Solar Chimney Ventilation Calculator

Understanding solar chimney stack effect

A solar chimney uses sun-warmed air in a vertical shaft to create buoyancy-driven exhaust. As the shaft heats up, the air inside becomes less dense than the air below, rises toward the outlet, and helps pull replacement air through a low-level opening without a fan.

This calculator applies a stack-effect approximation that is useful for early design checks and quick comparisons. It is a good way to ask whether a taller shaft, a larger free-flow area, or a bigger indoor-to-outdoor temperature difference changes the result enough to matter, but it does not account for wind pressure, leakage, partitions, or the hour-to-hour variation in solar gain.

If you are evaluating a retrofit, a sketch design, or a rough concept model, use the result as a screening estimate rather than a final answer. The biggest practical questions are usually whether the chimney can stay hotter than the surrounding air, whether the inlet can supply enough replacement air, and whether the building layout gives that air a clear path.

How to use the solar chimney calculator

1. Chimney height (m): enter the vertical distance from the inlet level to the outlet level. Height is the main source of stack pressure.
2. Chimney area (m²): enter the internal free-flow cross-sectional area of the shaft. Area scales flow approximately linearly.
3. Indoor temperature (°C): the air temperature at the base/inlet side, usually near the occupied zone or the plenum feeding the shaft.
4. Outdoor temperature (°C): the air temperature at the outlet/top side, often near roof level and ideally measured in shade if you want ambient conditions.
5. Discharge coefficient: a dimensionless factor (typical range 0.55–0.70) that bundles entrance, exit, and friction losses into one value.
6. Press Calculate to compute airflow in m³/s and m³/h. Use Copy Result to copy the summary line for notes or reports.

The model requires a positive temperature difference (ΔT = T_in − T_out > 0). If the roof or outdoor air is warmer than the air at the chimney base, buoyancy weakens and the calculator will flag the condition as outside the stack-effect model. Wind or mechanical exhaust can still move air in that situation, but that is a different ventilation mechanism.

Formula for solar chimney airflow and assumptions

For solar chimney airflow, the calculator uses a simplified buoyancy equation derived from Bernoulli’s principle and the ideal-gas relationship. It converts the entered temperatures from °C to Kelvin before calculating the temperature ratio, because air density depends on absolute temperature rather than Celsius temperature.

• Q = volumetric airflow rate (m³/s)
• C_d = discharge coefficient (dimensionless)
• A = chimney cross-sectional area (m²)
• g = gravitational acceleration (9.81 m/s²)
• H = chimney height (m)
• ΔT = T_in − T_out (K; numerically the same difference as °C)
• T_m = mean absolute temperature = (T_in + T_out)/2 (K)

Assumptions: steady flow, one dominant vertical shaft, modest temperature differences, and all entrance, exit, and friction losses rolled into a single coefficient. The equation does not model wind pressure, internal partitions, or heat transfer along the shaft walls. In practice, the discharge coefficient can shift when screens, louvers, bends, or rough surfaces add resistance.

Worked example: solar chimney airflow step-by-step

This solar chimney worked example uses a 3 m shaft with 0.5 m² free area, indoor air at 30 °C, outdoor air at 20 °C, and C_d = 0.65.

1. Convert to Kelvin: T_in = 30 + 273.15 = 303.15 K; T_out = 20 + 273.15 = 293.15 K.
2. Compute ΔT: 303.15 − 293.15 = 10 K.
3. Compute mean temperature: T_m = (303.15 + 293.15)/2 = 298.15 K.
4. Compute flow: Q = 0.65 × 0.5 × √(2 × 9.81 × 3 × (10/298.15)).
5. Convert to hourly flow: m³/h = Q × 3600.

The result is about 0.46 m³/s (roughly 1,640 m³/h), with small differences depending on rounding. In this equation, area and discharge coefficient scale the answer directly, while height and temperature difference enter under the square root, so a taller or hotter chimney increases flow with diminishing returns.

Design notes for solar chimney ventilation (what to check in practice)

When you turn a solar chimney estimate into a real design, the chimney is only one part of the system. The inlet, outlet, and the path between them need to be open enough for the estimated flow to exist in the building. If the inlet is too small, too indirect, or blocked by doors and partitions, the chimney can only pull as much air as the narrowest part of the route will allow.

