Chemical Engineering September 2015 - 66

Engineering Practice
A Universal Equation for Designing Pipelines
The pipe-flow equation presented here can be used to properly and easily size
pipelines for liquid, vapor and two-phase flow. Example calculations are also shown
Jung Seob Kim
SK E&C USA Inc.
Taek-kyoung Oh
SK E&C
Heather Jean Dunsheath
Covestro LLC
S
izing pipelines is a fundamental task for design
engineers, who typically use several equations
to size pipes for different flows (liquid/vapor/
two-phase). The flow equations, however, are
basically analogous. Incompressible flow calculations
are considered relatively simple and easy to do. However,
a major challenge faced by design engineers is sizing
a pipe flow that experiences significant variations in
the flow density and velocity.
Generally, calculations for vapor or two-phase piping
often involve repetitive calculations for accurate results.
Sizing a pressure-relief system that operates at very high
velocity and high pressure drop is a difficult application.
Vapor flow and two-phase flow in relief-discharge piping
involve rapid changes in density that result in very high
line velocities. The calculation methods of the American
Petroleum Institute (API) have been widely used in industries
for sizing relief system piping [1]. For vapor flow,
the relatively conservative isothermal equation is recommended.
And if the pipe system handles vapor and
flashing or non-flashing liquid, the homogeneous equilibrium
equation is suggested. Consequently, emergencyrelief-system
designers use several pipe-flow equations
to size relief system pipes [1].
This article presents a universal pipe-flow equaP
= Np dD3N5
tion to properly and easily size pipe lines for liquid
flow, vapor flow and two-phase flow, and suggests
appropriate and convenient calculation procedures.
The universal equation for pipe flows is developed by
modifying a universal mass-flux equation for sizing relief
valves previously developed by Kim and others
[2]. This article provides an overview of the pipe flow
equations and highlight the key considerations. Additionally,
four example calculations are provided to
illustrate the application of the universal equation for
pipe flows.
Re = d2
N /µ
P = Np dD3N5
= d2
N /µ
Review of existing equations
Those who design pipelines that are intended for fluid
transportation are expected to cope with the calculation
of pressure drop in a piping system. Pressure losses
consist of three different components for a pipe system
at a given velocity. Generally, total pressure loss in the
pipe system is the sum of friction loss, acceleration loss
and elevation loss, as shown in Equation (1). However,
P /V = 2.45W /m3
P = Np dD3N5
Re = d2
66
N /µ
P /V = 2.45W /m3
P /V = 2.45W /m3
Equation (2) is often expressed in terms of average specific
volume [3]. Therefore, the friction losses in pipelines
can be computed directly using Equation (2) or
Equation (3).
Re
(3)
Although the two equations seem to be identical, they
give different results when applied to vapor and twophase
flows because the average density is not the reciprocal
of the average specific volume. Equation (3)
has been found to generally over-predict friction losses
where the change in density is significant. However, the
ChemiCal engineering www.Chemengonline.Com september 2015
NomeNclature
C1
C2
D
G
f
g
L
M
N
n1
n2
P
v
Z
Constant in Equation (7), 24
Constant in Equation (7), 2.898× 106
Pipe inner diameter, ft
Mass flux, lb/s-ft2
The Fanning friction factor
Acceleration of gravity, ft/s2
Equivalent pipe length, ft
Mass flowrate, lb/h
Total pipe loss coefficient
P1/P0 in Equation (7)
P2/P0 in Equation (7)
Absolute pressure, psia
Specific volume, ft3/lb
Elevation, ft
α, β, ω Parameters for a pressure-specific volume correlation
ρ
Density, lb/ft3
Subscripts
0,1,2
avg
ec
Physical property data states
Arithmetic average
Equivalent choked (critical) conditions
Equation (1) does not precisely represent vapor and
two-phase systems that involve an additional compression
term.
(1)
For the friction loss term, one of the most useful and
important equations is the Darcy-Weisbach equation,
Equation (2).
(2)
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Chemical Engineering September 2015

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