calculation formulas for pipes

7/29/2019 Calculation Formulas For Pipes

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Calculation formulas 1/4

+GF+ CoolFit Plus Online Calculation DocumentationDeveloped by TechLogic

Pressure drops

(1)d

vLfp

200

2

where : density [kg/m3

]v: velocity [m/s]f: friction factorL: pipe length [m]d: inner pipe diameter [m]

For turbulent flow (Re>2320), f is constant at 0.02. For laminar flow (Re < 2320):

(2)Re

64f

where Re: Reynolds number [-]k: roughness [m]

: kinematic viscosity [m2/s]

(3)

dv Re

(4)

5

2

102

vpFi

where : contraction coefficient [-]v: velocity [m/s]

: density [kg/m3]

(5)

1000

2

v

Va

k

Qp

where Q [m3/h]: pipe flow

kv [m3/h]: valve flow characterist ic

[kg/m3]: density

Condensation

(6)T

A

A

T

A

AATLogAT

AAA

Tp

6

4 1010

10101325)('

5321

0

where A0 = 20.82648355A1 = 2948.997118A2 = 5.02808A3 = 29811.33781A4 = 32.923061A5 = 25.21934913A6 = 1302.8503T: absolute temperature in Kelvin

(7) )(')( TpTp

where [-]: relative air humidity

(8)

5771.23)(

9.404258.37

TpLn

Tdew


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(9)

total

jaf

purs

total

iaf

ipur

total

caffi

R

RTTTT

R

RTT

TT

R

RTTTT

)(

)(

)(

where Ti [C]: temperature of outer media pipeTf [C]: flow temperatureTa [C]: air temperatureTpur [C]: temperature of outer PURTs [C]: temperature of outer casing pipe (surface temperature)Ri [mK/W]: thermal resistance of insulationRc [mK/W]: thermal resistance of carrier pipeRj [mK/W]: thermal resistance of casing pipeRtotal [mK/W]: thermal resistance

Heat loss(10) )( af TTU [W/m]

where U [W/mK]: heat transmission coefficient of a single pipeTf [C]: flow temperatureTa []: air temperature

(11)ajci RRRR

U

1

[W/mK]

where Ri [mK/W]: thermal resistance of insulationRc[mK/W]: thermal resistance of carrier pipe

Rj [mK/W]: thermal resistance of casing pipeRa [mK/W]: thermal resistance of air

(12)

DhR

D

DLnR

d

dLnR

d

DLnR

a

ijj

icc

i

ii

1

2

1

2

1

2

1

[mK/W]

where Di [m]: internal diameter carrier pipeD [m]: external diameter casing pipedi [m]: internal diameter carrier piped [m]: external diameter carrier pipe

i [W/mK]: thermal conductivity of insulation

c [W/mK]: thermal conductivity of carrier pipe

j [W/mK]: thermal conductivity of casing pipeh [W/m

2K]: heat transfer coefficient of air

(13) rc hhh [W/mK]

where hc [W/m2K]: convective heat transfer coefficient

hr [W/m2K]: radiation heat transfer coefficient


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(14)4020

406080

0230..

.p

..

cD

)c(kV.h

[W/m2K]

where V [m/s]: air velocityk [W/mK]: thermal conductivity of air

[kg/m3]: air density

cp [J/kgK]: specific heat of airD [m]: casing pipe diameter

[m2/s]: kinematic viscosity of air

(15) 34 Thr [W/m2K]

where [-]: emittance

[W/m2K

4]: Stefan-Bolzmann constant

T [K]: air temperature in Kelvin

Pipe dimensioning

(16)v

Qdi 8.18 [mm]

Where di: inner pipe diameter [mm]Q: flow rate [m

3/h]

v: flow velocity [m/s]

(17)2

2

8.188.18

vdQ

v

Qd ii

Pipe supports

(18) 3qJEfL RcLAA

where fLA [-]: factor (0.80.92. For supported beam 0.8 is used and 0.92 is used for a subjected beam)Ec [N/mm

2]: modulus of elasticity

JR [mm4]: moment of inertia

q [N/mm]: load

Expansion/Contraction(19) TLL [mm]

where [1/C]: thermal coefficient of expansionL [m]: pipe length

T [C]: temperature difference

(20) TE [N/mm2]

where [mm/mK]: thermal coefficient of expansionE [N/mm

2]: modulus of elasticity

T [C]: temperature difference

(21) LdcLB [mm]

where c [-]: material constantd [mm]: pipe or jacket diameterL [-]: change in pipe length


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Temperature

(22) sp

x Tcm

LUExpTT

[C]

where T [C]: temperature difference between inlet and surroundings

U [W/mK]: heat transmission coefficient

L [m]: pipe length

m [kg/s]: mass flow of media

cp [J/kgK]: specific heat at constant pressure

Ts [C]: surrounding temperature

(23)

36001000 mQ

m

[kg/s]

where Q [l/h]: media flow

m [kg/m3]: density of media

(24)U

mcT

TLn

t

mediapx

3600

[h]

where mmedia [kg/m]: load of content

Tx [C]: temperature difference between cool down temperature and surroundings

T [C]: temperature difference between inlet and surroundings

U [W/mK]: heat transmission coefficient

L [m]: pipe length

cp [J/kgK]: specific heat at constant pressure

(25)

total

jaf

purs

total

iafipur

total

caffi

R

RTTTT

R

RTTTT

R

RTTTT

)(

)(

)(

where Ti [C]: temperature of outer media pipe

Tf [C]: flow temperature

Ta [C]: air temperature

Tpur [C]: temperature of outer PUR

Ts [C]: temperature of outer casing pipe (surface temperature)

Ri [mK/W]: thermal resistance of insulation

Rc [mK/W]: thermal resistance of carrier pipe

Rj [mK/W]: thermal resistance of casing pipe

Rtotal [mK/W]: thermal resistance

calculation formulas for pipes

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