertures by which the entrance or exit of air is facilitated as the buckets empty and fill. Figs. 200, 201 show the guide-blade gear. a, a, a are the sluice rods as before. At the top of each sluice rod is a small block c, having a projecting tongue, which slides in the groove of the circular cam plate d, d. This circular plate is supported on the frame e, and revolves on it by means of the flanged rollers f. Inside, at the top, the cam plate is toothed, and gears into a spur pinion connected with the hand wheel h. At gg is an inclined groove or shunt. When the tongues of the blocks c, c arrive at g, they slide up to a second groove, or the reverse, according as the cam plate is revolved in one direction or in the other. As this operation takes place with eachsluice successively, any number of sluices can be opened or closed as desired. The turbine is of 48 horse power on 5.12 ft. fall, and the supply of water varies from 35 to 112 cub. ft. per second. The efficiency in normal working is given as 73%. The mean diameter of the wheel is 6 ft., and the speed 27.4 revolutions per minute.
As an example of a partial admission radial flow impulse turbine, a 100 h.p. turbine at Immenstadt may be taken. The fall varies from 538 to 570 ft. The external diameter of the wheel is 41⁄2ft., and its internal diameter 3 ft. 10 in. Normal speed 400 revs. per minute. Water is discharged into the wheel by a single nozzle, shown in fig. 202 with its regulating apparatus and some of the vanes. The water enters the wheel at an angle of 22° with the direction of motion, and the final angle of the wheel vanes is 20°. The efficiency on trial was from 75 to 78%.
§ 199.Theory of the Impulse Turbine.—The theory of the impulse turbine does not essentially differ from that of the reaction turbine, except that there is no pressure in the wheel opposing the discharge from the guide-blades. Hence the velocity with which the water enters the wheel is simply
vi= 0.96 √2g (H − ɧ),
where ɧ is the height of the top of the wheel above the tail water. If the hydropneumatic system is used, then ɧ = 0. Let Qmbe the maximum supply of water, r1, r2the internal and external radii of the wheel at the inlet surface; then
ui= Qm/ {π(r22− r12)}.
The value of uimay be about 0.45 √2g (H − ɧ), whence r1, r2can be determined.
The guide-blade angle is then given by the equation
sin γ = ui/ vi= 0.45 / 0.94 = .48;
γ = 29°.
The value of uishould, however, be corrected for the space occupied by the guide-blades.
The tangential velocity of the entering water is
wi= vicos γ = 0.82 √2g (H − ɧ).
The circumferential velocity of the wheel may be (at mean radius)
Vi= 0.5 √2g (H − ɧ).
Hence the vane angle at inlet surface is given by the equation
cot θ = (wi− Vi) / ui= (0.82 − 0.5) / 0.45 = .71;
θ = 55°.
The relative velocity of the water striking the vane at the inlet edge is vri= uicosec θ = 1.22ui. This relative velocity remains unchanged during the passage of the water over the vane; consequently the relative velocity at the point of discharge is vro= 1.22ui. Also in an axial flow turbine Vo= Vi.
If the final velocity of the water is axial, then
cos φ = Vo/ vro= Vi/ vri= 0.5 / (1.22 × 0.45) = cos 24º 23′.
This should be corrected for the vane thickness. Neglecting this, uo= vrosin φ = vrisin φ = uicosec θ sin φ = 0.5ui. The discharging area of the wheel must therefore be greater than the inlet area in the ratio of at least 2 to 1. In some actual turbines the ratio is 7 to 3. This greater outlet area is obtained by splaying the wheel, as shown in the section (fig. 199).
§ 200.Pelton Wheel.—In the mining district of California about 1860 simple impulse wheels were used, termed hurdy-gurdy wheels. The wheels rotated in a vertical plane, being supported on a horizontal axis. Round the circumference were fixed flat vanes which were struck normally by a jet from a nozzle of size varying with the head and quantity of water. Such wheels have in fact long been used. They are not efficient, but they are very simply constructed. Then attempts were made to improve the efficiency, first by using hemispherical cup vanes, and then by using a double cup vane with a central dividing ridge, an arrangement invented by Pelton. In this last form the water from the nozzle passes half to each side of the wheel, just escaping clear of the backs of the advancing buckets. Fig. 203 shows a Pelton vane. Some small modifications have been made by other makers, but they are not of any great importance. Fig. 204 shows a complete Pelton wheel with frame and casing, supply pipe and nozzle. Pelton wheels have been very largely used in America and to some extent in Europe. They are extremely simple and easy to construct or repair and on falls of 100 ft. or more are very efficient. The jet strikes tangentially to the mean radius of the buckets, and the face of the buckets is not quite radial but at right angles to the direction of the jet at the point of first impact. For greatest efficiency the peripheral velocity of the wheel at the mean radius of the buckets should be a little less than half the velocity of the jet. As the radius of the wheel can be taken arbitrarily, the number of revolutions per minute can be accommodated to that of the machinery to be driven. Pelton wheels have been made as small as 4 in. diameter, for driving sewing machines, and as large as 24 ft. The efficiency on high falls is about 80%. When large power is required two or three nozzles are used delivering on one wheel. The width of the buckets should be not less than seven times the diameter of the jet.
