Darcy Weisbach, ELM & Relative Viscosity Dr.ir. Sape A. Miedema Head of Studies MSc Offshore & Dredging Engineering & Marine Technology Associate Professor of Dredging Engineering Faculty of 3mE Faculty CiTG Offshore & Dredging Engineering
Dredging A Way Of Life
Offshore A Way Of Life
What is Offshore & Dredging Engineering? Offshore & Dredging Engineering covers everything at sea that does not have the purpose of transporting goods & people and no fishery.
Darcy Weisbach
Darcy Weisbach L 1 p 2 l l l v ls D p 2 i l p l l v iw g L 2 g D l 2 ls p 1.3 2 5 0.2 5 l 2 2 5.7 5 5.7 5 ln lo g 0.9 10 3.7 D 0.9 p R e 3.7 D p R e
Labda Moody diagram for the determination of the Darcy Weisbach friction coefficient. The legend shows the relative roughness. S.A.M Moody Diagram 0.08 Moody Diagram 0.08 0.07 0.07 0.06 0.06 0.05 0.05 Labda 0.04 0.03 0.04 0.03 0.02 0.02 0.01 0.01 0.00 0.00 10 2 10 3 10 4 10 5 10 6 10 7 10 8 Re Laminar Smooth 0.000003 0.00001 0.0001 0.0003 0.001 0.003 0.01 0.02 0.03 0.04 0.05
Darcy-Weisbach friction factor λ (-) S.A.M Moody Friction Factor vs. Line Speed Darcy-Weisbach friction factor λ vs. Line speed v ls 0.030 Dp=0.0254 m Dp=0.0508 m 0.025 Dp=0.1016 m Dp=0.1524 m Dp=0.2032 m 0.020 Dp=0.2540 m Dp=0.3000 m 0.015 Dp=0.4000 m Dp=0.5000 m Dp=0.6000 m 0.010 Dp=0.7000 m Dp=0.8000 m Dp=0.9000 m 0.005 Dp=1.0000 m S.A.M. 0.000 1 2 3 4 5 6 7 Line speed v ls (m/sec) Dp=1.1000 m Dp=1.2000 m
Darcy-Weisbach friction factor λ (-) S.A.M Moody Friction Factor vs. Pipe Diameter 0.030 Darcy-Weisbach friction factor λ vs. Pipe diameter D p vls=1.00 m/sec 0.025 vls=2.00 m/sec 0.020 vls=3.00 m/sec 0.015 vls=4.00 m/sec 0.010 vls=5.00 m/sec vls=6.00 m/sec 0.005 vls=7.00 m/sec S.A.M. 0.000 0 0.2 0.4 0.6 0.8 1 1.2 Pipe diameter D p (m)
Moody Friction Factor Approximation 1 v D l ls p 2 0.0 1 2 1 6 1 p 0.0 8 9 0.1 5 3 7 D r a n g e : 0.1 7 0-0.2 0 2 2 ls 0.0 8 8 0.2 0 1 3 v r a n g e : 0.1 5 2-0.2 1 6
Equivalent Liquid Model
Equivalent Liquid Model L 1 p 2 m l m v ls D p 2 i m p m m l v g L 2 g D 2 ls l l p 1.3 2 5 0.2 5 l 2 2 5.7 5 5.7 5 ln lo g 0.9 10 3.7 D 0.9 p R e 3.7 D p R e
Relative Excess Hydraulic Gradient (E rhg ) S.A.M i 1 R C m s d v s l v 2 ls 2 g D p i 1 R C l s d v s E r h g R i m s d i C l v s i l
Relative Viscosity
Relative Viscosity ν m /ν l (-) S.A.M Relative Viscosity Collected Relative Viscosity Data, From 16 Sources 100 Experiments 10 Fit Line 4 Terms Upper Limit Lower Limit S.A.M. 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Volume Fraction Solids C v (-)
Relative Viscosity ν m /ν fl (-) S.A.M Relative Viscosity, Selected Collected Relative Viscosity Data, Reduced 100 10 Experiments Fit Line 2 Terms Fit Line 3 Terms Fit Line 4 Terms S.A.M. 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Volume Fraction Solids C v (-)
