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 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 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

Pg. 138 SHOULD READ “..divided by kinematic viscosity..” ERROR IN TEXT! Pg. 138 SHOULD READ “..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 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 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

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 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.

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 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)

The End