Hydrodynamics

•How organisms cope with the forces imposed on them by a dense and viscous medium

The Boundary layer

At the interface between moving water and a stationary substrate,the water velocity is 0, i.e. “no slip” condition

This means that there is a sharp shear or gradient in velocity nearthe substrate

It is within this velocity gradient that viscosity exerts its friction

We call the gradient region a boundary layer

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Boundary layerthickness U

This mayfly minimizes the force that the flowing water exerts on its body by: •Its flattened shape allowing it to occupy the boundary layer•Its behaviour which allows it to graze attached algae without breaking contact with the rock surface

Feeding atthe boundary layer—black fly larvae

DipteraSimuliidae

Aquatic organisms experience a drag force from their hydrodynamicenvironment

The fish swimming toward the left experiences a drag forceacting in the opposite direction

Drag force CDU2A

Actively moving animals like fishes don’t avoid drag like mayflies do, but actually swim against this force at considerable energetic cost. Their streamline shape however helps minimize this cost

The Drag force results from a complex of hydrodynamic phenomena

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(a) Inertial drag is the momentum flux pushing againstthe anterior surface of the fish = U2A

(b)Viscous drag results from Skin frictionfriction betweenthe sheets of fluid in the boundary layer=UA/l

(c) Pressure drag results from separation of theboundary flow from the body surfaceproducing a wake with turbulent eddies,As a result pressure at the rear << pressure at the front

The ratio of the inertial force over the viscous force produces a dimensionless constant called the Reynolds number

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Remember that the formula for drag = CDU2A

The drag coefficient (CD)is not a constant, but rather changes greatly with R. Normally it decreases sharply with R, as viscous forces (mainly skin friction) become much less important than inertial forces

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The Reynolds number (R) is a very useful indicator of the hydrodynamic regime

It can range over many orders of magnitude: For example,

A large whale swimming at 10 m/sec R=3 x 108

A tuna swimming at the same speed R=3 x 107

A small trout going 1m/sec R=3 x 105

A large copepod moving 10 cm/sec R=200

A Daphnia moving 1 cm/sec R=50

A rotifer moving 0.1cm/sec R=2

An 10 um diatom sinking at 1m/day R=0.001

Why aren’t small zooplankton streamlined in shape like fish?

How much big a burst of energy will a pike expend to capture prey?

Assume the pike is 50 cm long, and has a surface Area of 0.01m2 When striking prey such a fish can reach a speed of 2 m/secThe density of water is around 1000 kg/m3

The R for such a fish is around 1 x 10 6, which means the wakewill be turbulent, and the CD will be around 0.02Assume that the burst takes 1 sec, and covers 2m

Force required = drag, CDU2A

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How big a burst of energy will a pike expend to capture prey?

Energy/Work = Force x distance,

Energy expenditure/s = 0.8 N x 2 m/s = 1.6 Joules / s

In Power units, this burst requires 1.6 W to overcome the drag force

Force required = drag, CDU2AForce = (0.02)(1000 kg/m3)(2m/s)2(0.01m2) = 0.8 Newtons

1J/s=1W, which is a power unit

How profitable is this ?

•A 1 g perch contains around 6 kJ of energy and the fish can assimilate at least half of this. So clearly to invest 1.6 J to obtain3000 J is highly profitable

•On the other hand a small freshwater shrimp (0.01 g) would onlycontain 10 J, of which the fish would likely assimilate less than half.

•Large fish generally won’t expend large bursts of energy to get small prey because the profit margin isn’t as large and they can catch them without spending a lot of energy.

How profitable is this ?

•If however the pike caught the smaller prey while swimming casually at 0.5 m/sec, keeping its CD down to 0.007, the swimmingexpenditure would only be (0.007)(1000)(0.5)(0.5)(0.01)(0.5)/s=0.01 J/sec

•This energy output can be easily supplied aerobically by basal metabolism.

Another case where hydrodynamics plays an important rolein aquatic ecology is in regard to the sedimentation of small particles

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Departure from spherical shape will also increase viscous drag because it will add to r on the RHS, without increasing volume

Shapes of phytoplankton