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:
.
Re
64
=λ
(1)
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:
3
00250 .Re,
=λ
(2)
•For the turbulent flow in hydraulically smooth pipe III zone(Re >
4000 ,and Re < 105,and Re ∆e/d<10) the Blazius formula is fit:
,
Re
,
,250
31640
=λ
(3)
•In the same III zone when pressure is medium or high and plastic
pipes is used,the friction loss coefficient λ can be found:
70000 < Re < 700000
,
Re
,
,1940
1710
=λ
(4)
•For flows with moderate values of Re in the turbulent IV zone(Re
>4000, and 10 < Re ∆e/d <500 ) coefficient λ depend on both - the Re
number and relative roughness (λ = f ( Re, ∆e/d )).For this case the
formula of Altshull- Kunigelis can be used:
.
Redd
,
,
ee
250
68
110
+
∆
∆
+=λ
(5)
•For the flows in the rough turbulent V zone(Re >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:
.
d
,
,
e
250
110
∆
=λ
(6)
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
iron
0.045
Drawn tubing 0.0015
Plastic, glass 0.0 (hydraulically smooth)