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MMLU-Pro / 11613 / Estimate the depth to which a water pipe line is to be laid suchthat the water…

Problem

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question

Estimate the depth to which a water pipe line is to be laid suchthat the water flowing in the pipe does not freeze due to lowtemperatures at the surface. The mean temperature duringcold season is 5°C and minimum temperature goes downto - 10°C and exists for a maximum period of 48 hours. Assume the properties of the earth as k = 0.52 W/m - °K,\rho = 1840 kg/m^3 C_p = 2050 J/kg - °K. Table 1: The Complimentary Error Function erfc (\eta) = 1- {2 / \surd\pi}^\eta\int_oe^-(u)2 du \eta erfc (\eta) \eta erfc (\eta) 0.0 1.0000 1.1 0.11980 0.05 0.9436 1.2 0.08969 0.1 0.8875 1.3 0.06599 0.15 0.8320 1.4 0.04772 0.2 0.7773 1.5 0.03390 0.2S 0.7237 1.6 0.02365 0.3 0.6714 1.7 0.01621 0.35 0.6206 1.8 0.01091 0.4 0.5716 1.9 0.00721 0.45 0.5245 2.0 0.00468 0.5 0.4795 2.1 0.00298 0.55 0.4367 2.2 0.00186 0.6 0.3961 2.3 0.001143 0.65 0.3580 2.4 0.000689 0.7 0.3222 2.5 0.000407 0.75 0.2889 2.6 0.000236 0.8 0.2579 2.7 0.000134 0.85 0.2293 2.8 0.000075 0.9 0.2031 2.9 0.000041 0.95 0.1791 3.0 0.000022 1.00 0.1573

category

engineering

options

  1. 25 cm
  2. 35 cm
  3. 15 cm
  4. 50 cm
  5. 5 cm
  6. 45 cm
  7. 10 cm
  8. 20 cm
  9. 40 cm
  10. 30 cm

src

stemez-HeatTransfer

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Source and history

upstream_id / Original problem ID
11613
task_id
4e9d321e-088b-54dc-9f27-f75678b7c255
task_key
default--test--11613
task_revision_id
1
config / split
default / test

Official source

initial import