Hydrocarbon Processing - July 2022 - 35

Special Focus Valves, Pumps and Turbomachinery
I. GARCIA and A. GARCIA, Contributing Editors,
Houston, Texas
Accurately calculate flowrate through valves,
fittings and pipe under a turbulent flow regime
Calculating flowrate through long, straight pipe in a zone
Many books and handbooks tabulate (L/D)eq
of complete turbulence is easy using standard fluid mechanics
equations. In most industrial process designs, real piping systems
lie in the area known as the transition zone, meaning that
the friction factor depends on both the Reynolds (Re) number
of the flow and the relative roughness of the pipe. Conversely,
most real piping systems have valves and fittings that make calculating
flowrate more difficult.
This article presents equations that accurately calculate
flowrate through valves, fittings and pipe under a turbulent
flow regime (Re > 4,000) in systems where the energy loss is
then the sum of the losses of pipes and fittings.
Two equations provide a reasonable value of equivalent
length of straight pipe to account for valves and fittings, and
two other equations determine precise values of the friction
factor in smooth, new and rough pipes. These equations are excellent
resources to calculate flowrate in piping systems where
fittings cannot be disregarded. In this type of problem, the following
information is known:
1. Physical properties of fluid (density and viscosity)
2. Pipe size and its schedule
3. Total pressure drop or total head loss in the
piping system
4. Straight length of pipe
5. Character of internal surface of the pipe wall
6. Number and types of valves and fittings installed
in the piping system.1-5
Equivalent length of pipe. The following equations estimate
an equivalent length of pipe for valves and fittings. As
a general rule, the values of this equivalent length of pipe are
not real, but they allow the actual value of the friction factor
to be determined.
For smooth and clean commercial pipe (Eq. 1):
Le = 33 × K∑ ×
⎛
⎜⎝
= 44 × ∑K × ε-0.263
µ
ρ
⎞
⎟⎠
−0.24
× D( )1.36 ×
For rough pipe, use Eq. 2:
Le
× D1.263
where ∑K is determined as follows (Eq. 3):
∑K = ∑(L ⁄ D)eq
× ft + ∑K0
⎛
⎜⎝
hf
Ls
⎞
⎟⎠
0.12
(1)
(2)
(3)
La
= Le
+ Ls
and ft
values for
numerous fittings and valves. The adjusted length of pipe is
then (Eq. 4):
(4)
Friction factor. The value of the friction factor can be calculated
by the following equations. For smooth pipe (Eq. 5):
f = 0.0056 + 0.0189Λ-0.36
(5)
For clean commercial and rough pipe (Eq. 6):
0.25
f =
⎡
⎢⎣
Λ=
log
ρ
µ
⎛
⎝
0.000576
Λ
× hf ×
+ 0.27
D3
La
length of pipe defined as (Eq. 8):
Λ = 0.0002258 × Re × √f
ε
d
⎞
⎠
⎤
⎥⎦
2
where Λ is a conventional number defined as (Eq. 7):
(7)
Additionally, the number Λ is calculated with the actual
(8)
Actual equivalent length of pipe. Based on the friction
factor obtained above, the equivalent length of pipe is precisely
determined using Eq. 9, and the adjusted length of pipe is
checked by Eq. 4.
Le =
∑ K
f
× D
The desired flowrate is obtained using Eq. 10:
hf
q = 3.47835 × D2.5 ×
f × La
Checking the result. The mean velocity of flow, the Re
number and the relative roughness of the pipe (if any) are calculated
by traditional fluid flow equations. The friction factor
is then obtained by the Moody diagram or by equations
published in many papers, which agree with the calculations
achieved by Eqs. 5 and 6.
Hydrocarbon Processing | JULY 2022 35
(9)
(6)
(10)
Hydrocarbon Processing - July 2022

Table of Contents for the Digital Edition of Hydrocarbon Processing - July 2022
