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Reynolds Number (Re)

Reynolds Number (Re). Viscosity: resistance of a liquid to change of form . Inertia: resistance of an object (body) to a change in its state of motion . These two forces together influences an organism’s ability to move in water and how water flows.

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Reynolds Number (Re)

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  1. Reynolds Number (Re) • Viscosity:resistance of a liquid to change of form. • Inertia: resistance of an object (body) to a change in its state of motion. • These two forces together influences an organism’s ability to move in water and how water flows. • The ratio of inertial force to viscous force is Re of an object. • U = velocity of object relative to the fluid;l = object length; S = surface area; µ = dynamic viscosity; p = object density

  2. High Re values are associated with dense, fast and long (streamline) objects. • Low Re values are associate with small and slow objects, particularly those with a high surface to volume (S:V) ratio. • The Y-axis below could be switched from velocity to body size (length) a similar trend would be seen. Plankton Nekton Viscosity Inertia

  3. Molecular Diffusion: • Water molecules move constantly in a vibrating fashion, called Brownian Motion. • Browning Motion is increased by increased temperature. • Solutes in water also experience Brownian Motion. • Molecular diffusion it that solely due to solute and solvent Brownian Motion (expressed as the diffusion coefficient at a given temperature; D) and the solute concentration gradient between two locations. • The rate of molecular diffusion (J) is expressed by Fick’s Law. • Small organisms at low Re are dependent on molecular diffusion.

  4. Laminar versus Turbulent Flow • Laminar flow is unidirectional, turbulent flow is more chaotic. • At larger spatial scales (high Re) flow is often turbulent. Eddies may form. Solute diffusion becomes dominated by eddy transport for water parcels, not solely molecular diffusion. • At smaller spatial scales (low Re) flow is more often laminar, due to the viscous force dampening turbulence. • Flow across a surface experience a viscous (frictional) force, slowing velocity, and becoming more laminar. • The transition between turbulent and laminar flow is called the flowboundary layer. Laminar Flow Turbulent Flow

  5. object Flow Boundary Layer Thickness: • It ↓ with ↑ velocity. • It ↓ with ↓ surface roughness. • It ↓ with ↓ object size. • It ↓ with ↓ distance from the upstream edge of an object.

  6. Relationships between Re and flow type. • For any given object; lower Re will translate to more laminar flow. • Re is lower when velocity decreases. • Flow is more laminar at higher Re when the object is streamline (long).

  7. Fish Body Form Relates to Swimming Ability, Habitat, and Niche

  8. Colonial Diatom

  9. Water Movement:Convection vs Wind Waves Wind’s shear across surface water creates waves, whose force propagates with depth, moving water in smaller orbital paths creating turbulence. Stronger, longer blowing winds will create larger waves and deeper mixing. Convection currents (grey colder) create shear instability that leads to turbulent mixing.

  10. Z (m) Z (m) Z (m) Temperate Lake Mixing:Summer → Autumn → Winter • What climatic conditions change and how? • What mixing processes are involved? autumn winter summer

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