COMPRESSIBLE FLOW FRICTION

1. COMPRESSIBLE FLOW FRICTION Friction in gas pipelines

2. Coefficient  • In pipelines of gasses flow functional reliance l = f(De,Re) is valid.It means ,that friction depend from the equivalent roughness and flow regime. • For steel material of gas pipes equivalent roughness De = 0,1 mm . • For copper or plastic gas pipes De = 0,0015–0,003 mm only.(see Table) • According the Moody chart,5 zones of friction factor  is valid: • 1) Laminar flow.For laminar flow friction factor is independent of relative roughness,and can be estimated by formula: (1) Where : Re < 2000 –Reinold’s number;

3. 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  can be find according empirical formula Zaichenko: (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: (3) • In the same III zone when pressure is medium or high and plastic pipes is used,the friction loss coefficient  can be found: 70000 < Re < 700000 (4)

4. For flows with moderate values of Re in the turbulent IV zone(Re >4000, and 10 < Re e/d <500 ) coefficient  depend on both - the Re number and relative roughness ( = f ( Re, e/d )).For this case the formula of Altshull- Kunigelis can be used: (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.( = f (e/d))From the (5) formula we can find in that case: (6)

5. Equivalent Roughness efor New Pipes

6. Flow regime zones Minor pressure network Medium pressure network High pressure network I zone II zone III zone IV zone V zone 8 13 59 20 – – – 1 86 13 – – – 24 76 • 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 %

8. Turbulent flow regime in I.F.Moody diagram is characterized by a family of curves.The lowest curve of the family expresses  - 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 . • 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  = f(Re,e/d relationship are parallel to Re axis.It means that Re has no influence on , 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 , is read from a rough pipe zone of the chart.Then the actual meanings of Re is computed and friction factor is corrected.

9. 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: • n = 0,73 kg/m3; n = 14,310–6 m2/s; pn = 101,3 kPa • Re = (7) • Where : • Qn – gas flow rate in normal conditions,in m3/h. • When estimate that

10. and in the gas pipe line networks of minor pressure we can find: (8) , 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:

11. (9) • After estimation that for natural gasses rn = 0,73 kg/m3, n = 14,3·10–6 m2/s one can found: (10) = 8,5010–4 (11) S  8,5010–4 d–4,806 Where: Qn – gas flow rate,in m3/h; p2 - pressure loss,in Pa2

12. 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 . • The impact distance can be found by A.D.Altshul formula: lkl = 0,5 d . (12) Where: lkl – impact distance

13. When coefficient of minor loss  is calculate the velocity is measured after obstacle in the cross-section. • According the formula one can found: When:< 0,05 p1 r1 = r2andQ1= Q2 . (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  must be estimated.

14. SYMBOL MINOR LOSS COEFFICIENT  Sudden contraction Triplex in the junction Triplex in the bend Triplex between the bend Quadrilateral junction Quadrilateral bend Rounded bend 900 Cork tapds = 15  20 Valved = 15 20 25, 32, 40 ≥ 50 Valved = 50–100 mm d = 175–200 mm d  300 mm 0,35 1 1,5 3,0 2 3 0,3 4 2 11 7 6 5 0,5 0,25 0,15