At the Comstock mines, Nevada, there is a 36-in. Pelton wheel made of a solid steel disk with phosphor bronze buckets riveted to the rim. The head is 2100 ft. and the wheel makes 1150 revolutions per minute, the peripheral velocity being 180 ft. per sec. With a1⁄2-in. nozzle the wheel uses 32 cub. ft. of water per minute and develops 100 h.p. At the Chollarshaft, Nevada, there are six Pelton wheels on a fall of 1680 ft. driving electrical generators. With5⁄8-in. nozzles each develops 125 h.p.
§ 201.Theory of the Pelton Wheel.—Suppose a jet with a velocity v strikes tangentially a curved vane AB (fig. 205) moving in the same direction with the velocity u. The water will flow over the vane with the relative velocity v − u and at B will have the tangentialrelative velocity v − u making an angle α with the direction of the vane’s motion. Combining this with the velocity u of the vane, the absolute velocity of the water leaving the vane will be w = Bc. The component of w in the direction of motion of the vane is Ba = Bb − ab = u − (v − u) cos α. Hence if Q is the quantity of water reaching the vane per second the change of momentum per second in the direction of the vane’s motion is (GQ/g) [v − {u − (v − u) cos α}] = (GQ/g) (v − u) (1 + cos α). If a = 0°, cos α = 1, and the change of momentum per second, which is equal to the effort driving the vane, is P = 2(GQ/g) (v − u). The work done on the vane is Pu = 2(GQ/g) (v − u)u. If a series of vanes are interposed in succession, the quantity of water impinging on the vanes per second is the total discharge of the nozzle, and the energy expended at the nozzle is GQv2/2g. Hence the efficiency of the arrangement is, when α = 0°, neglecting friction,
η = 2Pu / GQv2= 4 (v − u) u/v2,
which is a maximum and equal to unity if u =1⁄2v. In that case the whole energy of the jet is usefully expended in driving the series of vanes. In practice α cannot be quite zero or the water leaving one vane would strike the back of the next advancing vane. Fig. 203 shows a Pelton vane. The water divides each way, and leaves the vane on each side in a direction nearly parallel to the direction of motion of the vane. The best velocity of the vane is very approximately half the velocity of the jet.
§ 202.Regulation of the Pelton Wheel.—At first Pelton wheels were adjusted to varying loads merely by throttling the supply. This method involves a total loss of part of the head at the sluice or throttle valve. In addition as the working head is reduced, the relation between wheel velocity and jet velocity is no longer that of greatest efficiency. Next a plan was adopted of deflecting the jet so that only part of the water reached the wheel when the load was reduced, the rest going to waste. This involved the use of an equal quantity of water for large and small loads, but it had, what in some cases is an advantage, the effect of preventing any water hammer in the supply pipe due to the action of the regulator. In most cases now regulation is effected by varying the section of the jet. A conical needle in the nozzle can be advanced or withdrawn so as to occupy more or less of the aperture of the nozzle. Such a needle can be controlled by an ordinary governor.
§ 203.General Considerations on the Choice of a Type of Turbine.—The circumferential speed of any turbine is necessarily a fraction of the initial velocity of the water, and therefore is greater as the head is greater. In reaction turbines with complete admission the number of revolutions per minute becomes inconveniently great, for the diameter cannot be increased beyond certain limits without greatly reducing the efficiency. In impulse turbines with partial admission the diameter can be chosen arbitrarily and the number of revolutions kept down on high falls to any desired amount. Hence broadly reaction turbines are better and less costly on low falls, and impulse turbines on high falls. For variable water flow impulse turbines have some advantage, being more efficiently regulated. On the other hand, impulse turbines lose efficiency seriously if their speed varies from the normal speed due to the head. If the head is very variable, as it often is on low falls, and the turbine must run at the same speed whatever the head, the impulse turbine is not suitable. Reaction turbines can be constructed so as to overcome this difficulty to a great extent. Axial flow turbines with vertical shafts have the disadvantage that in addition to the weight of the turbine there is an unbalanced water pressure to be carried by the footstep or collar bearing. In radial flow turbines the hydraulic pressures are balanced. The application of turbines to drive dynamos directly has involved some new conditions. The electrical engineer generally desires a high speed of rotation, and a very constant speed at all times. The reaction turbine is generally more suitable than the impulse turbine. As the diameter of the turbine depends on the quantity of water and cannot be much varied without great inefficiency, a difficulty arises on low falls. This has been met by constructing four independent reaction turbines on the same shaft, each having of course the diameter suitable for one-quarter of the whole discharge, and having a higher speed of rotation than a larger turbine. The turbines at Rheinfelden and Chevres are so constructed. To ensure constant speed of rotation when the head varies considerably without serious inefficiency, an axial flow turbine is generally used. It is constructed of three or four concentric rings of vanes, with independent regulating sluices, forming practically independent turbines of different radii. Any one of these or any combination can be used according to the state of the water. With a high fall the turbine of largest radius only is used, and the speed of rotation is less than with a turbine of smaller radius. On the other hand, as the fall decreases the inner turbines are used either singly or together, according to the power required. At the Zürich waterworks there are turbines of 90 h.p. on a fall varying from 101⁄2ft. to 43⁄4ft. The power and speed are kept constant. Each turbine has three concentric rings. The outermost ring gives 90 h.p. with 105 cub. ft. per second and the maximum fall. The outer and middle compartments give the same power with 140 cub. ft. per second and a fall of 7 ft. 10 in. All three compartments working together develop the power with about 250 cub. ft. per second. In some tests the efficiency was 74% with the outer ring working alone, 75.4% with the outer and middle ring working and a fall of 7 ft., and 80.7% with all the rings working.
