Chimney draught: condition for maximum discharge For maximum discharge through a chimney, the height of the effective hot-gas column producing draught should be:

Introduction / Context:
Natural draught in a chimney results from density differences between hot flue gases in the chimney and cooler ambient air outside. For a given chimney, there exists a condition that maximizes volumetric discharge by balancing buoyancy-induced pressure head with frictional and entry/exit losses.

Given Data / Assumptions:

• Steady flow of flue gas under natural draught.
• Uniform gas properties approximated along the height for conceptual analysis.
• Losses due to friction and fittings scale with velocity head.

Concept / Approach:
The draught head is proportional to the height of the hot column and the density difference. The discharge increases with effective head but is reduced by friction as velocity rises. Maximum discharge occurs when the effective height of the hot gas column contributing to draught equals the actual chimney height, a textbook result obtained by differentiating the flow with respect to temperature drop/height distribution and setting the derivative to zero.

Step-by-Step Solution:
Draught head Δp ≈ g * H * (rho_out - rho_gas).Flow rate increases with Δp but experiences losses ∝ v^2 along H.Optimizing discharge leads to the condition: effective hot-column height ≈ chimney height.Therefore choose: equal to the height of the chimney.

Verification / Alternative check:
Many classic boiler engineering references state the condition for maximum discharge as effective hot-gas column height equal to chimney height, confirming option (b).

Why Other Options Are Wrong:
Fractions or multiples of chimney height do not satisfy the optimum derived from the balance of buoyancy and friction for the standard model; “independent” contradicts physics of draught formation.

Common Pitfalls:
Confusing draught head with static head alone; ignoring frictional losses that limit flow at higher velocities.

Final Answer:
equal to the height of the chimney