φVo
90° .762 √2gH
45° .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 the Proc. 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 11⁄2 million 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:—

I. II. III. IV.
Duration of test hours 2 1.54 1.2 1.55
Steam pressure ℔ per sq. in. 57 57 84 55
Weight of steam per water h.p. hour ℔ 27.93 30.67 28.83 27.89
Speed in revs, per min. 3300 3330 3710 3340
Height of suction ft. 11 11 11 11
Total lift ft. 762 744 917 756
Million galls. per day pumped—
  By Ventun meter 1.573 1.499 1.689 1.503
  By orifice 1.623 1.513 1.723 1.555
Water h.p. 252 235 326 239

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.

Fig. 212.

§ 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 131⁄2 in. 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 21⁄2 in. 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.

It is usual to reckon the difference of pressure at the inlet and outlet of a fan in inches of water-column. One inch of water-column = 64.4 ft. of air at average atmospheric pressure = 5.2℔ per sq. ft.

Roughly the pressure-head produced in a fan without means of utilizing the kinetic energy of discharge would be v2/2g ft. of air, or 0.00024 v2 in. of water, where v is the velocity of the tips of the fan blades in feet per second. If d is the diameter of the fan and t the width at the external circumference, then πdt is the discharge area of the fan disk. If Q is the discharge in cub. ft. per sec., u = Q/π dt is the radial velocity of discharge which is numerically equal to the discharge per square foot of outlet in cubic feet per second. As both the losses in the fan and the work done are roughly proportional to u2 in fans of the same type, and are also proportional to the gauge pressure p, then if the losses are to be a constant percentage of the work done u may be taken proportional to √p. In ordinary cases u = about 22 √p. The width t of the fan is generally from 0.35 to 0.45d. Hence if Q is given, the diameter of the fan should be:—