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 *v*^{2}/2*g* ft. of air, or
0.00024 *v*^{2} 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 π*dt* 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 *u*^{2} 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 0.45*d*. Hence if Q is
given, the diameter of the fan should be:—

*t*= 0.35

*d*,

*d*= 0.20 √ (Q / √

*p*)

For

*t*= 0.45

*d*,

*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 5.2*p*Q 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 *w*^{2}/2*g* foot-pounds per ℔ of air as kinetic energy. In Q cubic feet
or 0.0807Q ℔ the kinetic energy is 0.00125 Q*w*^{2} 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

*p*Q / 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

_{2}= (5.2

*p*Q + 0.00125 Q

*w*

^{2}) / 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.

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 *p*_{c} 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* = *p*_{c} + 0.0004q^{2} in. of
water, so that if *p*_{c} is given, *p* can be found approximately. The
pressure *p* depends on the circumferential speed *v* of the fan disk—

p = 0.00025 v^{2} in. of waterv = 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

*dtq*= 47 to 56

*dt*√

*p*

For

*t*= .35

*d*,

*d*= 0.22 to 0.25 √(Q / √

*p*) ft.

*t*= .45

*d*,

*d*= 0.20 to 0.22 √(Q / √

*p*) ft.

*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), N_{2}H_{4} or H_{2} N·NH_{2}, a compound
of hydrogen and nitrogen, first prepared by Th. Curtius in 1887
from diazo-acetic ester, N_{2}CH·CO_{2}C_{2}H_{5}. 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
C_{3}H_{3}N_{6}(CO_{2}H)_{3}, but which A. Hantzsch and O. Silberrad
(*Ber.*, 1900, 33, p. 58) showed to be C_{2}H_{2}N_{4}(CO_{2}H)_{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:—

KSO_{3} | N⋅NO→ | KSO_{3} | N⋅NH_{2}→K_{2}SO_{4}+N_{2}H_{4}. |

KO | H |