(See Paper No. CCCLXXXVI., The Mechanical Theory of Chimney Draught.)

With so small a value as T' T< 2° it must be evident that, in finding hby the ordinary method, it is sufficiently accurate to suppose all the air in the chimney to be at the temperature 7, thus taking no account of its slight change in density between the top and bottom.

66

[NOTE. This paper received discussion jointly with the other paper by the same author, entitled The Mechanical Theory of Chimney Draught," printed as No. CCCLXXXVI. of the papers of this meeting.]

CCCLXXXVI.

THE MECHANICAL THEORY OF CHIMNEY DRAUGHT.

BY J. BURKITT WEBB, HOBOKEN, N. J.

(Member of the Society.)

In a previous paper the statement was made that when the draught of a chimney is produced by the heat of a furnace its velocity does not depend directly upon the expenditure of heat, and therefore is not a problem in thermo-dynamics. It was further stated that the velocity depended directly upon the action of gravity, and the phenomenon was likened to that of a clock, whose speed of running is controlled by a pendulum. By the winding up of a weight energy is stored and thus placed at the disposal of the mechanism, but the rate at which the mechanism uses the energy is controlled by gravity.

The chimney may also be compared to a vessel kept full of water, which is allowed to flow out of a hole at the bottom; the velocity of the issuing jet depends upon the head of water in the vessel, and so in the chimney the velocity of the issuing hot air depends upon a head of hot air. In both cases, if the flow is to be kept up continuously, as much must be supplied as flows out, and this requires water to be lifted in the one case and air in the other.

We shall in this paper show exactly how gravity acts in producing the velocity of the hot air in a chimney, and how the heat acts to keep gravity wound up, so to speak.

Let CD (Fig. 139) be a chimney, say, 330 feet high by 1 footsquare section, full of hot air, and let AB be a shaft 100 feet square, of the same height, full of cold air, BC being a passage connecting the two. For the sake of simplicity we shall assume that the air in the chimney is so hot that its density is but half that of the cold air, and that after the air is heated no heat is abstracted by a boiler or lost through the walls. By placing the grate near the bottom of the large cold-air shaft it will be so large as to offer no perceptible obstruction to the passage of the air, and we

may also suppose that the grate bars are simply wires capable of being heated by electricity, so that there will be no coals to obstruct the flow and so that the heat can be turned on and off by making and breaking the circuit. Let p EF be such a grating of wires.

The cold-air shaft having 10,000 times the section of the chimney, and the cold air only half the density of the hot, the velocity in the shaft will be but 2000 of that in the chimney, and therefore neglectable.

It must be evident at once that, if the C chimney be in full draught and if the current be broken so as to stop the supply of heat, no diminution of the velocity will result until all the hot air between FE and C has passed into the chimney. But this space FEC can be made of any capacity, so that the effect upon the

p

Elevation

F

E

B

F

A

Ground Plan

B

E

Fig. 139.

velocity of stopping the supply of heat can be postponed indefinitely, which proves that the heating of the air has no direct effect in producing the velocity.

We have, therefore, to consider separately

The effect of heating the air and the production of the velocity. The pressure of the atmosphere at A and D being the same may be left out of the problem.

THE EFFECT OF HEATING THE AIR.

Suppose the chimney to be in full draught, the hot air issuing at D with a velocity of, say, 100 feet per second, and let the heat be shut off. During the next second 100 cubic feet of hot air will escape at D and an equal volume will pass out of the cold-air shaft through the grating without undergoing any expansion, so that the upper surface of the air in the shaft must fall of a foot. Suppose, in the next place, that there is no draught in the chimney, a damper at C being closed, and let the grate be of such capacity as to hold 50 cubic feet of air, which we will suppose to be cold. Now close the circuit and heat the air until it expands from 50 to 100 cubic feet. This will raise the surface of the air at A of a foot.

When the chimney is in full draught and the heat supplied

continuously both of these processes are going on together. The surface at A is falling of a foot each second, on account of the flow of the air, and it is being lifted of a foot, by reason of the expansion of the air, the two operations being independent of each other.

The effect of heating the air is then simply to keep raising the cold air in AB, which acts as a weight to keep the apparatus running-i.e., to keep the chimney drawing-one-half of this weight being balanced against the weight of the hot-air column, and the other half being employed in maintaining the draught.

A

In some clocks the operation of winding interferes with the running; in others it does not. I once arranged an astronomical clock in a manner corresponding so exactly in its principle with that of chimney draught that a description of it may advantageously be given. A (Fig. 140) OOB is a pendulum clock. B is the main arbor to which the power is applied; on this arbor is a wheel, with a V-groove in its periphery, around which passes an endless cord. This cord, passing also around a similar wheel free to rotate in the direction of the hands only, sustains a larger and a smaller weight, as shown. By rotating the wheel C the clock can be wound without interrupting the action of the weight upon B, whereas in an ordinary clock, with a cord simply wound on a drum at B, the winding up of the weight interrupts its pull on the shaft B and may cause the pendulum to lose a beat, or, if the winding is done very slowly, the clock may stop.

W

Fig. 140.

There is nothing to prevent the winding from being done so slowly as to become a continuous operation, the weight being lifted each second the exact distance that it falls, so that it remains stationary.

We may easily vary the construction in Fig. 139 so as visibly to separate the action of raising the weight from that of producing the velocity.

Suppose (Fig. 141) that the cold-air shaft be extended to twice its former height and connected at the top with a similar shaft GH, opening at the bottom with a grating of wires to heat the entering air.

The atmospheric pressure must be supposed the same at A as at D, and it could be made so by having a gasometer top AH with

sufficient weight to make up for the different actual barometric pressures at D and A.

In such an apparatus the hot grate would keep GH full of hot air, having substantially no velocity, the action of the heat being to make each cubic foot of cold air 2 feet high, or to expand a column half HG high into one with the height HG, the weight re

maining the same, so that the hot-air column, plus the pressure p, must balance the atmospheric pressure p, at the bottom.

At the top there would be a constant flow from H toward A, to keep the shaft AB full.

THE PRODUCTION OF THE VELOCITY.

The portion of the apparatus ABCD would be devoted to producing the velocity of exit at D, and this velocity would evidently be that due to the height AD, or to the excess of the height of the column of hot air AB over that of a column of cold air of equal weight and section.

We shall have, then, velocity = √2g (AD).

Were it advisable to take account of the change in density between the bottom and top of the columns of air, we should need a thermo-dynamic formula to express it exactly, but, as this whole change is not 1% in the height of the chimney, it may be neglected, or, if it be desired to take it into account, the density may be sup