§ 204.Speed Governing.—When turbines are used to drive dynamos direct, the question of speed regulation is of great importance. Steam engines using a light elastic fluid can be easily regulated by governors acting on throttle or expansion valves. It is different with water turbines using a fluid of great inertia. In one of the Niagara penstocks there are 400 tons of water flowing at 10 ft. per second, opposing enormous resistance to rapid change of speed of flow. The sluices of water turbines also are necessarily large and heavy. Hence relay governors must beused, and the tendency of relay governors to hunt must be overcome. In the Niagara Falls Power House No. 1, each turbine has a very sensitive centrifugal governor acting on a ratchet relay. The governor puts into gear one or other of two ratchets driven by the turbine itself. According as one or the other ratchet is in gear the sluices are raised or lowered. By a subsidiary arrangement the ratchets are gradually put out of gear unless the governor puts them in gear again, and this prevents the over correction of the speed from the lag in the action of the governor. In the Niagara Power House No. 2, the relay is an hydraulic relay similar in principle, but rather more complicated in arrangement, to that shown in fig. 206, which is a governor used for the 1250 h.p. turbines at Lyons. The sensitive governor G opens a valve and puts into action a plunger driven by oil pressure from an oil reservoir. As the plunger moves forward it gradually closes the oil admission valve by lowering the fulcrum end f of the valve lever which rests on a wedge w attached to the plunger. If the speed is still too high, the governor reopens the valve. In the case of the Niagara turbines the oil pressure is 1200 ℔ per sq. in. One millimetre of movement of the governor sleeve completely opens the relay valve, and the relay plunger exerts a force of 50 tons. The sluices can be completely opened or shut in twelve seconds. The ordinary variation of speed of the turbine with varying load does not exceed 1%. If all the load is thrown off, the momentary variation of speed is not more than 5%. To prevent hydraulic shock in the supply pipes, a relief valve is provided which opens if the pressure is in excess of that due to the head.
§ 205.The Hydraulic Ram.—The hydraulic ram is an arrangement by which a quantity of water falling a distance h forces a portion of the water to rise to a height h1, greater than h. It consists of a supply reservoir (A, fig. 207), into which the water enters from some natural stream. A pipe s of considerable length conducts the water to a lower level, where it is discharged intermittently through a self-acting pulsating valve at d. The supply pipe s may be fitted with a flap valve for stopping the ram, and this is attached in some cases to a float, so that the ram starts and stops itself automatically, according as the supply cistern fills or empties. The lower float is just sufficient to keep open the flap after it has been raised by the action of the upper float. The length of chain is adjusted so that the upper float opens the flap when the level in the cistern is at the desired height. If the water-level falls below the lower float the flap closes. The pipe s should be as long and as straight as possible, and as it is subjected to considerable pressure from the sudden arrest of the motion of the water, it must be strong and strongly jointed. a is an air vessel, and e the delivery pipe leading to the reservoir at a higher level than A, into which water is to be pumped. Fig. 208 shows in section the construction of the ram itself. d is the pulsating discharge valve already mentioned, which opens inwards and downwards. The stroke of the valve is regulated by the cotter through the spindle, under which are washers by which the amount of fall can be regulated. At o is a delivery valve, opening outwards, which is often a ball-valve but sometimes a flap-valve. The water which is pumped passes through this valve into the air vessel a, from which it flows by the delivery pipe in a regular stream into the cistern to which the water is to be raised. In the vertical chamber behind the outer valve a small air vessel is formed, and into this opens an aperture1⁄4in. in diameter, made in a brass screw plug b. The hole is reduced to1⁄16in. in diameter at the outer end of the plug and is closed by a small valve opening inwards. Through this, during the rebound after each stroke of the ram, a small quantity of air is sucked in which keeps the air vessel supplied with its elastic cushion of air.
During the recoil after a sudden closing of the valve d, the pressure below it is diminished and the valve opens, permitting outflow. In consequence of the flow through this valve, the water in the supply pipe acquires a gradually increasing velocity. The upward flow of the water, towards the valve d, increases the pressure tending to lift the valve, and at last, if the valve is not too heavy, lifts and closes it. The forward momentum of the column in the supply pipe being destroyed by the stoppage of the flow, the water exerts a pressure at the end of the pipe sufficient to open the delivery valve o, and to cause a portion of the water to flow into the air vessel. As the water in the supply pipe comes to rest and recoils, the valve d opens again and the operation is repeated. Part of the energy of the descending column is employed in compressing the air at the end of the supply pipe and expanding the pipe itself. This causes a recoil of the water which momentarily diminishes the pressure in the pipe below the pressure due to the statical head. This assists in opening the valve d. The recoil of the water is sufficiently great to enable a pump to be attached to the ram body instead of the direct rising pipe. With this arrangement a ram working with muddy water may be employed to raise clear spring water. Instead of lifting the delivery valve as in the ordinary ram, the momentum of the column drives a sliding or elastic piston, and the recoil brings it back. This piston lifts and forces alternately the clear water through ordinary pump valves.
