Theory Pressure Drop Evaluation Along Pipelines
Theory Pressure Drop Evaluation Along Pipelines
Theory Pressure Drop Evaluation Along Pipelines
The distance between Point A and Point B (or length the fluid must travel) and
equivalent length (pressure losses) introduced by valves and fittings.
These basic parameters are needed to design a piping system. Assuming steady-state
flow, there are a number of equations, which are based upon the general energy equation
that can be employed to design the piping system. The variables associated with the fluid
(i.e., liquid, gas, or multiphase) affect the flow. This leads to the derivation and
development of equations that are applicable to a particular fluid. Although piping
systems and pipeline design can get complex, the vast majority of the design problems
encountered by the engineer can be solved by the standard flow equations.
Bernoulli equation
The basic equation developed to represent steady-state fluid flow is the Bernoulli
equation which assumes that total mechanical energy is conserved for steady,
incompressible, inviscid, isothermal flow with no heat transfer or work done. These
restrictive conditions can actually be representative of many physical systems.
The
equation
is
stated
(Eq.
where
Z
pressure, psi,
density, lbm/ft3,
velocity, ft/sec,
and
H
L
as
1)
equation
(Eq. 2)
further
expresses
head
loss
as
and
(Eq.
where
H
L
velocity, ft/sec,
3)
density, lbm/ft3,
and
d
where
density, lbm/ft3,
viscosity, lbm/ft-sec.
and
The
Reynolds
number
for
liquids
can
be
Equation 5
where
viscosity, cp,
expressed
as
G
Q1
velocity, ft/sec.
and
V
The
Reynolds
number
for
gases
can
be
expressed
as
Equation 6
where
viscosity, cp,
specific gravity of gas at standard conditions relative to air (molecular weight divided
by 29),
and
Q
g
The Moody friction factor, f, expressed in the previous equations, is a function of the
Reynolds number and the roughness of the internal surface of the pipe and is given by
Fig. 3. The Moody friction factor is impacted by the characteristic of the flow in the pipe.
For laminar flow, where Re is < 2,000, there is little mixing of the flowing fluid, and the
flow velocity is parabolic; the Moody friction factor is expressed as f = 64/Re. For
turbulent flow, where Re > 4,000, there is complete mixing of the flow, and the flow
velocity has a uniform profile; f depends on Re and the relative roughness (/D). The
relative roughness is the ratio of absolute roughness, , a measure of surface
imperfections to the pipe internal diameter, D. Table 9.1 lists the absolute roughness for
several types of pipe materials.
Table 1
If the viscosity of the liquid is unknown, Fig. 4 can be used for the viscosity of crude oil,
Fig. 5 for effective viscosity of crude-oil/water mixtures, and Fig. 6 for the viscosity of
natural gas. In using some of these figures, the relationship between viscosity in
centistokes and viscosity in centipoise must be used
(Eq.
where
7)
and
S
G
specific gravity.
where
d
Ql
S
G
and