Linked variables (Fr = French, G = gauge):

• Gauge: G = 19.375 − (7.807 × ln(d))  [ln = natural log]
• French: Fr = π × d  ⇒  d = Fr / π
• Invert gauge: d = exp((19.375 − G) / 7.807)
• Behaviour: moving either diameter slider updates its Fr & G; the inner slider’s maximum auto-tracks the current outer diameter.

Occlusion maths (coaxial circles):

• Areas: A₁ = π·d₁²/4 (outer), A₂ = π·d₂²/4 (inner)
• % Occlusion of larger tube: (A₂/A₁) × 100
• Residual flow capacity (proportional flow): (A₁ − A₂)/A₁ × 100
• Residual CSA: A₁ − A₂. CSA = Cross-sectional area.
• Residual CSA “≈ Fr”: equivalent diameter deq = √(4·CSA/π), then Freq = π·deq, rounded to the nearest 0.5 Fr (no decimal if whole).