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Calculation of pressure drop in the horizontal pipeline

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Calculation of pressure drop in the horizontal pipeline

Author: Valery Ochkov (http://twt.mpei.ac.ru/ochkov/v_ochkov.htm)

Introduction

 

This application calculates the of pressure drop in the horizontal pipeline

Friction coefficient

 

restart; with(ThermophysicalData); with(Units[Standard])

`&lambda;_friction` := proc (Delta, Reynolds) if 0 <= Reynolds and Reynolds < 2300 then 64/Reynolds elif 2300 <= Reynolds and Reynolds < 4000 then NaN elif 4000 <= Reynolds and Reynolds < 10/Delta then .3164/Reynolds^.25 elif 10/Delta <= Reynolds and Reynolds < 560/Delta then .11*(Delta+68/Reynolds)^.25 else .11*Delta^.25 end if end proc

Input Data

 

 

Inner pipe diameter: d := Units:-Standard:-`*`(32, Unit('mm')):

Length of pipe: L := Units:-Standard:-`*`(120, Units:-Standard:-Unit('m')):

Relative roughness of the inner surface of the pipe: Delta := 0.4e-3:

Fluid temperature: t := Units:-Standard:-`*`(80, Units:-Standard:-Unit('degC')):

Units:-Standard:-`*`(Fluid, pressure):

Fluid := water: 

g := Units:-Standard:-`*`(9.81, Units:-Standard:-`*`(Units:-Standard:-Unit('m'), Units:-Standard:-`/`(Units:-Standard:-`^`(Units:-Standard:-Unit('s'), 2)))):

Fluid mass flow:``

q := Units:-Standard:-`*`(4, Units:-Standard:-Unit(Units:-Standard:-`*`('tonne', Units:-Standard:-`/`('h')))):

Calculations

 

Fluid density:

rho := Property(density, pressure = p, temperature = t, Fluid);

972.1929651*Units:-Unit(kg/m^3)

(4.1)

Fluid volume flow:

Q := Units:-Standard:-`*`(q, Units:-Standard:-`/`(rho))

4.114409530*Units:-Unit(m^3/h)

(4.2)

Tube section

F := Units:-Standard:-`*`(Units:-Standard:-`*`(Pi, Units:-Standard:-`^`(d, 2)), Units:-Standard:-`/`(4)); -1; evalf[5](F)

8.042500000*Units:-Unit(cm^2)

(4.3)

Fluid velocity

v := Units:-Standard:-`*`(Q, Units:-Standard:-`/`(F))

1.421069042*Units:-Unit(m/s)

(4.4)

Fluid dynamic viscosity

mu := ThermophysicalData:-Property(viscosity, pressure = p, temperature = t, Fluid);

0.3542922180e-3*Units:-Unit(Pa*s)

(4.5)

Fluid kinematic viscosity

nu := Units:-Standard:-`*`(mu, Units:-Standard:-`/`(rho))

0.3644258194e-6*Units:-Unit(m^2/s)

(4.6)

Flow Reynolds*Number

Reynolds := Units:-Standard:-`*`(Units:-Standard:-`*`(v, d), Units:-Standard:-`/`(nu))

124783.1710

(4.7)

The*drag*coefficient*of*friction

lambda := `&lambda;_friction`(Delta, Reynolds)

0.1928609715e-1

(4.8)

Hence the pressure drop in the horizontal pipeline

`&Delta;h` := Units:-Standard:-`*`(Units:-Standard:-`*`(lambda, Units:-Standard:-`*`(L, Units:-Standard:-`/`(d))), Units:-Standard:-`*`(Units:-Standard:-`^`(v, 2), Units:-Standard:-`/`(Units:-Standard:-`*`(2, g))))

7.444010408*Units:-Unit(m)

(4.9)

... and pressure loss

`&Delta;p` := Units:-Standard:-`*`(Units:-Standard:-`*`(rho, g), `&Delta;h`)

.7006672860*Units:-Unit(atm)

(4.10)

``

``