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THE THEORY OF JETS                               67

This height, which has been given by Professor M. A. Pavlow

for thirty-six of the best American and European open-hearth

furnaces, varies in his table from 500 to 1875

Returning to the formula upon page 64,

?;2sin2 B    273+*i

~     2g          tm+t<

it may be seen that the depth to which the gaseous jet descends
increases with the increase in it, that is to say, with the temperature
in the heating chamber of the furnace. It is clear that when the
chamber is cold, that is, when * = 0, H has its minimum value.
When tt = tm, H becomes infinite. This shows that if a certain
velocity is impressed upon some of the particles in the midst of a
fluid, and if no account is taken of internal friction, the displace-
ment and the duration of the motion of these particles will be

If the temperature within the chamber of the open-hearth
furnace U is not equal to 0 nor to the temperature of the hot gases
tm of the jet of flame, the depth H to which the jet descends will
become greater and greater as the difference between tm  tt
becomes less, that is to say, it will be greatest when the gases
filling the chamber are lightest. Thus, for example, a jet of
kerosene directed downward into water will penetrate it to a
greater depth than it will if directed into mercury. In a furnace
chamber filled with hot gases the jet of hot gases will descend to a
greater distance than it will into a chamber filled with atmospheric
air, cold and heavy.

All those who have assisted at the starting up of an open-hearth
furnace know that at first the flame in the cold furnace clings to the
roof and drops further and further toward the hearth, as the tem-
perature of the furnace gradually increases. In heating up a new
furnace, it is necessary to make the bottom, by burning it on in
place, that is to say, to form it of its different elements, incorporat-
ing a small quantity of refractory clay with a silica sand, or a
small quantity of basic slag or of dolomite containing from 3 to 7
per cent of magnesium silicate. This bottom cannot be made
except at a temperature of from 1600 to 1700, and it is impossible


Rev. de la Sod etc russe de Mttallurgic, 1910, pp. 169-183.