Pumps
§ 206. The different classes of pumps correspond almost exactly to the different classes of water motors, although the mechanical details of the construction are somewhat different. They are properly reversed water motors. Ordinary reciprocating pumps correspond to water-pressure engines. Chain and bucket pumps are in principle similar to water wheels in which the water acts by weight. Scoop wheels are similar to undershot water wheels, and centrifugal pumps to turbines.
Reciprocating Pumpsare single or double acting, and differ from water-pressure engines in that the valves are moved by the water instead of by automatic machinery. They may be classed thus:—
1.Lift Pumps.—The water drawn through a foot valve on the ascent of the pump bucket is forced through the bucket valve when it descends, and lifted by the bucket when it reascends. Such pumps give an intermittent discharge.
2.Plunger or Force Pumps, in which the water drawn through the foot valve is displaced by the descent of a solid plunger, and forced through a delivery valve. They have the advantage thatthe friction is less than that of lift pumps, and the packing round the plunger is easily accessible, whilst that round a lift pump bucket is not. The flow is intermittent.
3.The Double-acting Force Pumpis in principle a double plunger pump. The discharge fluctuates from zero to a maximum and back to zero each stroke, but is not arrested for any appreciable time.
4.Bucket and Plunger Pumpsconsist of a lift pump bucket combined with a plunger of half its area. The flow varies as in a double-acting pump.
5.Diaphragm Pumpshave been used, in which the solid plunger is replaced by an elastic diaphragm, alternately depressed into and raised out of a cylinder.
As single-acting pumps give an intermittent discharge three are generally used on cranks at 120°. But with all pumps the variation of velocity of discharge would cause great waste of work in the delivery pipes when they are long, and even danger from the hydraulic ramming action of the long column of water. An air vessel is interposed between the pump and the delivery pipes, of a volume from 5 to 100 times the space described by the plunger per stroke. The air in this must be replenished from time to time, or continuously, by a special air-pump. At low speeds not exceeding 30 ft. per minute the delivery of a pump is about 90 to 95% of the volume described by the plunger or bucket, from 5 to 10% of the discharge being lost by leakage. At high speeds the quantity pumped occasionally exceeds the volume described by the plunger, the momentum of the water keeping the valves open after the turn of the stroke.
The velocity of large mining pumps is about 140 ft. per minute, the indoor or suction stroke being sometimes made at 250 ft. per minute. Rotative pumping engines of large size have a plunger speed of 90 ft. per minute. Small rotative pumps are run faster, but at some loss of efficiency. Fire-engine pumps have a speed of 180 to 220 ft. per minute.
The efficiency of reciprocating pumps varies very greatly. Small reciprocating pumps, with metal valves on lifts of 15 ft., were found by Morin to have an efficiency of 16 to 40%, or on the average 25%. When used to pump water at considerable pressure, through hose pipes, the efficiency rose to from 28 to 57%, or on the average, with 50 to 100 ft. of lift, about 50%. A large pump with barrels 18 in. diameter, at speeds under 60 ft. per minute, gave the following results:—
The very large steam-pumps employed for waterworks, with 150 ft. or more of lift, appear to reach an efficiency of 90%, not including the friction of the discharge pipes. Reckoned on the indicated work of the steam-engine the efficiency may be 80%.
Many small pumps are now driven electrically and are usually three-throw single-acting pumps driven from the electric motor by gearing. It is not convenient to vary the speed of the motor to accommodate it to the varying rate of pumping usually required. Messrs Hayward Tyler have introduced a mechanism for varying the stroke of the pumps (Sinclair’s patent) from full stroke to nil, without stopping the pumps.
§ 207.Centrifugal Pump.—For large volumes of water on lifts not exceeding about 60 ft. the most convenient pump is the centrifugal pump. Recent improvements have made it available also for very high lifts. It consists of a wheel or fan with curved vanes enclosed in an annular chamber. Water flows in at the centre and is discharged at the periphery. The fan may rotate in a vertical or horizontal plane and the water may enter on one or both sides of the fan. In the latter case there is no axial unbalanced pressure. The fan and its casing must be filled with water before it can start, so that if not drowned there must be a foot valve on the suction pipe. When no special attention needs to be paid to efficiency the water may have a velocity of 6 to 7 ft. in the suction and delivery pipes. The fan often has 6 to 12 vanes. For a double-inlet fan of diameter D, the diameter of the inlets is D/2. If Q is the discharge in cub. ft. per second D = about 0.6 √Q in average cases. The peripheral speed is a little greater than the velocity due to the lift. Ordinary centrifugal pumps will have an efficiency of 40 to 60%.
The first pump of this kind which attracted notice was one exhibited by J. G. Appold in 1851, and the special features of his pump have been retained in the best pumps since constructed. Appold’s pump raised continuously a volume of water equal to 1400 times its own capacity per minute. It had no valves, and it permitted the passage of solid bodies, such as walnuts and oranges, without obstruction to its working. Its efficiency was also found to be good.
