CHE443 8_25_20.pdf - scaling inertial stress stress viscous...

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scaling : inertial stress : p UZ viscous stress : r UIL gravitational stress - stress : ML - ' T - Z ' gapb UID ML - ' T - Z = CLT - Z ]a[m[ if CLT - if - CL Id b - - l a - - I d- - I = > c - - O
gravitational stress : pg L surface stress : NL comparing inertial and viscous visions larger F- flow YETI ' :# turbulent - flow
Use a ratio of stresses to determine which one dominates : inertial stress - - Viscous stress = PUZ dimensionless group . II. out . .ee#:Ye : R kinematic viscosity
If Re a c l - - viscous flow " or " laminar flow " I f Re > > I - ' inertial flow " or ' turbulent flow r . Others ' . ÷%t : fr - - ¥ Froude ) inertial JE : we = e ( Weber )
jiffies : ca - - capillary ) §IEa : Bo - - ISI ( Bond ) viscous gravity : EI - - E - - II
so what ? - What flow regime are we in - How to solve a flow problem e. g . Can we neglect gravity ? Reynolds number if Re < a 1 , we can neglect inertial effects
System Ree bacterium 1 × 10-5 ufluid.ec channel 1 blood artery 8 × 10 ' oil pipeline 3--105 qi . towards re - - II gyu }tow .es s tubulence
if Re I 2000 viscous or laminar regime Not all dimensionless groups are based on ratios of stresses Ma - sp¥f ( Mach ) sound kn = ( Knudsen )
rtial Pressure FEE EE , viscous shear

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