79T 90 RATIONAL CONSTRUCTION OF FURNACES It is frequently necessary to subdivide a current of cold air or gas which is being heated, as in the hot-blast stove or in furnace regenerators. This problem may be solved as follows : Figs. 48 and 49 show a current of .a cold gas circulating through a channel, having walls heated to incandescence. Assume that the stream of cold gas being heated has been equally divided between two velocities of these two streams are denoted by ui and u>> and the friction in the two branches in millimeters of water is & and &. The condition necessary for the maintenance of equilibrium, in this case, is that the increase of the hydrostatic pressure in the two branches q\ and r/2 shall be equal. If there were no loss of hydrostatic pressure in impressing the velocities ?/i and u? upon the two branches and in overcoming the fric- tional resistance & and & of the two channels to the passage of the gas, the hydrostatic pressure in millimeters of water in the channel q\ of a height h would be, taking 1.29 kg as the weight of a cubic meter of the furnace gas at°° J1. I 1.29A <> f }\ For the branch qz, the hydrostatic pressure would be *° A part of these increases in the hydrostatic pressure will be expended in overcoming the frictional resistances & and £>, and in impressing the velocities HI and uz upon the columns of gas. These last losses, in millimeters of water, may be expressed in the following manner : wi2 1.29 , uS 1.29 —X: - and — and the condition for the equality of the increases in hydrostatic pressure in the two branches is given by the following equation: In this equation there are six variables; five of these must be known in order to fix the value of the sixth. For example, the checker openings around the outside of the checker- work of a Cowper hot-blast stove lose a great deal more heat by radiation and by the cooling effect of the outside of the stove than the central passes. By reason of this they have a much greater cooling effect upon the current , of hot gases, and therefore the current of gases flowing downward through |l these openings is reinforced, since if fe<*i, ii2>%. By measuring fe and th it is not difficult to find —. Us