District Heating Pipe Heat Loss

Network Parameters

Insulation thickness 80 mm

Pipe run length 800 m

Water flow rate 15 kg/s

Ground temperature 8 °C

Live Readouts

Delivery temperature—

Total heat loss—

Delivery efficiency—

cold

hot

How it works

Hot water leaves the plant at supply temperature T_s and flows through a steel pipe wrapped in insulation, buried at depth h in soil at ground temperature T_g. Heat leaks radially outward through two resistances in series — the insulation and the surrounding soil:

R' = R_ins + R_soil   [m·K/W]
R_ins  = ln(r_ins / r_pipe) / (2π k_ins)
R_soil = ln(2h / r_ins) / (2π k_soil)

As the water travels distance x down the pipe, it loses heat at a rate proportional to how far its temperature sits above the ground — an exponential relaxation with a characteristic decay length set by the flow's heat capacity versus the pipe's resistance:

T(x) = T_g + (T_s − T_g)·exp(−x / L_c)
L_c = ṁ·c_p·R'          (c_p = 4186 J/kg·K, water)
q'(x) = [T(x) − T_g] / R'   local loss, W per metre

Thicker insulation raises R' and stretches L_c, so the water stays hot for longer. Higher flow rate ṁ also stretches L_c — the water has less time in the pipe to cool per kilogram delivered, though it demands a bigger pump. A longer run or a colder ground both push more of the pipe past the point where the exponential has decayed, raising total loss and lowering delivery efficiency η = [T(x=L) − T_g] / [T_s − T_g].

The pipe surface colour tracks the local water temperature — orange near the plant, fading toward blue as heat bleeds into the soil.
Flowing spheres are water parcels; their colour is the same temperature-decay curve sampled along the run.
This is the standard steady-state model used to size insulation and set maximum feasible run lengths for real district-heating networks (EN 13941 uses the same series-resistance approach).

◀ plant (T_s) consumer (T_del) ▶

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