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The head as a function of air flow volume is in general presented in diagrams as shown below

The operation of a fan is often expressed in the terms of pressure
pt = ps + pd = constant (1)
where
pt = total pressure (Pa, N/m2)
ps = static pressure (Pa, N/m2)
pd = dynamic pressure (Pa, N/m2)
The dynamic pressure can be expressed as
pd = ρ v2 / 2 (2)
where
ρ = density of air (kg/m3)
v = flow velocity (m/s)

Head developed by the fan can be expressed as
dp = ps2 - ps1 + (v22 - v12) ρ / 2 (3)
where
subscription 1 is the inlet of the fan and subscription 2 is the outlet
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