Fig. 209 shows the ordinary form of a centrifugal pump. The pump disk and vanes B are cast in one, usually of bronze,
and the disk is keyed on the driving shaft C. The casing A has a spirally enlarging discharge passage into the discharge pipe K. A cover L gives access to the pump. S is the suction pipe which opens into the pump disk on both sides at D.
Fig. 210 shows a centrifugal pump differing from ordinary centrifugal pumps in one feature only. The water rises through a suction pipe S, which divides so as to enter the pump wheel W at the centre on each side. The pump disk or wheel is very similar to a turbine wheel. It is keyed on a shaft driven by a belt on a fast and loose pulley arrangement at P. The water rotating in the pump disk presses outwards, and if the speed is sufficient a continuous flow is maintained through the pump and into the discharge pipe D. The special feature in this pump is that the water, discharged by the pump disk with a whirling velocity of not inconsiderable magnitude, is allowed to continue rotation in a chamber somewhat larger than the pump. The use of this whirlpool chamber was first suggested by Professor James Thomson. It utilizes the energy due to the whirling velocity of the water which in most pumps is wasted in eddies in the discharge pipe. In the pump shown guide-blades are also added which have the direction of the stream lines in a free vortex. They do not therefore interfere with the action of the water when pumping the normal quantity, but only prevent irregular motion. At A is a plug by which the pump case is filled before starting. If the pump is above the water to be pumped, a foot valve is required to permit the pump to be filled. Sometimes instead of the foot valve a delivery valve is used, an air-pump or steam jet pump being employed to exhaust the air from the pump case.
§ 208.Design and Proportions of a Centrifugal Pump.—The design of the pump disk is very simple. Let ri, robe the radii of the inlet and outlet surfaces of the pump disk, di, dothe clear axial width at those radii. The velocity of flow through the pump may be takenthe same as for a turbine. If Q is the quantity pumped, and H the lift,ui= 0.25 √2gH.2πridi= Q / ui.(1)Also in practicedi= 1.2 ri....Hence,ri= .2571 √ (Q / √H).(2)Usuallyro= 2ri,anddo= dior1⁄2diaccording as the disk is parallel-sided or coned. The water enters the wheel radially with the velocity ui, anduo= Q / 2πrodo.(3)Fig. 211.Fig. 211 shows the notation adopted for the velocities. Suppose the water enters the wheel with the velocity vi, while the velocity of the wheel is Vi. Completing the parallelogram, vriis the relative velocity of the water and wheel, and is the proper direction of the wheel vanes. Also, by resolving, uiand wiare the component velocities of flow and velocities of whir of the velocity viof the water. At the outlet surface, vois the final velocity of discharge, and the rest of the notation is similar to that for the inlet surface.Usually the water flows equally in all directions in the eye of the wheel, in that case viis radial. Then, in normal conditions of working, at the inlet surface,vi= uiwi= 0tan θ = ui/ Vivri= uicosec θ = √ (ui2+ Vi2).(4)If the pump is raising less or more than its proper quantity, θ will not satisfy the last condition, and there is then some loss of head in shock.At the outer circumference of the wheel or outlet surface,vro= uocosec φwo= Vo− uocot φvo= √ {uo2+ (Vo− uocot φ)2}(5)Variation of Pressure in the Pump Disk.—Precisely as in the case of turbines, it can be shown that the variation of pressure between the inlet and outlet surfaces of the pump isho− hi= (Vo2− Vi2) / 2g − (vro2− vri2) / 2g.Inserting the values of vro, vriin (4) and (5), we get for normal conditions of workingho− hi= (Vo2− Vi2) / 2g − uo2cosec2φ / 2g + (ui2+ Vi2) / 2g= Vo2/ 2g − uo2cosec2φ / 2g + ui2/ 2g.(6)Hydraulic Efficiency of the Pump.—Neglecting disk friction, journal friction, and leakage, the efficiency of the pump can be found in the same way as that of turbines (§ 186). Let M be the moment of the couple rotating the pump, and α its angular velocity; wo, rothe tangential velocity of the water and radius at the outlet surface; wi, rithe same quantities at the inlet surface. Q being the discharge per second, the change of angular momentum per second is(GQ/g) (woro− wiri).HenceM = (GQ/g) (woro− wiri).In normal working, wi= 0. Also, multiplying by the angular velocity, the work done per second isMα = (GQ/g) woroα.But the useful work done in pumping is GQH. Therefore the efficiency isη = GQH / Mα = gH / woroα = gH / woVo.(7)§ 209. Case 1.Centrifugal Pump with no Whirlpool Chamber.