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The heat loss from a pipe is calculated in two parts: inside the pipe and outside the pipe

User inputs are in RED

Formulas in Column F are from the reference listed at the bottom of the worksheetCell names (preceded by underscore_) are listed in Column B

Data Inputs

Fluid flowing inside the pipe

G Flow rate 500 m3/h

ro Density 1,000 kg/m3

mu Viscosity 0.005 Pa-s

k Thermal conductivity 0.64 W/m-K

c Heat capacity 4,180 J/kg-K

T1 Temperature of fluid entering pipe 176 C

Pipe parameters

di inside diameter 207.3 mm

do outside diameter 219.1 mm

L pipe length 1,000 m

kp pipe thermal conductivity 45 W/m2-K

e emittance of pipe or insulation cover 0.80

Insulation parameters

it insulation thickness 25.4 mm

ki insulation thermal conductivity 0.035 W/m2-K

Environmental conditions (pipe is outdoors)

T4 Temperature of the air -5 C

w Wind velocity 5 m/s

Calculate radial distances from center-line to:

R1 inside pipe wall 0.1037 m

R2 outside pipe wall 0.1096 m

R3 outside insulation 0.1350 m

Calculate the Reynolds number inside the pipe

Ap Pipe cross sectional area 0.0338 m2

v Velocity 4.12 m/s

Re Reynolds number 170,612

Calculate the Prandtl number

Pr Prandtl number 32.7

Calculate the Inside heat transfer coefficient

HEAT LOSS / GAIN FROM PIPE

By Stephen Hall

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The formula depends on the flow region

For Laminar flow (Re < 2100) use Sieder and Tate

For this illustration, assume viscosity at wall = bulk viscosity

Laminar flow calculation N/A

For Transition flow (2100

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dair Density of air (treat as perfect gas) 1.30 kg/m3

muair Dynamic viscosity of air 1.71E-05 Pa-s estimated

' kinematic

For no wind condition,

Coefficient of expansion = 1/T for perfect gas assumption

Beta Coefficent of expansion 0.00367 K^-1

Gr Grasoff number (L = pipe OD), abs value 3.32E+07Prair Prandtl number 0.72

Gr x Pr 2.40E+07

Nuair Nusselt number 37.10

Outside heat transfer coef, no wind 3.27 W/m2-K

Calculation for the case where wind is present

Note that for very low wind velocity (

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Heat loss per meter 182.2 W/m

Downstream temperature 175.7 C

Reference: Cao, Eduardo, Heat Transfer in Process Engineering, McGraw-Hill, 2010

Spreadsheet prepared by Stephen Hall 4/9/2013

This is the calculation method included in PIPESIZE. See www.pipesizingsoftware.com

http://www.pipesizingsoftware.com/http://www.pipesizingsoftware.com/

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guess between ambient and fluid temperatures, then substitute value from below (_T3calculated)

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ith the Sutherland equation

viscosity = dynamic viscosity / density

Factors for Hilpert Equation

Re B n

0.4 0.891 0.33

4 0.821 0.385

40 0.615 0.466

4000 0.174 0.615

40000 0.0239 0.805

e

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Sp Ht Therm C

1.012 -150 2.793 1.026 0.0116 3.08 8.21 0.76

1.010 -100 1.98 1.009 0.016 5.95 5.82 0.74

1.008 -50 1.534 1.005 0.0204 9.55 4.51 0.725

1.006 0 1.293 1.005 0.0243 13.3 3.67 0.715

1.007 20 1.205 1.005 0.0257 15.11 3.43 0.713

1.008 40 1.127 1.005 0.0271 16.97 3.2 0.711

1.008 60 1.067 1.009 0.0285 18.9 3 0.709

1.009 80 1 1.009 0.0299 20.94 2.83 0.708

1.010 100 0.946 1.009 0.0314 23.06 2.68 0.703

1.011 120 0.898 1.013 0.0328 25.23 2.55 0.7

1.012 140 0.854 1.013 0.0343 27.55 2.43 0.695

1.012 160 0.815 1.017 0.0358 29.85 2.32 0.69

1.013 180 0.779 1.022 0.0372 32.29 2.21 0.69

1.014 200 0.746 1.026 0.0386 34.63 2.11 0.685

1.016 250 0.675 1.034 0.0421 41.17 1.91 0.68

1.018 300 0.616 1.047 0.0454 47.85 1.75 0.68

1.020 350 0.566 1.055 0.0485 55.05 1.61 0.68

1.022 400 0.524 1.068 0.0515 62.53 1.49 0.68

7.23714E-05

0.023883641

0.036910488

cs = 1.005 + 1.82H where 1.005 kJ/kgC is the heat capacity of dry air, 1.82 kJ/kgC the heat capacity of wat

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r vapor, and H is the specific humidity in kg water vapor per kg dry air in the mixture

0

0.01

0.02

0.03

0.04

0.05

0.06

-200 -100 0 100 200 300 400 500

Series2

Linear (Series2)

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below 0