Layout Cost Explorer — the real cost of a metre

Route

STRAIGHT-LINE DISTANCE L₀ EXTRA ROUTE LENGTH ADDED (the dog-leg) LINE SIZE FLOW DESIGN ΔT ABOVE INSTALLED TEMP

—whole-life cost of this route (US$, 20 yr PV)

— true cost of one metre of this line

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What the model does

Cost rules (transparent, order-of-magnitude): installed pipe ≈ 0.79·DN^1.15 $/m; rack steel, shoes and supports = +30 % of that; pumping = Darcy–Weisbach ΔP (ε = 0.046 mm, L_eq = 1.25·L for fittings) → shaft power at η = 0.65 → 8000 h/yr at 0.09 $/kWh, present-valued over 20 yr at 8 % (factor 9.82); flexibility penalty = 380·DN^0.9 $ (bellows + two main anchors + guides + one mid-life replacement), charged in full when the route offers no offset leg and falling to zero once the dog-leg leg length reaches the guided-cantilever requirement ℓ_req = √(3·E·D_o·Δ / S_A) with E = 203 GPa, S_A = 150 MPa, α = 1.2×10⁻⁵/°C.

What it deliberately cannot price: safety spacing, escape routes, maintenance access, crane laydown, constructability, operator reach. Those are constraints, not line items — they delete routes from the menu before any cost is compared. So every number here is a lower bound on why the shortest route loses.