12 Internal Flows in Marine Organisms
12.1 Introduction
In contrast to the fluid mechanics of flows 'external' to the aquatic animal
body, our knowledge of the 'internal' flows is rather limited. Aquatic organisms
are filled with various pipes and channels through which fluids flow. Biological systems of internal flow are both diverse and complex, partly due to the
non-Newtonian character of fluids themselves, partly due to the complicated
network of the internal pipes and channels, and basically due to the unknown
roughness of pipe walls.
In this chapter we will briefly concentrate on selected fluid mechanics problems. We restrict ourselves to laminar flow only, as within marine organisms
very rarely do flows become turbulent where Reynolds numbers exceed the value
of about 2000. Most of the circulatory systems of aquatic animals involve pulsative flow of non-Newtonian fluids in pipes with shapes and cross-sectional
areas changing in time.
The metabolic rate of an animal is maintained through the steady consumption of fuel and oxygen. The amount of energy needed to propel an animal has
been described in the last chapter and here we concentrate on gas-exchange
organs, lungs and gills. These organs must have a size and diffusion capacity
adequately scaled to the oxygen needs. We will demonstrate how the fractal
approach may be useful to measure lung or gill area.
12.2 Flow in Pipes Revisited
From Eq. (2.99), it can be found that the velocity distribution in a circular
pipe for laminar flow is (see Fig. 12.1):
b..p [(D)2 2]
u(r) = 4f1,l "2 - r .
(12.1)
At the pipe wall (r = D /2), velocity is zero, while at the pipe axis (r = 0),
velocity reaches its maximum value of (b..p/4/-L1)(D /2)2. The cumulative disS. R. Massel, Fluid Mechanics for Marine Ecologists
© Springer-Verlag Berlin Heidelberg 1999
12.1 Introduction
In contrast to the fluid mechanics of flows 'external' to the aquatic animal
body, our knowledge of the 'internal' flows is rather limited. Aquatic organisms
are filled with various pipes and channels through which fluids flow. Biological systems of internal flow are both diverse and complex, partly due to the
non-Newtonian character of fluids themselves, partly due to the complicated
network of the internal pipes and channels, and basically due to the unknown
roughness of pipe walls.
In this chapter we will briefly concentrate on selected fluid mechanics problems. We restrict ourselves to laminar flow only, as within marine organisms
very rarely do flows become turbulent where Reynolds numbers exceed the value
of about 2000. Most of the circulatory systems of aquatic animals involve pulsative flow of non-Newtonian fluids in pipes with shapes and cross-sectional
areas changing in time.
The metabolic rate of an animal is maintained through the steady consumption of fuel and oxygen. The amount of energy needed to propel an animal has
been described in the last chapter and here we concentrate on gas-exchange
organs, lungs and gills. These organs must have a size and diffusion capacity
adequately scaled to the oxygen needs. We will demonstrate how the fractal
approach may be useful to measure lung or gill area.
12.2 Flow in Pipes Revisited
From Eq. (2.99), it can be found that the velocity distribution in a circular
pipe for laminar flow is (see Fig. 12.1):
b..p [(D)2 2]
u(r) = 4f1,l "2 - r .
(12.1)
At the pipe wall (r = D /2), velocity is zero, while at the pipe axis (r = 0),
velocity reaches its maximum value of (b..p/4/-L1)(D /2)2. The cumulative disS. R. Massel, Fluid Mechanics for Marine Ecologists
© Springer-Verlag Berlin Heidelberg 1999