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

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

Properties of Some Common Fluids

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

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

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

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

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

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

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

Herring larva - Clupea harengus

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: 865-876.

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: 865-876.

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: 865-876.

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

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

Laminar versus turbulent flow

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

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

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

Principle of continuity

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 ~ 200-400 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

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.

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.

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

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)

Reducing drag by pointing branches into current

Blue crab: Callinectes sapidus Side orientation reduces drag

Behavioral reduction of drag - withdrawal of tentacle crown in anemone

The End