Transcript Reynolds Number (Re) - Penn State York Home Page

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.
Fi
SU
U l


Fv

 SU 


 l 
2
• U = velocity of object relative to the fluid; l = object length;
S = surface area; µ = dynamic viscosity; p = object density
• 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
Viscosity
Nekton
Inertia
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.

C1  C2 
J D
x1  x2 
Laminar versus Turbulent Flow
• Laminar flow is unidirectional, turbulent flow is more chaotic.
Laminar Flow
Turbulent Flow
• 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 flow
boundary layer.
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.
object
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).
Fish Body Form Relates to
Swimming Ability, Habitat, and Niche
Colonial Diatom
Water Movement:
Convection vs Wind Waves
Convection currents (grey
colder) create shear instability
that leads to turbulent mixing.
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.
Temperate Lake Mixing:
Summer → Autumn → Winter
• What climatic conditions change and how?
• What mixing processes are involved?
Z (m)
Z (m)
summer
Z (m)
autumn
winter