How this calculation works
A fan does not deliver its free-air flow against every resistance. Its operating point is where the pressure it can supply matches the pressure the system requires. This page makes that intersection visible rather than applying a speed ratio directly to an unchanged delivered flow.
Pfan = P0 × speed ratio² − aQ²; Psystem = Pstatic + bQ²; Q = sqrt((scaled P0 − Pstatic)/(a + b)) when positiveA worked example
The baseline fan has a 600 Pa shutoff and 2000 m³/h free-delivery endpoint, giving coefficient 0.00015 Pa/(m³/h)². The system’s 100 Pa dynamic loss at 1000 m³/h gives coefficient 0.0001. After subtracting the 100 Pa static requirement, the intersection satisfies 500 = 0.00025Q². Airflow is about 1414.214 m³/h at 300 Pa, with about 0.1964 kW input at sixty-percent efficiency.
Good to know
Assumed smooth quadratic curves only; no manufacturer curve fit, unstable region, variable efficiency, density change or installed equipment approval. Use actual fan and system information for selection. Matching two simplified curves does not establish noise, motor loading, duct integrity or safe operation.
Reference: NC State Extension — fans and system pressure (opens in a new tab) ↗
What the model answers
A fan does not deliver its free-air flow against every resistance. Its operating point is where the pressure it can supply matches the pressure the system requires. This page makes that intersection visible rather than applying a speed ratio directly to an unchanged delivered flow.
The fan curve is assumed quadratic between baseline shutoff pressure and free-delivery flow. The system has a fixed static component plus a squared-flow dynamic component. These are explicit model choices, not a fit to a full manufacturer test curve.
The Duct leakage pressure conversion calculator models the response of leakage paths to pressure. Leakage can change an actual system curve, but this fan model does not infer those paths from a single leakage reading.
Measure and enter consistently
Enter baseline fan endpoints for the same density and setup. The speed ratio is new speed divided by baseline speed. Geometry and density remain unchanged under the simplified speed scaling.
Dynamic system loss is the part associated with the entered reference airflow. Keep static pressure separate so it is not counted again inside that dynamic loss. Efficiency is one overall constant for the power estimate.
Interpret the result
If scaled shutoff pressure cannot exceed the static requirement, the page reports zero ideal forward flow. It does not model reverse flow, stall or behavior of a running fan against a blocked or incompatible system.
Air power is volume flow per second times pressure. Dividing by the entered total efficiency estimates input power. An actual fan’s efficiency varies along its curve, so changing speed while fixing efficiency is a scenario assumption rather than measured performance.
Work through the numbers
The baseline fan has a 600 Pa shutoff and 2000 m³/h free-delivery endpoint, giving coefficient 0.00015 Pa/(m³/h)². The system’s 100 Pa dynamic loss at 1000 m³/h gives coefficient 0.0001.
After subtracting the 100 Pa static requirement, the intersection satisfies 500 = 0.00025Q². Airflow is about 1414.214 m³/h at 300 Pa, with about 0.1964 kW input at sixty-percent efficiency.
Where this model stops
Assumed smooth quadratic curves only; no manufacturer curve fit, unstable region, variable efficiency, density change or installed equipment approval.
Use actual fan and system information for selection. Matching two simplified curves does not establish noise, motor loading, duct integrity or safe operation.
A few questions, answered
Why does static pressure matter when speed falls?
The fan must first overcome that fixed requirement. Below it, the model has no positive forward-flow intersection.
Is this simply the cube-law energy calculator?
No. It first solves a changed operating point against the entered system curve, then estimates power there.