Engineering task and calculation objective
The STAK module calculates the static stack (chimney) draft and the stack draft losses according to the Energietechnische Arbeitsmappe (14th edition), a standard German energy engineering reference. The static draft arises from the density difference between the warm flue gas column in the stack and the colder ambient air; opposing it are the flow losses due to pipe friction and the exit velocity. The module reports the draft, friction loss and draft loss separately — each also converted to the actual barometric pressure at ground level.
Having to calculate the stack draft is part of the design of every natural-draft combustion plant and of the rating of existing chimneys: the remaining net draft must cover the pressure drops of the furnace, heating surfaces and flue gas path, otherwise an induced-draft fan is required. The input quantities are the flue gas temperature and flue gas standard density, air temperature and air standard density, barometric pressure at ground level, plus stack height, diameter, exit velocity and pipe roughness.
Since the draft is proportional to the density difference, it depends sensitively on the flue gas and outdoor temperatures: in summer, or with a lowered flue gas temperature (condensing operation), the natural draft collapses — a frequent cause of draft problems after boiler modernizations.
Standard and calculation basis: Energietechnische Arbeitsmappe 14. Auflage: 1995
Calculation workflow
- Densities at operating conditions: From the standard densities of flue gas and air, the densities at the flue gas and air temperatures are calculated via the gas equation; optionally, an additional conversion to the actual barometric pressure at ground level is performed.
- Static draft: The draft results from the stack height and the density difference between the outside air and the flue gas column: Δp = g·H·(ρair − ρflue gas). It is the theoretically available negative pressure at the stack base with the gas at rest.
- Friction loss in the stack: From the diameter, height, exit velocity and pipe roughness, the friction factor is determined (also reported for the reference value k = 1 mm) and the frictional pressure loss of the flue gas flow over the stack height is calculated.
- Draft loss and net draft: The friction loss and the dynamic pressure lost with the exit velocity form the stack draft loss. The difference between draft and draft loss is the usable net draft, which must cover the pressure drops of the firing system and the flue gas path.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Temperature of flue gas | TG | K |
| Density of flue gas at NTP | ρG,N | kg/m³ |
| Air temperature | TL | K |
| Density of air at NTP | ρL,N | kg/m³ |
| Air pressure at ground level | p | Pa |
| Height of chimney | H | m |
| Diameter of chimney | D | m |
| Velocity at outlet | v | m/s |
| Wall roughness | k | m |
| Density of flue gas | ρG | kg/m³ |
| Density of air | ρL | kg/m³ |
| Intensity of chimney draught | ΔpSo | Pa |
| Intensity of chimney draught at p | ΔpS | Pa |
| Loss of chimney draught | ΔpA0 | Pa |
| Loss of chimney draught at p | ΔpA | Pa |
| Friction factor | λ | - |
| Friction factor at k = 1 mm | λk1 | - |
| Frictional pressure drop | ΔpR0 | Pa |
| Frictional pressure drop at p | ΔpR | Pa |
| lambda/lamk1 | λ/λk1 llk1 | - |
Worked example
A stack of height H = 60 m discharges flue gas at 200 °C (standard density ρN,RG = 1.30 kg/m³). The outside air is at 15 °C (standard density ρN,L = 1.293 kg/m³); the barometric pressure equals standard pressure. This worked example calculates the static stack draft.
Given values
| Stack height H | 60 m |
| Flue gas temperature | 200 °C = 473.15 K |
| Flue gas standard density | 1.30 kg/m³ |
| Air temperature | 15 °C = 288.15 K |
| Air standard density | 1.293 kg/m³ |
| Barometric pressure | Standard pressure (1,013.25 hPa) |
Solution
Densities at operating conditions
Conversion of the standard densities with the gas equation (pressure = standard pressure):
ρRG = 1.30 · 273.15 / 473.15 = 0.751 kg/m³
ρL = 1.293 · 273.15 / 288.15 = 1.226 kg/m³
Static draft
Δpdraft = g · H · (ρL − ρRG) = 9.81 · 60 · (1.226 − 0.751) Pa
Δpdraft ≈ 280 Pa ≈ 2.8 mbar
From this theoretical draft, the friction and exit losses of the stack must still be deducted; the remainder is available to cover the pressure drops of the boiler and the flue gas path.
Result
| Flue gas density (200 °C) | 0.751 kg/m³ |
| Air density (15 °C) | 1.226 kg/m³ |
| Static draft | ≈ 280 Pa |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Why is the calculation based on standard densities that are then converted to operating conditions?
The composition of the flue gas is usually specified as a density at standard conditions (0 °C, 1,013.25 hPa), for instance from a combustion calculation. Using the ideal gas equation, the density at the actual flue gas temperature and actual barometric pressure is determined from it. The barometric pressure is particularly relevant at elevated sites: at 500 m altitude, the air and flue gas densities — and with them the draft — are already about 6% lower than at sea level.
Which flue gas temperature should be used?
The governing value is the mean temperature of the gas column in the stack, not the boiler outlet temperature. The flue gas cools inside the stack — considerably so in uninsulated or single-shell chimneys. Calculating with the inlet temperature overestimates the draft; with long, poorly insulated flues and part-load operation, dropping below the dew point with resulting condensate damage is an additional risk.
When is natural draft no longer sufficient?
The usable draft grows only linearly with the stack height and the density difference, whereas modern boilers with tightly packed heating surfaces and flue gas heat recovery exhibit high gas-side pressure drops combined with low flue gas temperatures. If the balance of draft minus draft loss is not sufficient to cover the plant losses — including a reserve for unfavorable weather conditions and part load — an induced-draft fan must be provided; the QVEN module then delivers its power requirement.