As everyone who has used a fireplace knows when a fire burns in a furnace, a draft, or slight vacuum is induced that causes the hot combustion gases and entrained particulate matter to flow up and out of the stack. The reason is that the hot gas in the stack is less dense than air at ambient temperature leading to a lower hydrostatic head inside the stack than at the furnace inlet. The theoretical draft D (N/m²) is the difference in these hydrostatic heads; the actual draft takes into account pressure losses undergone by the gases flowing in the stack.

Let T_s (K) be the average temperature in a stack of height L(m) and Ta the ambient temperature, and let M and Ma be the average molecular weights of the gases inside and outside the stack. Assume that the pressures inside and outside the stack are both equal to atmospheric pressure, P_a?(N/m²) (in fact, the pressure inside the stack is normally a little lower).

(a) Use the ideal gas equation of state to prove that the theoretical draft is given by the expression

(b) Suppose the gas in a 53-rn stack has an average temperature of 655 K and contains 18 mole% CO₂, 2% O₂, and 80% N₂ on a day when barometric pressure is 755 mm Hg and the outside temperature is 294 K. Calculate the theoretical draft (cm H₂O) induced in the furnace.

D(N/m) PLg PaLg (M R Ta M, T,