6 Life in a Fluid Medium

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# 6 Life in a Fluid Medium - PowerPoint PPT Presentation

6 Life in a Fluid Medium. CONSIDER FLUID MOVING IN STREAMLINES: Water flow can be visualized as streamlines Particles entrained in flow move with streamlines and do not cross. Streamline. Cylinder (in cross section). Some important properties of fluids Density :  units of g cm -3

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### 6Life in a Fluid Medium

CONSIDER FLUID MOVING IN STREAMLINES:

Water flow can be visualized as streamlines

Particles entrained in flow move with

streamlines and do not cross

Streamline

Cylinder (in cross section)

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

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

### ERROR IN TEXT!

“..divided by kinematic viscosity..”

We can make a calculation of Re if an object is

moving in water or stationary, with the water moving

past the object.

Reynolds number implications
• Re > 1000 : inertial forces predominate
• Re < 1 : viscous forces predominate
Reynolds number implications 2
• Re > 1000 : inertial forces predominate
• Re < 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)
Reynolds number implications 3
• Re > 1000 : inertial forces predominate
• Re < 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)
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
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 > 1% less than the mainstream current, increases in thickness as the mainstream current velocity increases
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 > 1% less than the mainstream current, increases in thickness as the mainstream current velocity increases

Boundary layer

Bottom surface

Principle of Continuity
• Assume fluid is incompressible and moving through a pipe
Principle of Continuity 2
• Assume fluid is incompressible and moving through a pipe
• What comes in must go out!
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.
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
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.
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.

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-sectional area of the flagellated chambers, relative to the

exit current opening of the sponge

Bernoulli’s Principle
• Pressure varies inversely with the velocity of the fluid

Upper air stream

Wing moving

Lower air stream

Bernoulli’s 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

Bernoulli’s 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

Worm

Burrow

Bernoulli’s 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.

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.

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.

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)