1 - Acta Technica Corviniensis

where: “ν ” represents the constitutive coefficient ofthe kinematics’ viscosity.The flow regime can be: laminar: Re < Recrt = 2320 ; turbulent: Re > Recrt = 2320 .The problem of determining the λ coefficient is thefundamental problem of pipe calculation. Nikuradse isthe first who undertook a systematic study of thiscoefficient, establishing its relationship with the flowregime and the relative roughness, and drawing thediagram that bears his name [2].An American engineer Lewis F Moody (1880‐1953)prepared the diagram shown in figure 1 for use withordinary commercial pipes. Today, the Moodydiagram is still widely used and is the best meansavailable for estimating the friction factor.The fact that λ depends both on the Reynoldsnumber and the wall roughness, makes it difficult touse unique formulas to calculate it, assuming that l,ν , d, v and k (equivalent roughness) are known [2].ACTA TECHNICA CORVINIENSIS – Bulletin of Engineering5Blasius ‐ for Re < 101λ =(6)4100Re5Prandtl ‐ for 10 < Re < 3⋅101= 2lg Re λ i −0,λ66( ) 8(7) Konakov ‐ for 3 ⋅ 10 < Re < 101= 1,8lg Re−1,5(8)λb.2. The pipe is under transition from hydraulicallysmooth to hydraulically rough 9.4 < CRIT < 200, thelinear loss coefficient depends on the flow regime, butalso on the equivalent roughness of the pipekλ = λ(Re, ) , being applicable the relation ofdColebrook‐White:1 ⎛⎞⎜ 2.51 k= −2lg+ ⎟ (9)λ ⎜⎟⎝ Re λ i3.71d⎠b.3. Hydraulically rough pipe – CRIT > 200, the linearloss coefficient depends only on the equivalent⎛ k ⎞roughness of the pipe λ = λ⎜⎟ , being applicable the⎝ d ⎠relation of Karman‐Nikuradse:1 ⎛ k ⎞= 2lg⎜⎟+ 1.14(10)λ ⎝ d ⎠798Figure 2. Moody diagrama) If Re < Recrt = 2320 (the flow regim laminar), forcalculation of the Hagen‐Poiseuille ’ s relationshipusing:64λ =(4)Reb) If Re > Recrt = 2320 (the flow regim turbulent),using Moody ’ s criterion:kCRIT = Re λi(5)dTo assess this criterion, we approximate λ, admittingthat its value is within the range:λ i = (0.02‐0.04).Depending on the value of this criterion, whichdescribes the nature of the pipe, we shall apply one ofthe relations:b.1. Hydraulically smooth pipe – CRIT < 9.4, the linearloss coefficient depends only on the flow regimeλ=λ(Re). Therefore, we shall apply one of the relations:Figure 3. Algorithm to determinatethe linear loss cofficient λHaving the λ coefficient calculated with one of theabove relations (case of the turbulent regime), we willcheck the value of Moody's criterion, which mustcorrespond to the initially admitted domain.Otherwise, “λ” shall be recalculated applying theformula of the new value of the criterion, i.e. of thenew hydraulic character of the pipe.SIMULATION OF LINEAR LOAD LOSSES, USING THE WORKINGMEDIUM “ADINA”The ADINA CFD program provides state‐of‐the‐artfinite element and control volume capabilities forincompressible and compressible flows. The flows maycontain free surfaces and moving interfaces betweenfluids, and between fluids and structures.The procedure used in ADINA CFD is based on finiteelement and finite volume discretization schemes,2012. Fascicule 3 [July–September]