—When no special provision is made to utilize the energy of motion of the water leaving the wheel, and the pump discharges directly into a chamber in which the water is flowing to the discharge pipe, nearly the whole of the energy of the water leaving the disk is wasted. The water leaves the disk with the more or less considerable velocity vo, and impinges on a mass flowing to the discharge pipe at the much slower velocity vs. The radial component of vois almost necessarily wasted. From the tangential component there is a gain of pressure(wo2− vs2) / 2g − (wo− vs)2/ 2g= vs(wo− vs) / g,which will be small, if vsis small compared with wo. Its greatest value, if vs=1⁄2wo, is1⁄2wo2/2g, which will always be a small part of the whole head. Suppose this neglected. The whole variation of pressure in the pump disk then balances the lift and the head ui2/2g necessary to give the initial velocity of flow in the eye of the wheel.ui2/ 2g + H = Vo2/ 2g − uo2cosec2φ / 2g + ui2/ 2g,H = Vo2/ 2g − uo2cosec2φ / 2gorVo= √ (2gH + uo2cosec2φ).(8)and the efficiency of the pump is, from (7),η = gH / Vowo= gH / {V (Vo− nocot φ) },= (Vo2− uo2cosec2φ) / {2Vo(Vo− uocot φ) },(9)For φ = 90°,η = (Vo2− uo2) / 2Vo2,which is necessarily less than1⁄2. That is, half the work expended in driving the pump is wasted. By recurving the vanes, a plan introduced by Appold, the efficiency is increased, because the velocity voof discharge from the pump is diminished. If φ is very small,cosec φ = cot φ;and thenη = (Vo, + uocosec φ) / 2Vo,which may approach the value 1, as φ tends towards 0. Equation (8) shows that uocosec φ cannot be greater than Vo. Putting uo= 0.25 √(2gH) we get the following numerical values of the efficiency and the circumferential velocity of the pump:—φηVo90°0.471.03 √2gH45°0.561.06 ”30°0.651.12 ”20°0.731.24 ”10°0.841.75 ”φ cannot practically be made less than 20°; and, allowing for the frictional losses neglected, the efficiency of a pump in which φ = 20° is found to be about .60.§ 210. Case 2.Pump with a Whirlpool Chamber, as in fig. 210.—Professor James Thomson first suggested that the energy of the water after leaving the pump disk might be utilized, if a space were left in which a free vortex could be formed. In such a free vortex the velocity varies inversely as the radius. The gain of pressure in the vortex chamber is, putting ro, rwfor the radii to the outlet surface of wheel and to outside of free vortex,vo2(1 −ro2)=vo2(1 − k2),2grw22gifk = ro/ rw.The lift is then, adding this to the lift in the last case,H = {Vo2− uo2cosec2φ + vo2(1 − k2)} / 2g.Butvo2= Vo2− 2Vouocot φ + uo2cosec2φ;∴ H = {(2 − k2) Vo2− 2kVouocot φ − k2uo2cosec2φ} / 2g.(10)Putting this in the expression for the efficiency, we find a considerable increase of efficiency. Thus withφ = 90° andk =1⁄2,η =7⁄8nearly,φ a small angle andk =1⁄2,η = 1 nearly.With this arrangement of pump, therefore, the angle at the outer ends of the vanes is of comparatively little importance. A moderate angle of 30° or 40° may very well be adopted. The following numerical values of the velocity of the circumference of the pump have been obtained by taking k =1⁄2, and uo= 0.25√(2gH).φVo90°.762 √2gH45°.842 ”30°.911 ”20°1.023 ”The quantity of water to be pumped by a centrifugal pump necessarily varies, and an adjustment for different quantities of water cannot easily be introduced. Hence it is that the average efficiency of pumps of this kind is in practice less than the efficiencies given above. The advantage of a vortex chamber is also generally neglected. The velocity in the supply and discharge pipes is also often made greater than is consistent with a high degree of efficiency. Velocities of 6 or 7 ft. per second in the discharge and suction pipes, when the lift is small, cause a very sensible waste of energy; 3 to 6 ft. would be much better. Centrifugal pumps of very large size have been constructed. Easton and Anderson made pumps for the North Sea canal in Holland to deliver each 670 tons of water per minute on a lift of 5 ft. The pump disks are 8 ft. diameter. J. and H. Gwynne constructed some pumps for draining the Ferrarese Marshes, which together deliver 2000 tons per minute. A pump made under Professor J. Thomson’s direction for drainage works in Barbados had a pump disk 16 ft. in diameter and a whirlpool chamber 32 ft. in diameter. The efficiency of centrifugal pumps when delivering less or more than the normal quantity of water is discussed in a paper in theProc. Inst. Civ. Eng.vol. 53.
§ 208.Design and Proportions of a Centrifugal Pump.—The design of the pump disk is very simple. Let ri, robe the radii of the inlet and outlet surfaces of the pump disk, di, dothe clear axial width at those radii. The velocity of flow through the pump may be takenthe same as for a turbine. If Q is the quantity pumped, and H the lift,
ui= 0.25 √2gH.2πridi= Q / ui.
(1)
Also in practice
di= 1.2 ri....
Hence,
ri= .2571 √ (Q / √H).
(2)
Usually
ro= 2ri,
and
do= dior1⁄2di
according as the disk is parallel-sided or coned. The water enters the wheel radially with the velocity ui, and
uo= Q / 2πrodo.
(3)
Fig. 211 shows the notation adopted for the velocities. Suppose the water enters the wheel with the velocity vi, while the velocity of the wheel is Vi. Completing the parallelogram, vriis the relative velocity of the water and wheel, and is the proper direction of the wheel vanes. Also, by resolving, uiand wiare the component velocities of flow and velocities of whir of the velocity viof the water. At the outlet surface, vois the final velocity of discharge, and the rest of the notation is similar to that for the inlet surface.