Solar gain is the engine that makes the chimney work. Dark absorptive surfaces, glazing, and insulation can increase shaft air temperature, while shading and reflective finishes can reduce it. Thermal mass can smooth performance over time, but it can also delay peak flow. Wind can either assist or oppose stack effect depending on direction and outlet geometry, so a cowl, hood, or well-placed outlet can make the estimate more realistic.

For comfort and indoor air quality, it helps to translate airflow into a building metric such as air changes per hour (ACH). If you know the ventilated volume V (m³), then ACH ≈ (m³/h) / V. For example, 900 m³/h through a 300 m³ space is about 3 ACH. That is a useful comparison when you are testing different solar chimney layouts, but local code requirements and the needs of the occupancy still take priority.

The discharge coefficient table below is a starting point, not a universal truth. Use the row that best matches the shaft construction, and adjust downward if screens, louvers, or tight transitions add resistance at the inlet or outlet.

Solar chimney limitations and when to use a different method

This solar chimney calculator is intentionally simple, which makes it useful for screening but easy to overread. It can overestimate performance when friction losses are high (long shafts, rough surfaces, tight bends), when inlet or outlet areas are restrictive, or when the temperature difference is not sustained by solar heating. It can also underestimate performance when wind assists the outlet or when the shaft is much hotter than the indoor air because of strong solar gain.

• Low-rise buildings: short height reduces stack pressure, so meaningful flow may require large areas or multiple shafts.
• Hot/humid climates: small ΔT reduces buoyancy; wind-driven ventilation, night flushing, or hybrid fans may be needed.
• Transient conditions: clouds, shading, and thermal mass cause time-varying flow; night-time reversal is possible.
• Complex airflow paths: multiple openings, internal partitions, and wind pressures require multi-zone or CFD analysis.

If you need higher confidence, estimate inlet and outlet pressure losses separately, include wind pressure coefficients for the facade and roof, and validate the setup with measurements or a calibrated airflow model.

Frequently asked questions about solar chimney ventilation

What temperature should I enter for “indoor” and “outdoor”?

Use the air temperature at the chimney inlet for indoor temperature and the air temperature near the chimney outlet for outdoor temperature. In many cases the outlet is near the roof, where air can be warmer than at ground level. If the outlet is sun-exposed, consider using a shaded ambient value for outdoor temperature and treat additional heating as part of the effective ΔT you expect the chimney to create.

Does a bigger chimney always mean better ventilation?

Larger area generally increases flow, but only if the rest of the system can support it. The inlet, internal air path, and outlet details can become the limiting resistance. Also, very large shafts may be harder to heat uniformly, which can reduce the temperature rise that drives buoyancy.

Why does the calculator require indoor air warmer than outdoor air?

The simplified stack equation used here assumes buoyancy drives upward flow because the air column in the solar chimney is warmer and therefore less dense than the surrounding air. If ΔT is zero or negative, the buoyancy term becomes zero or imaginary in the square root, and the model is not applicable. In real buildings, wind can still drive flow even with ΔT ≤ 0, but that is a different mechanism.

How do I choose a discharge coefficient?

Start with 0.65 for a reasonably smooth shaft with decent inlet and outlet detailing. Use a lower value (0.55–0.60) if you expect screens, louvers, rough surfaces, or sharp transitions. Use a higher value (up to about 0.70) for smooth, well-rounded entries and exits. If you have measured data or manufacturer loss information, that should take precedence.

Can I use this for night flushing?

Yes, as a rough estimate, if indoor air remains warmer than outdoor air at night, for example after a hot day. However, night-time radiative cooling can also cool the chimney and change the direction of flow. If reverse flow is a concern, include dampers or operable vents and consider a time-based model.

If you are comparing passive and hybrid strategies, you may also find these helpful: attic ventilation sizing calculator, heat recovery ventilator savings calculator, and the indoor CO₂ ventilation planner. Together, these tools can help you compare airflow targets, energy impacts, and indoor air quality constraints across different ventilation approaches.

Summary: solar chimney ventilation takeaways

Use this Solar Chimney Ventilation Calculator to estimate buoyancy-driven airflow from a heated vertical shaft. Enter height, area, temperatures, and a discharge coefficient to get airflow in m³/s and m³/h, then compare the result with inlet sizing, expected solar heating, wind exposure, and the way air actually moves through the building. If the answer looks unrealistic, check the temperature direction, the free area at the inlet and outlet, and whether the chimney is likely to stay warmer than the surrounding air. For final design decisions, validate with more detailed methods and, where possible, measurements.