1. 5 Life in a Fluid Medium Notes for Marine Biology:
Function, Biodiversity, Ecology
By Jeffrey S. Levinton

2. 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

3. Properties of Some Common Fluids

4. Reynolds Number, Re: measure of relative importance
of viscous and inertial forces in fluid, dimensionless
If Seawater is used, then Re increases with
increasing velocity and size

5. Estimating the value of l (size) and V (velocity)

6. 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

7. Reynolds Number, Re: measure of relative importance
of viscous and inertial forces in fluid, dimensionless
If Seawater is used, then Re increases with
increasing velocity and size

8. Reynolds number implications
Re > 1000 : inertial forces predominate
Re < 1 : viscous forces predominate
Conclude that objects exist under very different conditions in the same seawater, depending on their size and velocity

9. Reynolds number implications
Re > 1000 : inertial forces predominate
Re < 1 : viscous forces predominate
If you are very small, you are living in a viscous medium, and the moment you stop working to move you will stop
If you are large and can generate a fairly high velocity you can propel yourself and you will have inertia and you will “coast”
Some organisms can live under both conditions. For example a copepod feeding moves very slowly and lives at very low Re, but a copepod swimming to escape from a predator generates thrust with its swimming appendages and operates under higher Re, and has inertia

10. Reynolds Number, Re: measure of relative importance
of viscous and inertial forces in fluid, dimensionless
WHAT IF VISCOSITY MATTERS??
KINEMATIC VISCOSITY DECREASES
WITH INCREASING TEMPERATURE

11. Herring larva - Clupea harengus

12. Temperature range of 5-15°C - kinematic viscosity decreases 45%!
Low temperature: viscosity dominates
High temperature: inertia dominates
Cool experiment: place material in water that increases kinematic viscosity: small larvae reduce amplitude of tail beating!
Effect only important in cool waters, not in warmer waters where change of temperature has much less effect on k. viscosity
WEIRD OUTCOME: IT COSTS LESS TO SWIM AT THE HIGHER TEMPERATURE!!!
von Herbing 2002 Journal of Fish Biology 61:

13. Change in kinematic viscosity: note that viscosity decreases substantially with increasing temperature, which allows easier swimming
After von Herbing 2002 Journal of Fish Biology 61:

14. Metabolic cost of swimming for cod larvae Gadus morhua decreases from 5 to 10 degrees C
after von Herbing 2002 Journal of Fish Biology 61:

15. Particles entrained in flow move with streamlines and do not cross
Properties of Flow, Pressure
Streamline
Cylinder (in cross section)
Particles entrained in flow move with
streamlines and do not cross

16. 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, i.e., when Re increases

17. Laminar versus turbulent flow

18. 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

19. In boundary layer, water velocity is <99% of mainstream velocity.

20. Principle of Continuity
Assume fluid is incompressible and moving through a pipe

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

22. 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

23. 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

24. 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

25. Principle of continuity

26. Continuity, Applied to Sponge Pumping
Sponges consist of networks of chambers, lined with cells called choanocytes
Velocity of exit current can be 1-2 cm/s (10,000-20,000 µm per sec)
But, velocity generated by choanocytes is 50 µm per sec. How do they generate such a high exit velocity?
Ratio of velocity at exit to choanocytes ~
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.

27. 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

28. Bernoulli’s Principle
Pressure varies inversely with the velocity of the fluid
Upper air stream
Wing moving
Lower air stream

29. 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

30. 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

31. 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.

32. Pressure Drag
Water moving past an object creates drag: pressure difference up and downstream of object
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.

33. Drag and fish form. The fish on left is streamlined and creates relatively little pressure drag while swimming. The fish on right 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

34. 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 cross weaving)

35. Reducing drag by pointing branches into current

36. Blue crab: Callinectes sapidus Side orientation reduces drag

37. Behavioral reduction of drag - withdrawal of tentacle crown in anemone

38. The End