Usually the water flows equally in all directions in the eye of the wheel, in that case viis radial. Then, in normal conditions of working, at the inlet surface,
vi= uiwi= 0tan θ = ui/ Vivri= uicosec θ = √ (ui2+ Vi2).
vi= ui
wi= 0
tan θ = ui/ Vi
vri= uicosec θ = √ (ui2+ Vi2).
(4)
If the pump is raising less or more than its proper quantity, θ will not satisfy the last condition, and there is then some loss of head in shock.
At the outer circumference of the wheel or outlet surface,
vro= uocosec φwo= Vo− uocot φvo= √ {uo2+ (Vo− uocot φ)2}
vro= uocosec φ
wo= Vo− uocot φ
vo= √ {uo2+ (Vo− uocot φ)2}
(5)
Variation of Pressure in the Pump Disk.—Precisely as in the case of turbines, it can be shown that the variation of pressure between the inlet and outlet surfaces of the pump is
ho− hi= (Vo2− Vi2) / 2g − (vro2− vri2) / 2g.
Inserting the values of vro, vriin (4) and (5), we get for normal conditions of working
ho− hi= (Vo2− Vi2) / 2g − uo2cosec2φ / 2g + (ui2+ Vi2) / 2g= Vo2/ 2g − uo2cosec2φ / 2g + ui2/ 2g.
(6)
Hydraulic Efficiency of the Pump.—Neglecting disk friction, journal friction, and leakage, the efficiency of the pump can be found in the same way as that of turbines (§ 186). Let M be the moment of the couple rotating the pump, and α its angular velocity; wo, rothe tangential velocity of the water and radius at the outlet surface; wi, rithe same quantities at the inlet surface. Q being the discharge per second, the change of angular momentum per second is
(GQ/g) (woro− wiri).
Hence
M = (GQ/g) (woro− wiri).
In normal working, wi= 0. Also, multiplying by the angular velocity, the work done per second is
Mα = (GQ/g) woroα.
But the useful work done in pumping is GQH. Therefore the efficiency is
η = GQH / Mα = gH / woroα = gH / woVo.
(7)
§ 209. Case 1.Centrifugal Pump with no Whirlpool Chamber.—When no special provision is made to utilize the energy of motion of the water leaving the wheel, and the pump discharges directly into a chamber in which the water is flowing to the discharge pipe, nearly the whole of the energy of the water leaving the disk is wasted. The water leaves the disk with the more or less considerable velocity vo, and impinges on a mass flowing to the discharge pipe at the much slower velocity vs. The radial component of vois almost necessarily wasted. From the tangential component there is a gain of pressure
(wo2− vs2) / 2g − (wo− vs)2/ 2g= vs(wo− vs) / g,
which will be small, if vsis small compared with wo. Its greatest value, if vs=1⁄2wo, is1⁄2wo2/2g, which will always be a small part of the whole head. Suppose this neglected. The whole variation of pressure in the pump disk then balances the lift and the head ui2/2g necessary to give the initial velocity of flow in the eye of the wheel.
ui2/ 2g + H = Vo2/ 2g − uo2cosec2φ / 2g + ui2/ 2g,
H = Vo2/ 2g − uo2cosec2φ / 2g
or
Vo= √ (2gH + uo2cosec2φ).
(8)
and the efficiency of the pump is, from (7),
η = gH / Vowo= gH / {V (Vo− nocot φ) },= (Vo2− uo2cosec2φ) / {2Vo(Vo− uocot φ) },
(9)
For φ = 90°,
η = (Vo2− uo2) / 2Vo2,
which is necessarily less than1⁄2. That is, half the work expended in driving the pump is wasted. By recurving the vanes, a plan introduced by Appold, the efficiency is increased, because the velocity voof discharge from the pump is diminished. If φ is very small,
cosec φ = cot φ;
and then
η = (Vo, + uocosec φ) / 2Vo,
which may approach the value 1, as φ tends towards 0. Equation (8) shows that uocosec φ cannot be greater than Vo. Putting uo= 0.25 √(2gH) we get the following numerical values of the efficiency and the circumferential velocity of the pump:—
φ cannot practically be made less than 20°; and, allowing for the frictional losses neglected, the efficiency of a pump in which φ = 20° is found to be about .60.
§ 210. Case 2.Pump with a Whirlpool Chamber, as in fig. 210.—Professor James Thomson first suggested that the energy of the water after leaving the pump disk might be utilized, if a space were left in which a free vortex could be formed. In such a free vortex the velocity varies inversely as the radius. The gain of pressure in the vortex chamber is, putting ro, rwfor the radii to the outlet surface of wheel and to outside of free vortex,
if
k = ro/ rw.
The lift is then, adding this to the lift in the last case,
H = {Vo2− uo2cosec2φ + vo2(1 − k2)} / 2g.
But
vo2= Vo2− 2Vouocot φ + uo2cosec2φ;
∴ H = {(2 − k2) Vo2− 2kVouocot φ − k2uo2cosec2φ} / 2g.
(10)
Putting this in the expression for the efficiency, we find a considerable increase of efficiency. Thus with
With this arrangement of pump, therefore, the angle at the outer ends of the vanes is of comparatively little importance. A moderate angle of 30° or 40° may very well be adopted. The following numerical values of the velocity of the circumference of the pump have been obtained by taking k =1⁄2, and uo= 0.25√(2gH).
