Reynolds Number

Angular momentum

L conserved angular velocity declines as r increases - the nearer a fluid parcel gets to the axis of rotation, the faster it will circulate

Viscous forces

Promotes laminar flow

Inertial forces

Promotes turbulent flow The greater the inertia of a fluid, the more likely it is to separate from a surface and generate turbulence

Re guidelines in pipes

Re < 2000 = laminar flow Re > 4000 = turbulent flow Re > 100 000 = flow around cylinder or sphere transitions to turbulent Low Re = viscosity dominated flow regime High Re = inertia dominated flow regime

Biological range of Re

Re > 100 = flow becomes increasingly turbulent - inertial forces dominant Re < 100 = flow is slow, ordered and laminar - viscous forces dominate

Factor that drives flowing fluids towards becoming laminar

Viscous forces Viscosity - tendency of a fluid to stick to itself and move together

Outside of a vortex

all flow-lines are sheared by slower moving fluid on their outside edge, and the faster moving fluid on their inside edge shear increases as angular momentum increases exponentially towards center

Turbulent flow

disordered flow irreproducible and irreversible efficient mixing vorticity

Angular velocity

how fast object is rotating about it's axis radians/second ex. 2pi radians/second = one full rotation per second

Factors that drive flowing fluids towards becoming turbulent

inertial forces - increasing fluid density - increasing velocity - increasing characteristic length (more SA there is to flow across, more time there is for turbulence to develop)

Vortex - spinning fluids

object on outside of vortex translates in circle around central axis object on inside of vortex rotates in circle around central axis

Moment of inertia

objects with mass that rotates - objects resistance to starting or stopping spinning mass x radius^2 x angular velocity

Laminar flow

ordered flow reversible and reproducible no mixing

Tangential velocity

radius x angular velocity declines as r increases

Reynolds number

ratio of inertial force to viscous force dimensionless number used to predict whether flow is laminar or turbulent

Vortex

region within fluid where the flow moves around a central axis

Generating vortices

shearing of concentric rings of fluid at low Re = viscous forces dominate, so vortices can have large rotational cores to shear streams of viscous fluid past one another requires energy in absence of energy being added, viscous shearing will cause vortex to grind to a stop and dissipate

Solid Body Rotation

solid rotates around central axis entire solid object moves as one entity - no shearing, no slipping

Kinematic viscosity

viscosity/density ratio of fundamental properties of a fluid unit= L^2/T = Stokes

Center of a vortex

viscous forces at centre eliminate the shearing and pull core into rigid body rotation