### Author Topic: A Simplified Pipeline Calculations Program: Liquid Flow (1)  (Read 2821 times)

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##### A Simplified Pipeline Calculations Program: Liquid Flow (1)
« on: February 13, 2012, 04:06:05 am »
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Author : Tonye K. Jack
International Journal of Scientific & Engineering Research Volume 3, Issue 1, January-2012
ISSN 2229-5518

Abstract— and Program Objective - A multi-functional single screen desktop companion program for piping calculations using Microsoft EXCELTM with its Visual basic for Applications (VBA) automation tool is presented. The program can be used for the following piping geometries – circular, rectangular, triangular, square, elliptical and annular. Fluid properties are obtained from built-in fluid properties functions.

Index Terms— engineered spreadsheet solutions, liquid pipline flow, pipeline design, pipeline fluid properties, piping program, pipeline sizing.

1   INTRODUCTION
THE piping designer will often be saddled with the task of designing for different pipe configurations (circular, square ducts, etc.). Conducting such piping designs, can often involve repetitive calculations whether for simple horizontal pipelines or piping of complex terrains. Modern computer- assisted - tools are now often employed as aids in achieving these, if time and cost permits. Often times, for minor changes to existing installations or retrofitting, a customer (pipeline owner) would contract an engineering consultancy to conduct an analysis check that will involve desktop routine calculations such as determining pressure drops, or head loss, flow rate or pipe geometry (diameter, length,  cross-sectional area, etc.) that can be assigned to an engineer for quick answers. Simple spreadsheet calculators can be developed to aid such small routine calculations. One such program is shown here with all required equations to assist in developing one.

2 REQUIRED GENERAL EQUATIONS FOR INCOMPRESSIBLE FLOW

Reynolds Number:
(1)

Flow Velocity:
(2)
Area:              (3)

(4)

Friction Factor:  The friction factor, f, is obtained as follows:

For Laminar Flow: The applicable equations for laminar flows (Re≤2100) can be defined in terms of a laminar flow factor, Lf, which varies depending on the pipe geometry. The equation is of the form:

(5)

For Turbulent Flow, the friction factor, f is obtained by the Colebrook-White equation

(6)

Flowrate:

For Laminar Flow:

(7)
For Turbulent Flow:

(

(9)

Range of application:    10-6 ≤ (ε/D) ≤ 2 x 10-2
3 x 103 ≤ Re ≤ 3 x 108

Solution for Diameter:

(10)

(11)

Range of application:    10-6 ≤ (ε/D) ≤ 2 x 10-2
3 x 103 ≤ Re ≤ 3 x 108

Pressure Drop

(12)

Shear Stress in Wall:

(13)

Power required to pump through the line:

(14)

3 PIPE GEOMETRY AND FRICTION FACTOR
3.1 CIRCULAR SECTION PIPE:

The Laminar Flow factor is defined by the relation:

Lf  = Laminar Flow factor = f. Re = 64            (15)

For Turbulent Flow, f, is obtained by the Colebrook-White formula, “(6),”.

Also, for Turbulent Flow within the limits defined below, explicit values for the friction factor, f is obtained by the Swamee-Jain relationship, “(16),”.

(16)

Range of application:    10-6 ≤ (ε/D) ≤ 2 x 10-2
3 x 103 ≤ Re ≤ 3 x 108

The Microsoft Excel TM Solver Add-in, has two built-in interpolation search solution methods – the Newton method and the Conjugate Gradient method. By rewriting the equation to be solved in the solution form required (see “17,”) in the Microsoft ExcelTM cells, the Solver Add-in option dialog box under the Tools menu, allows for desired constraints to be set as follows:

Set Target Cell:
Equal To:
Subject to:   Guess value:

(17)
The Microsoft ExcelTM Goal Seek option is also useful.
Furthermore, the solution method provides for limiting the number of iterations, the degree of precision desired and the level of convergence (i.e. the decimal floating points). The error margin involved in the iteration calculation is indicated by the Tolerance percentage.  Care should be exercised to avoid a risk of having a circular reference – repeated recalculation of particular cell values as input and output.

Miller [1], suggest that a single iteration will produce a result within 1% of the Colebrook-White formula, if the initial esti-mate is calculated from the Swamee-Jain equation.