The quantity of water to be pumped by a centrifugal pump necessarily varies, and an adjustment for different quantities of water cannot easily be introduced. Hence it is that the average efficiency of pumps of this kind is in practice less than the efficiencies given above. The advantage of a vortex chamber is also generally neglected. The velocity in the supply and discharge pipes is also often made greater than is consistent with a high degree of efficiency. Velocities of 6 or 7 ft. per second in the discharge and suction pipes, when the lift is small, cause a very sensible waste of energy; 3 to 6 ft. would be much better. Centrifugal pumps of very large size have been constructed. Easton and Anderson made pumps for the North Sea canal in Holland to deliver each 670 tons of water per minute on a lift of 5 ft. The pump disks are 8 ft. diameter. J. and H. Gwynne constructed some pumps for draining the Ferrarese Marshes, which together deliver 2000 tons per minute. A pump made under Professor J. Thomson’s direction for drainage works in Barbados had a pump disk 16 ft. in diameter and a whirlpool chamber 32 ft. in diameter. The efficiency of centrifugal pumps when delivering less or more than the normal quantity of water is discussed in a paper in theProc. Inst. Civ. Eng.vol. 53.
§ 211.High Lift Centrifugal Pumps.—It has long been known that centrifugal pumps could be worked in series, each pump overcoming a part of the lift. This method has been perfected, and centrifugal pumps for very high lifts with great efficiency have been used by Sulzer and others. C. W. Darley (Proc. Inst. Civ. Eng., supplement to vol. 154, p. 156) has described some pumps of this new type driven by Parsons steam turbines for the water supply of Sydney, N.S.W. Each pump was designed to deliver 11⁄2million gallons per twenty-four hours against a head of 240 ft. at 3300 revs. per minute. Three pumps in series give therefore a lift of 720 ft. The pump consists of a central double-sided impeller 12 in. diameter. The water entering at the bottom divides and enters the runner at each side through a bell-mouthed passage. The shaft is provided with ring and groove glands which on the suction side keep the air out and on the pressure side prevent leakage. Some water from the pressure side leaks through the glands, but beyond the first grooves it passes into a pocket and is returned to the suction side of the pump. For the glands on the suction side water is supplied from a low-pressure service. No packing is used in the glands. During the trials no water was seen at the glands. The following are the results of tests made at Newcastle:—
In trial IV. the steam was superheated 95° F. From other trials under the same conditions as trial I. the Parsons turbine uses 15.6 ℔ of steam per brake h.p. hour, so that the combined efficiency of turbine and pumps is about 56%, a remarkably good result.
§ 212.Air-Lift Pumps.—An interesting and simple method of pumping by compressed air, invented by Dr J. Pohlé of Arizona, is likely to be very useful in certain cases. Suppose a rising main placed in a deep bore hole in which there is a considerable depth of water. Air compressed to a sufficient pressure is conveyed by an air pipe and introduced at the lower end of the rising main. The air rising In the main diminishes the average density of the contents of the main, and their aggregate weight no longer balances the pressure at the lower end of the main due to its submersion. An upward flow is set up, and if the air supply is sufficient the water in the rising main is lifted to any required height. The higher the lift above the level in the bore hole the deeper must be the point at which air is injected. Fig. 212 shows an airlift pump constructed for W. H. Maxwell at the Tunbridge Wells waterworks. There is a two-stage steam air compressor, compressing air to from 90 to 100 ℔ per sq. in. The bore hole is 350 ft. deep, lined with steel pipes 15 in. diameter for 200 ft. and with perforated pipes 131⁄2in. diameter for the lower 150 ft. The rest level of the water is 96 ft. from the ground-level, and the level when pumping 32,000 gallons per hour is 120 ft. from the ground-level. The rising main is 7 in. diameter, and is carried nearly to the bottom of the bore hole and to 20 ft. above the ground-level. The air pipe is 21⁄2in. diameter. In a trial run 31,402 gallons per hour were raised 133 ft. above the level in the well. Trials of the efficiency of the system made at San Francisco with varying conditions will be found in a paper by E. A. Rix (Journ. Amer. Assoc. Eng. Soc.vol. 25,1900). Maxwell found the best results when the ratio of immersion to lift was 3 to 1 at the start and 2.2 to 1 at the end of the trial. In these conditions the efficiency was 37% calculated on the indicated h.p. of the steam-engine, and 46% calculated on the indicated work of the compressor. 2.7 volumes of free air were used to 1 of water lifted. The system is suitable for temporary purposes, especially as the quantity of water raised is much greater than could be pumped by any other system in a bore hole of a given size. It is useful for clearing a boring of sand and may be advantageously used permanently when a boring is in sand or gravel which cannot be kept out of the bore hole. The initial cost is small.
§ 213.Centrifugal Fans.—Centrifugal fans are constructed similarly to centrifugal pumps, and are used for compressing air to pressures not exceeding 10 to 15 in. of water-column. With this small variation of pressure the variation of volume and density of the air may be neglected without sensible error. The conditions of pressure and discharge for fans are generally less accurately known than in the case of pumps, and the design of fans is generally somewhat crude. They seldom have whirlpool chambers, though a large expanding outlet is provided in the case of the important Guibal fans used in mine ventilation.