Relative Viscosity, Approximation m r 1 2.5 C v s E in s te in l 1 2.5 C 1 0.0 5 C 0.0 0 2 7 3 e m 2 r v s v s l 1 6.6 C vs T h o m a s R e la tiv e D y n a m ic V is c o s ity R e la tiv e K in e m a tic V is c o s ity m m m r l l l r
Experiments
Relative excess hydraulic gradient E rhg (-) S.A.M Solids Effect in Pure Liquid Relative excess hydraulic gradient E rhg vs. Hydraulic gradient i l Fixed Bed Cvs=c. 1.000 0.100 Sliding Bed Cvs=c. Mean Heterogeneous Flow Cvs=c. Homogeneous Flow Cvs=Cvt=c. Resulting Erhg curve Cvs=c. Fixed Bed, Sliding Bed & Het. Flow Cvt=c. Fixed Bed, Sliding Bed & Sliding Flow Cvt=c. Limit Deposit Velocity 0.010 Ratio Potential/Kinetic Energy Cv=0.480 Cv=0.450 Cv=0.400 0.001 0.001 0.010 0.100 1.000 Hydraulic gradient i l (-) S.A.M. Dp=0.2000 m, d=0.20 mm, Rsd=0.46, Cv=0.450, μsf=0.415
Relative excess hydraulic gradient E rhg (-) S.A.M Solids Effect with Relative Viscosity Relative excess hydraulic gradient E rhg vs. Hydraulic gradient i l Fixed Bed Cvs=c. 1.000 0.100 Sliding Bed Cvs=c. Mean Heterogeneous Flow Cvs=c. Homogeneous Flow Cvs=Cvt=c. Resulting Erhg curve Cvs=c. Fixed Bed, Sliding Bed & Het. Flow Cvt=c. Fixed Bed, Sliding Bed & Sliding Flow Cvt=c. Limit Deposit Velocity 0.010 Ratio Potential/Kinetic Energy Cv=0.480 Cv=0.450 0.001 0.001 0.010 0.100 1.000 Hydraulic gradient i l (-) Cv=0.400 S.A.M. Dp=0.2000 m, d=0.20 mm, Rsd=0.46, Cv=0.450, μsf=0.415
Relative excess hydraulic gradient E rhg (-) S.A.M Solids Effect in Pure Liquid Relative excess hydraulic gradient E rhg vs. Hydraulic gradient i l Fixed Bed Cvs=c. 1.000 0.100 0.010 Sliding Bed Cvs=c. Mean Heterogeneous Flow Cvs=c. Homogeneous Flow Cvs=Cvt=c. Resulting Erhg curve Cvs=c. Fixed Bed, Sliding Bed & Het. Flow Cvt=c. Fixed Bed, Sliding Bed & Sliding Flow Cvt=c. Limit Deposit Velocity Ratio Potential/Kinetic Energy Cv=0.240 0.001 0.001 0.010 0.100 1.000 Hydraulic gradient i l (-) S.A.M. Dp=0.1585 m, d=0.04 mm, Rsd=4.00, Cv=0.240, μsf=0.415
Relative excess hydraulic gradient E rhg (-) S.A.M Solids Effect with Relative Viscosity Relative excess hydraulic gradient E rhg vs. Hydraulic gradient i l Fixed Bed Cvs=c. 1.000 0.100 0.010 Sliding Bed Cvs=c. Mean Heterogeneous Flow Cvs=c. Homogeneous Flow Cvs=Cvt=c. Resulting Erhg curve Cvs=c. Fixed Bed, Sliding Bed & Het. Flow Cvt=c. Fixed Bed, Sliding Bed & Sliding Flow Cvt=c. Limit Deposit Velocity 0.001 0.001 0.010 0.100 1.000 Hydraulic gradient i l (-) Ratio Potential/Kinetic Energy Cv=0.240 S.A.M. Dp=0.1585 m, d=0.04 mm, Rsd=4.00, Cv=0.240, μsf=0.415
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