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:—
For t = 0.35d, d = 0.20 √ (Q / √p)
For t = 0.45d, d = 0.18 √ (Q / √p)
If p is the pressure difference in the fan in inches of water, and N the revolutions of fan,
| v = πdN/60 | ft. per sec. |
| N = 1230√p/d | revs. per min. |
As the pressure difference is small, the work done in compressing the air is almost exactly 5.2pQ foot-pounds per second. Usually, however, the kinetic energy of the air in the discharge pipe is not inconsiderable compared with the work done in compression. If w is the velocity of the air where the discharge pressure is measured, the air carries away w2/2g foot-pounds per ℔ of air as kinetic energy. In Q cubic feet or 0.0807Q ℔ the kinetic energy is 0.00125 Qw2 foot-pounds per second.
The efficiency of fans is reckoned in two ways. If B.H.P. is the effective horse-power applied at the fan shaft, then the efficiency reckoned on the work of compression is
η = 5.2pQ / 550 B.H.P.
On the other hand, if the kinetic energy in the delivery pipe is taken as part of the useful work the efficiency is
η2 = (5.2 pQ + 0.00125 Qw2) / 550 B.H.P.
Although the theory above is a rough one it agrees sufficiently with experiment, with some merely numerical modifications.
An extremely interesting experimental investigation of the action of centrifugal fans has been made by H. Heenan and W. Gilbert (Proc. Inst. Civ. Eng. vol. 123, p. 272). The fans delivered through an air trunk in which different resistances could be obtained by introducing diaphragms with circular apertures of different sizes. Suppose a fan run at constant speed with different resistances and the compression pressure, discharge and brake horse-power measured. The results plot in such a diagram as is shown in fig. 213. The less the resistance to discharge, that is the larger the opening in the air trunk, the greater the quantity of air discharged at the given speed of the fan. On the other hand the compression pressure diminishes. The curve marked total gauge is the compression pressure + the velocity head in the discharge pipe, both in inches of water. This curve falls, but not nearly so much as the compression curve, when the resistance in the air trunk is diminished. The brake horse-power increases as the resistance is diminished because the volume of discharge increases very much. The curve marked efficiency is the efficiency calculated on the work of compression only. It is zero for no discharge, and zero also when there is no resistance and all the energy given to the air is carried away as kinetic energy. There is a discharge for which this efficiency is a maximum; it is about half the discharge which there is when there is no resistance and the delivery pipe is full open. The conditions of speed and discharge corresponding to the greatest efficiency of compression are those ordinarily taken as the best normal conditions of working. The curve marked total efficiency gives the efficiency calculated on the work of compression and kinetic energy of discharge. Messrs Gilbert and Heenan found the efficiencies of ordinary fans calculated on the compression to be 40 to 60% when working at about normal conditions.
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| Fig. 213. |
Taking some of Messrs Heenan and Gilbert’s results for ordinary fans in normal conditions, they have been found to agree fairly with the following approximate rules. Let pc be the compression pressure and q the volume discharged per second per square foot of outlet area of fan. Then the total gauge pressure due to pressure of compression and velocity of discharge is approximately: p = pc + 0.0004q2 in. of water, so that if pc is given, p can be found approximately. The pressure p depends on the circumferential speed v of the fan disk—
| p = 0.00025 v2 in. of water v = 63 √p ft. per sec. |
The discharge per square foot of outlet of fan is—
q = 15 to 18 √p cub. ft. per sec.
The total discharge is
Q = π dtq = 47 to 56 dt √p
t = .45d, d = 0.20 to 0.22 √(Q / √p) ft.
N = 1203 √ p/d.
These approximate equations, which are derived purely from experiment, do not differ greatly from those obtained by the rough theory given above. The theory helps to explain the reason for the form of the empirical results. (W. C. U.)
HYDRAZINE (Diamidogen), N2H4 or H2 N·NH2, a compound
of hydrogen and nitrogen, first prepared by Th. Curtius in 1887
from diazo-acetic ester, N2CH·CO2C2H5. This ester, which is
obtained by the action of potassium nitrate on the hydrochloride
of amidoacetic ester, yields on hydrolysis with hot concentrated
potassium hydroxide an acid, which Curtius regarded as
C3H3N6(CO2H)3, but which A. Hantzsch and O. Silberrad
(Ber., 1900, 33, p. 58) showed to be C2H2N4(CO2H)2, bisdiazoacetic
acid. On digestion of its warm aqueous solution with
warm dilute sulphuric acid, hydrazine sulphate and oxalic acid
are obtained. C. A. Lobry de Bruyn (Ber., 1895, 28, p. 3085)
prepared free hydrazine by dissolving its hydrochloride in
methyl alcohol and adding sodium methylate; sodium chloride
was precipitated and the residual liquid afterwards fractionated
under reduced pressure. It can also be prepared by reducing
potassium dinitrososulphonate in ice cold water by means of
sodium amalgam:—
| KSO3 |  N⋅NO→ | KSO3 | N⋅NH2→K2SO4+N2H4. |
| KO | H |
