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

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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 near the substrate It is within this velocity gradient that viscosity exerts its friction We call the gradient region a boundary layer Boundary layer thickness U

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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

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Feeding at the boundary layer—black fly larvae Diptera Simuliidae

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Aquatic organisms experience a drag force from their hydrodynamic environment The fish swimming toward the left experiences a drag force acting in the opposite direction Drag force CDU2ACDU2A 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

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The Drag force results from a complex of hydrodynamic phenomena l U (a) Inertial drag is the momentum flux pushing against the anterior surface of the fish = U 2 A (b)Viscous drag results from Skin friction friction between the sheets of fluid in the boundary layer = UA/l (c) Pressure drag results from separation of the boundary flow from the body surface producing a wake with turbulent eddies, As a result pressure at the rear << pressure at the front

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The ratio of the inertial force (dynamic pressure) over the viscous force produces a dimensionless constant called the Reynolds number Remember that the formula for drag = C D U 2 A The drag coefficient (C D )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 CDCD R

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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/secR=3 x 10 8 A tuna swimming at the same speed R=3 x 10 7 A small trout going 1m/sec R=3 x 10 5 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/dayR=0.001

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

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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 0.01m 2 When striking prey such a fish can reach a speed of 2 m/sec The density of water is around 1000 kg/m 3 The R for such a fish is around 1 x 10 6, which means the wake will be turbulent, and the C D will be around 0.02 Assume that the burst takes 1 sec, and covers 2m Force required = drag, C D U 2 A

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How much 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, C D U 2 A Force = (0.02)(1000 kg/m 3 )(2m/s) 2 (0.01m 2 ) = 0.8 Newtons 1J/s=1W, which is a power unit

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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 obtain 3000 J is highly profitable On the other hand a small freshwater shrimp (0.01 g) would only contain 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.

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How profitable is this ? If however the pike caught the smaller prey while swimming casually at 0.5 m/sec, keeping its C D down to 0.007, the swimming expenditure 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.

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Another case where hydrodynamics plays an important role in aquatic ecology is in regard to the sedimentation of small particles Departure from spherical shape will also increase viscous drag because it will add to r on the RHS, without increasing volume

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Shapes of phytoplankton

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