Expansion tank sizing

where
V_t = volume of expansion tank, m³
V_s = volume of water in system, m³
t₁ = lower temperature, °C
t₂ = higher temperature, °C
P_a = atmospheric pressure, kPa
P₁ = pressure at lower temperature, kPa
P₂ = pressure at higher temperature, kPa
v1 = specific volume of water at lower temperature, m³/kg
v2 = specific volume of water at higher temperature, m³/kg
α = linear coefficient of thermal expansion, m/(m.K)
   = 11.7 x 10^-6 m/(m.K) for steel
   = 17.1 x 10^-6 m/(m.K) for copper
Δt = (t₂ – t₁ ), K