68 PHYSICS, 
_ meter with a water or mercury column, and the amount of pressure esti- 
mated by the height of the column., Supposing air subject to the pressure 
of one atmosphere to pour into a vacuum, we know that the pressure of one 
atmosphere holds ‘n equilibrium a column of water 32 feet or 10.4 metres in 
height, and that the density of air is 770 times less than that of water; con- 
sequently, a column of air having this density throughout, must be 8008 
metres high to maintain in equilibrium the pressure of the atmosphere, and 
in this case the velocity of discharge would be = W2 x 9.8 X 8008 = 396 
metres, = nearly 1300 feet. 
If the space into which the stream is to pass already contain air of a 
slight tension, the tendency to escape is dependent upon the difference of 
the two tensions. Expressing by H the height of a column of air repre- 
senting the difference of these tensions, and having the density of the more 
strongly compressed air, the velocity of discharge will be = ~/2g¢H> where 
g indicates the velocity at the end of the first eu (9.8 metres, or about 31 
et: see page 202) [Physics 28]. The factor, H, must be developed by a series 
of inferences and calculations. Suppose gas to escape into the open air from 
a gas-burner, the pressure in the gasometer is determined by a column of 
water of measured height which we may call 4; it is then only necessary 
to ascertain how high a column of a gas like that consumed in the 
gasometer will be necessary to hold this pressure of water in equilibrium. 
It we had to deal with air of mean atmospheric pressure, then for the 
column of water, 4, a column of air of 770 may be taken; as, however, 
the gas is more condensed, the column of air need not be so high. Now, 
however, atmospheric air is compressed by a column of water thirty-two 
feet high, which pressure may be called 6, while the gas has to sustain a 
pressure of b’ 4-4, where 0’ indicates the height of a column of water at the 
barometric pressure of the same instant. The density of air at the mean 
pressure is therefore to the pressure in the gasometer, as b:b’--h; the gas 
/ 
is therefore mii 18 denser than atmospheric air, and, instead of 770h, we 
must take a this being the value of H, and consequently ¢= 
t] 
/ 29 170! ei ; the quantity, M, discharged in ¢ seconds through an aperture 
whose cross section is m, will then amount to ft ay ae yeas Never- 
| 
theless, here, as in the case of liquids, a considerable deduction must ve 
made in practice, and the above result must be multiplied by a definite 
fractional factor. In water this is 0.64, and is constant; in gases it is 
variable, and can only be obtained by trial. Cylindrical and conical escape- 
pipes increase the amount of discharge. 
The laws of friction and of lateral pressure in the conducting pipes 
agree as to the rest with what has been determined for liquids; and the 
phenomena of suction likewise take place in the motion of gases, just as in 
the flow of liquids. 
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