COMPRESSIBLE FLOW
FRICTION
Friction in gas pipelines
Coefficient λ
•In pipelines of gasses flow functional reliance λ = f(∆ e,Re) is
valid.It means ,that friction depend from the equivalent roughness
and flow regime.
•For steel material of gas pipes equivalent roughness ∆ e = 0,1 mm .
•For copper or plastic gas pipes ∆ e = 0,0015–0,003 mm only.(see
Table)
•According the Moody chart,5 zones of friction factor λ is valid:
1) Laminar flow.For laminar flow friction factor is independent
of relative roughness,and can be estimated by formula:
64
λ= . (1)
Re
Where : Re < 2000 –Reinold’s number;
•For the transition II zone,(2000 < Re < 4000),the flow can be
laminar or turbulent(or an unsteady mix of both) depending on the
specific circumstances involved.Coefficient λ can be find according
empirical formula Zaichenko:
λ = 0,00253 Re . (2)
•For the turbulent flow in hydraulically smooth pipe III zone(Re >
4000 ,and Re < 105,and Re ∆ e/d•For flows with moderate values of Re in the turbulent IV zone(Re
>4000, and 10 < Re ∆ e/d 4000, and
Re ∆ e/d >500) surface roughness completely dominates the
character of the flow near the wall.(λ = f (∆ e/d))From the (5) formula
we can find in that case:
0 ,25
∆e
λ = 0 ,11 . (6)
d
Equivalent Roughness ∆ efor New Pipes
Pipe Equivalent Roughness, in mm
Riveted steel 0.9 – 9.0
Concrete 0.3 – 3.0
Wood stave 0.18 – 0.9
Cast iron 0.26
Galvanized iron 0.15
Commercial steel or wrought 0.045
iron
Drawn tubing 0.0015
Plastic, glass 0.0 (hydraulically smooth)
•NOTE: Even for hydraulically smooth pipes the friction factor is not
zero.That is,there is a head loss in any pipe,no matter how smooth the
surface is made.This is a result of the no-slip boundary conditions
that requires any fluid to stick to any solid surface it flows over.There
is always some microscopic surface roughness that produces the no-
slip behavior on the molecular level, even when the roughness is
considerably less then the viscous sub layer thickness.
•According the practice and investigations of gas flow in pipelines it
can be conclude that we can found all 5 flow resistance zones in steel
gas pipe network. Table .Flow regimes in gas networks, in %
Flow regime Minor Medium High
zones pressure pressure pressure
network network network
I zone 8 – –
II zone 13 – –
III zone 59 1 –
IV zone 20 86 24
V zone – 13 76
•Turbulent flow regime in I.F.Moody diagram is characterized by a
family of curves.The lowest curve of the family expresses λ - Re
relationship for ∆ e/d = 0.It is a smooth pipe case – pipe wall
roughness elements are hidden in a laminar film and the roughness
makes no influence on the friction factor λ.
•Each of the rest curves of the family represents definite relative
roughness ∆ e/d.Thus, a friction factor here depends from both Re and
∆ e/d.
•At the right side of the diagram the curves expressing λ = f(Re,∆ e/d
relationship are parallel to Re axis.It means that Re has no influence
on λ, it depends on relative roughness ∆ e/d only.It is a rough pipe
case.
•Reynolds number Re and relative roughness ∆ e/d are to be known to
read friction factor on the Moody diagram. When flow rate Q is
computed and there is no possibility to compute Re ,λ is read from a
rough pipe zone of the chart.Then the actual meanings of Re is
computed and friction factor is corrected.
Formulae of practical gas pipe
network calculation
•They are derived from the last ones when normal conditions of the gas
flowing in the pipe linesis estimated:
ρ n = 0,73 kg/m3; ν n = 14,3⋅ 10–6 m2/s; pn = 101,3 kPa
Qn
Re = 2827 dν (7)
n
Where :
Qn – gas flow rate in normal conditions,in m3/h.
•When estimate that Q 2
∆p L = 0 ,81λρ 5
l,
d
0 ,3164
λ= 0 ,25
,
Re
and in the gas pipe line networks of minor pressure we can find:
Q1,75
∆ p L = 6,473 ⋅ 10-9 4 ,75 l = s l Q1,75 (8)
,
d
Here s = 6,473·10–9 d –4,75 – an comparative pressure losses;
Q – flow rate,in m3/h.
•When we are calculated pressure losses of plastic pipelines in the
medium or high pressure gas networks then:
2
Q
∆ p = p − p = 1,62λ ρ n pn l .
2 2
1
2
2
n
5
d
0 ,171
λ= 0 ,194
,
Re
Q1,806
∆ p 2 = p1 − p2 = 0,010139ρ n ν 0 ,194
2 2
n 4 ,806
l (9)
d
•After estimation that for natural gasses ρ n = 0,73 kg/m3, ν n =
14,3·10–6 m2/s one can found:
2 Q1,806
n 1,806
∆p = 8,50⋅ 10–4 4,806
l =S l Qn , (10)
d
(11)
S = 8,50⋅ 10 d –4 –4,806
Where: Qn – gas flow rate,in m3/h;
∆p2 - pressure loss,in Pa2
The coefficients of minor loss in gas pipelines
•These coefficients are found experimentally.
•The meaning of minor coefficient depend on obstacle geometry and
measurement as well as flow regimes.( influence of regimes is
when Re < 105 and more significant - when laminar flow exist)
•When the distance between neighboring elements of obstacles is
small the impact on flow resistance can be .That must be estimated
in the case by modification of minor coefficient ζ.
•The impact distance can be found by A.D.Altshul formula:
ζ
lkl = 0,5 d . (12)
λ
Where: lkl – impact distance
•When coefficient of minor loss ζ is calculate the velocity is
measured after obstacle in the cross-section. 2
•According the formula Q one can found:
∆ p = 0,81ρ Σ ζ
v .
4
d
Q12 2
Q2
∆ pv = 0,81 ρ 1ζ 1 4 = 0,81 ρ 2ζ 2 4
d1 d2
. When: ∆p v < 0,05 p1 ρ 1 = ρ 2 and Q1 = Q2
4
d1
ζ1 = ζ 2
d
2 (13)
•The triplex tap is assign to section with less flow rate when
calculating
•For gas network of town ∆ pv = (5 – 10)% of ∆ pL
•For short and complicate inner gas pipelines all ζ must be estimated.
SYMBOL MINOR LOSS COEFFICIENT ζ
0,35
udden contraction
1
riplex in the junction 1,5
3,0
riplex in the bend
2
riplex between the bend 3
0,3
uadrilateral junction
4
2
uadrilateral bend 11
7
6
ounded bend 900 5
0,5
0,25
ork tap ds = 15 0,15
≥ 20
alve d = 15
20
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