The heat a buried hot-water pipe loses per metre equals its temperature excess over the ground divided by the sum of the insulation’s and the soil’s thermal resistances, and the insulation term dominates: a 60.3 mm steel pipe at 80 °C in 8 °C ground loses 171 W per metre bare, 26.7 W with 25 mm of wool-class insulation (conductivity 0.041 W/m·K), 17.5 W with 50 mm and 12.1 W with 100 mm. Keep the insulation dry, because at an assumed wet conductivity of 0.5 the 50 mm layer loses 114.5 W per metre, 6.5 times more.
Part of District Heating
Deriving the heat loss of buried hot-water pipe, comparing insulation thicknesses and materials, and testing the result on the real network.
Derivation: Two Resistances In Series
Heat flows radially out of the pipe through the insulation and then through the soil. For a cylinder of length L with inner radius r₁ and outer radius r₂, Fourier’s law integrates to Q = 2π × k × L × ΔT ÷ ln(r₂ ÷ r₁). Per metre, the thermal resistance of the insulation is
R′_ins = ln(r_o ÷ r_i) ÷ (2π × k_ins)
in m·K/W. The corpus uses the same cylinder formula for tank jackets in Super Insulation. The soil term for a pipe of outer diameter D_o with its axis a depth H below a surface at ground temperature uses the method of images:
R′_soil = ln(4H ÷ D_o) ÷ (2π × k_soil)
The heat loss per metre is q′ = (T_pipe − T_ground) ÷ (R′_ins + R′_soil). The soil formula is quoted from memory of standard heat-transfer texts; at H = 0.8 m and r_o = 0.08 m the exact form, arccosh(H ÷ r_o) = 2.991, differs from ln(4H ÷ D_o) = 2.994 by 0.1%.
Worked Example: 50 mm Of Insulation At 80 °C
Inputs: steel pipe outside diameter 60.3 mm (r_i = 0.03015 m); insulation 50 mm thick (r_o = 0.08015 m) with k = 0.041 W/m·K, the wool value in Natural Insulation Materials; axis depth H = 0.8 m; soil k = 1.5 W/m·K (an assumed damp-soil value, not from the corpus); ground temperature 8 °C (assumed mean).
- R′_ins = ln(0.08015 ÷ 0.03015) ÷ (2π × 0.041) = 0.9777 ÷ 0.2576 = 3.795 m·K/W.
- R′_soil = ln(4 × 0.8 ÷ 0.1603) ÷ (2π × 1.5) = 2.994 ÷ 9.425 = 0.318 m·K/W.
- Total = 4.113 m·K/W.
- Supply at 80 °C: q′ = (80 − 8) ÷ 4.113 = 17.5 W/m. Return at 50 °C: (50 − 8) ÷ 4.113 = 10.2 W/m. The pair loses 27.7 W per metre of trench.
The Table
Each row uses the same 60.3 mm pipe, depth, soil and ground temperature, supply 80 °C and return 50 °C. The trench is 400 m; a season is 4,800 h; the heat delivered is 230 MWh (30 houses, 4 kW design, 40% load).
| Insulation | Supply W/m | Return W/m | Pair W/m | 400 m, kW | Season, MWh | Share of 230 MWh |
|---|---|---|---|---|---|---|
| None (bare steel) | 171 | 100 | 270.5 | 108 | 519 | 225% |
| Wool, 25 mm | 26.7 | 15.5 | 42.2 | 16.9 | 81 | 35% |
| Wool, 50 mm | 17.5 | 10.2 | 27.7 | 11.1 | 53 | 23% |
| Wool, 100 mm | 12.1 | 7.1 | 19.2 | 7.7 | 37 | 16% |
| Shavings, 100 mm (k 0.058) | 16.8 | 9.8 | 26.6 | 10.7 | 51 | 22% |
| Straw, 100 mm (k 0.096) | 26.8 | 15.6 | 42.4 | 16.9 | 81 | 35% |
| Straw, 200 mm | 20.1 | 11.7 | 31.9 | 12.8 | 61 | 27% |
| Wool, 50 mm, wet (k 0.5, assumed) | 114.5 | 66.8 | 181.3 | 72.5 | 348 | 151% |
Conductivities for wool, shavings and straw are the corpus values; k = 0.5 for wet insulation is an illustration, since the corpus gives no wet value (liquid water itself conducts at about 0.6 W/m·K). What the rows show:
- A wet 50 mm layer at k = 0.5 loses 114.5 ÷ 17.5 = 6.5 times the dry loss of 17.5 W/m on the supply pipe.
- A bare pipe loses more heat than the houses use: 519 MWh against 230 MWh. Insulation is not optional.
- 100 mm of straw does the same work as 25 mm of wool (42.4 against 42.2 W/m), because conductivity is 0.096 against 0.041 and the ln term grows slowly with thickness.
- Each doubling of the thickness gives diminishing returns: 26.7 to 17.5 W/m (−34%) and then 17.5 to 12.1 (−31%). Going from 25 to 50 mm of wool saves 14.5 W/m, 69.6 kWh per metre per season, which at 11.44 MJ of useful heat per kg of wood is 21.9 kg per metre, or 8.8 t of wood a season over 400 m.
What Barely Matters, And What Does
| Parameter varied (wool 50 mm) | Values | Pair loss W/m |
|---|---|---|
| Soil conductivity | 0.72 / 1.5 / 2.5 | 25.6 / 27.7 / 28.6 |
| Burial depth | 0.5 / 0.8 / 1.2 m | 28.1 / 27.7 / 27.4 |
| Ground temperature | 0 / 8 / 12 °C | 31.6 / 27.7 / 25.8 |
Soil type and depth barely move the answer because the insulation carries 92% of the resistance. The ground temperature does, by about ±14%, and it is a seasonal, local quantity: measure it at pipe depth in midwinter. Supply and return in one trench warm the soil between them, so treating each pipe alone slightly overestimates the pair; this page does not quantify the effect.
Method: Keeping Insulation Dry And Whole
- Wrap the insulation in a waterproof layer, or run the pipe in a larger duct (the carrier page suggests plastic sheeting or a waterproof outer pipe).
- Seal the ends and joints of the casing; moisture enters at the ends of runs.
- Bed the pipe in sand or fine gravel and drain the trench so that it never fills.
- Insulate every valve, flange and bend; a bare fitting is a short length of bare pipe.
- Never insulate before the pipe has been pressure-tested and left to dry.
Instrument It: A Loop Test
With the houses isolated and the supply connected to the return at the far end, circulate water at a measured flow. The heat the network loses is Q = m × c × (T_out − T_back) at the plant. For 11.1 kW and a flow of 0.3 kg/s the temperature drop is 11,100 ÷ (0.3 × 4,180) = 8.9 K, easy to read with two thermometers. Measure flow with a bucket and a stopwatch. Compare with the table: a result well above the expected loss points to wet insulation, a missing section or a leak.
Common Mistakes
- Choosing thickness for the first-year cost. The loss is paid every hour of the season.
- Using a dry k for a buried pipe. Check it is dry, or use a higher k.
- Forgetting the return pipe. It is cooler, but still 37% of the pair loss.
Safety
Hot pipe, wet insulation, scalding steam
A leaking joint in wet insulation can send hot water or steam out through a trench, and a pipe wrapped in wet material hides the leak. Do not walk or drive on trenches that have steamed or settled, mark leaks and shut off the section before digging, and treat any water that has been in the loop as 80 °C.
What’s Next
- Learn next: Burial Depth & Trenching — where the pipe goes
- Combine with: Fuel Consumption Estimates — what the loss costs in wood