6%20Life%20in%20a%20Fluid%20Medium

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6 Life in a Fluid Medium
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CONSIDER FLUID MOVING IN STREAMLINES Water
flow can be visualized as streamlines Particles
entrained in flow move with streamlines and do
not cross
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Streamline
Cylinder (in cross section)
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Some important properties of fluids Density ??
units of g cm-3 Dynamic viscosity ??molecular
stickiness, units of (force x
time)/area Kinematic Viscosity ???gooeyness or
how easily it flows, how likely is to break out
in a rash of vortices, units of
(length2/time) Kinematic viscosity dynamic
viscosity/density
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Properties of Some Common Fluids
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Reynolds Number, Re measure of relative
importance of viscous and inertial forces in fluid
Note that we are always working with seawater, so
we Consider no variation in ? or ???Therefore we
conclude That Re increases with velocity V and
size of object l
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ERROR IN TEXT!

• Pg. 138 SHOULD READ
• ..divided by kinematic viscosity..

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We can make a calculation of Re if an object is
moving in water or stationary, with the water
moving past the object.
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Reynolds numbers for a range of
swimming organisms and sperm
ANIMAL AND VELOCITY Re
Large whale swimming at 10 m/s 300,000,000
Tuna swimming at 10 m/s 30,000,000
Copepod swimming at 20 cm/s 30,000
Sea urchin sperm at 0.2 mm/s 0.03
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Reynolds number implications

• Re gt 1000 inertial forces predominate
• Re lt 1 viscous forces predominate

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Reynolds number implications 2

• Re gt 1000 inertial forces predominate
• Re lt 1 viscous forces predominate
• World of very small size and velocity is a
  viscous world takes continuous work to move an
  object at this Re range particles will stop
  moving when no work exerted (e.g., ciliate can
  stop instantaneously and reverse direction by
  simply stopping waving of external cilia)

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Reynolds number implications 3

• Re gt 1000 inertial forces predominate
• Re lt 1 viscous forces predominate
• World of very small size and velocity is a
  viscous world takes continuous work to move an
  object at this Re range particles will stop
  moving when no work exerted (e.g., ciliate can
  stop instantaeously and reverse direction by
  simply stopping waving of external cilia)
• World of large size and high velocity is an
  inertial world if work is done, object will tend
  to continue to move in fluid (e.g., supertanker
  at full speed will continue to move several km
  after propulsive power shut off)

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Laminar versus turbulent flow

• Laminar flow - streamlines are all parallel, flow
  is very regular
• Turbulent flow - streamlines irregular to chaotic
• In a pipe, laminar flow changes to turbulent flow
  when pipe diameter increases, velocity increases,
  or fluid density increases beyond a certain point

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Laminar versus turbulent flow
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Water Moving Over a Surface

• Well above the surface the water will flow at a
  mainstream velocity
• But, at the surface, the velocity will be zero.
  This is known as the no-slip condition
• From the surface to the mainstream, there is a
  transition zone, known as the boundary layer
• The boundary layer, defined as zone near surface
  where velocity is gt 1 less than the mainstream
  current, increases in thickness as the mainstream
  current velocity increases

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Water Moving Over a Surface 2

• Well above the surface the water will flow at a
  mainstream velocity
• But, at the surface, the velocity will be zero.
  This is known as the no-slip condition.
• From the surface to the mainstream, there is a
  transition zone, known as the boundary layer
• The boundary layer, defined as zone near surface
  where velocity is gt 1 less than the mainstream
  current, increases in thickness as the mainstream
  current velocity increases

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Boundary layer
Bottom surface
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Principle of Continuity

• Assume fluid is incompressible and moving through
  a pipe

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Principle of Continuity 2

• Assume fluid is incompressible and moving through
  a pipe
• What comes in must go out!

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Principle of Continuity 3

• Assume fluid is incompressible and moving through
  a pipe
• What comes in must go out!
• Velocity of fluid through pipe is inversely
  proportional to cross section of pipe.

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Principle of Continuity 4

• Assume fluid is incompressible and moving through
  a pipe
• What comes in must go out!
• Velocity of fluid through pipe is inversely
  proportional to cross section of pipe.
• Example If diameter of pipe is doubled, velocity
  of fluid will be reduced by half

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Principle of Continuity 5

• Assume fluid is incompressible and moving through
  a pipe
• What comes in must go out!
• Velocity of fluid through pipe is inversely
  proportional to cross section of pipe.
• Example If diameter of pipe is doubled, velocity
  of fluid will be reduced by half
• Principle applies to a single pipe, but it also
  applies to the case where a pipe splits into
  several equal subsections. Product of velocity
  and cross sectional area sum of products of all
  the velocity and sum of cross-sectional areas of
  smaller pipes.

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Principle of continuity
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Continuity, Applied to Sponge Pumping

• Sponges consist of networks of chambers, lined
  with cells called choanocytes
• Velocity of exit current can be 10 cm/s
• But, velocity generated by choanocytes is 50 ?m
  per sec. How do they generate such a high exit
  velocity?
• Answer is in cross-sectional area of choanocytes,
  whose total cross-sectional area are thousands of
  times greater than the cross section of the exit
  current areas.

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Flagellated chamber
Exit current
Choanocytes
The low velocity of the water from flagellated
choanocyte cells in flagellated chambers is
compensated by the far greater total cross-section
al area of the flagellated chambers, relative to
the exit current opening of the sponge
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Bernoullis Principle

• Pressure varies inversely with the velocity of
  the fluid

Upper air stream
Wing moving
Lower air stream
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Bernoullis Principle 2

• Pressure varies inversely with the velocity of
  the fluid
• Means that pressure gradients can be generated by
  different velocities in different areas on a
  surface

Upper air stream
Wing moving
Lower air stream
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Bernoullis Principle 3

• Pressure varies inversely with the velocity of
  the fluid
• Means that pressure gradients can be generated by
  different velocities in different areas on a
  surface
• Example Top surface of a wing has stronger
  curvature than bottom of wing, air travels faster
  on top, pressure is lower, which generates lift.

Upper air stream
Wing moving
Lower air stream
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Worm
Burrow
Bernoullis Principle Top Difference below and
above flatfish creates lift. Bottom Raised
burrow entrance on right places it in faster
flow, which creates pressure gradient and flow
through burrow.
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Drag

• Water moving past an object creates drag
• At high Reynolds number, the pressure difference
  up and downstream explains the pressure drag.
  Streamlining and placing the long axis of a
  structure parallel to the flow will both reduce
  pressure drag
• At low Reynolds number, the interaction of the
  surface with the flow creates skin friction.

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Drag and fish form. The left hand fish is
streamlined and creates relatively little
pressure drag while swimming. the right hand fish
is more disk shaped and vortices are created
behind the fish, which creates a pressure
difference and, therefore, increased pressure
drag. This disk shape, however, allows the fish
to rapidly turn.
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Sessile Forms - how to reduce drag?

• Problem You are attached to the bottom and
  sticking into the current
• Drag tends to push you down stream - you might
  snap!
• Examples Seaweeds, corals
• Solutions
• Flexibility - bend over in current
• Grow into current
• 3. Strengthen body (some seaweeds have
  crossweaving)

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The End