What is Bernoulli’s Principle? Give examples of its diverse ‘use’ or ‘exploitation’ in animals
All living organisms inhabit a world governed by mechanical laws and processes. For all organisms, too, the primary daily task is the search for food. This is not only limited in quantity but can also be energetically costly to obtain. As a result many animals have evolved ways of harnessing these mechanical processes to assist them in performing tasks which would otherwise require the expenditure of chemical energy. In the world of energy economy these adaptations can prove crucial to survival.
The major form of mechanical energy that exists is expressed in the form of flows (air and water currents driven by the sun). When these fluids flow across a solid surface (such as the ground or an animal’s body) the velocity difference can be converted into useful forms of energy. This energy can either be used to move a fluid (called induced flow) or a solid through the application of the principle of conservation of energy in a steadily moving fluid called Bernoulli’s Principle after the Swiss mathematician Daniel Bernoulli who formulated it in 1738.
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Bernoulli’s Principle considers the relationship between the pressure, velocity and elevation in a moving fluid, the compressibility and viscosity of which are negligible and the flow of which is steady or laminar. It states, in effect “that the total mechanical energy of the flowing fluid, comprising the energy associated with fluid pressure, gravitational potential energy of elevation, and the kinetic energy of fluid motion, remains constant” (Encyclopaedia Britannica). This implies that “if a fluid moves horizontally so that there is no change in gravitational potential energy, the pressure of the fluid must decrease whenever its velocity increases so that its total energy remains constant” (Vogel, 1978). Two major processes arise from this principle: the induced movement of either a solid or a fluid (liquid or gas). Living organisms employ either one, or the other, or both.
The first is adequately illustrated by the phenomenon known as lift. A simple demonstration of lift is to hold the edge of a piece of paper to your lips and blow across its upper surface – the paper should rise as a result of the reduced air pressure above it caused by the faster moving air.
The second is the induced flow of fluids. Another mechanical process known as viscous entrainment is also effective here and can contribute to the effect produced by Bernoulli’s Principle. Viscous entrainment is the force that causes fluid to be drawn out of a pipe whose opening is orientated perpendicularly to the flow of the current. For an example of how induced flow can operate consider a fluid moving through a horizontal pipe that narrows and widens at various points. The fluid will speed up in the narrow sections (by the continuity principle), and so it will exert the least pressure in those areas were the diameter is smallest. This is known as a Venturi Tube.
If a small pressure-measuring device is connected between the two areas this can be proved: the fluid in the small tube of the device will flow from the area of high pressure (at the wide aperture) to the region of low pressure (at the low aperture). Another application is demonstrated by the flow of smoke up a chimney. When the wind speed increases the flow of smoke increases, regardless of the direction of the wind, because the pressure at the top of the chimney is low. Viscous entrainment contributes to this effect.
Further applications can be demonstrated by examining the pressure on bodies at certain points along their shape when they are exposed to a flowing fluid. Consider a solid body of radially symmetrical streamlined form with fluid flowing lengthwise along it. At the front of the body local flow is zero and the pressure is high, because the current has been brought to a halt. At the sides, where the width is greatest, the velocity of the fluid is high: the body is an obstruction that reduces the space available and the fluid has speeded up to get around. Therefore the pressure is low. This model shows how pressure differences can be created in swimming fish, for example, to create an environment in which the induced flow of a fluid can be produced.
The model mentioned above is the similar to the situation in which lift is produced. Consider a solid formed by cutting the previous solid in half laterally and exposed to a fluid again flowing lengthwise along it. Here again the pressure will be lowest on the side where the width is greatest, however on the opposite side the velocity and hence pressure will remain unchanged (because we have cut the solid in half) therefore the solid will move towards the area of low pressure. If performed vertically this is called lift.
In summary therefore we can say that Bernoulli’s principle basically describes the affect of pressure differences created when currents of different velocities move across a solid surface. This surface can either be fixed or mobile. If it is fixed then there are two recognised geometric forms in nature that have evolved to utilise the pressure gradients produced – Type I and Type II. These geometric forms are designed to capture a current and use it regardless of which direction it is coming from (i.e. turning a multidirectional current into a unidirectional one). Mobile organisms are more specialised because they are able to move to orientate themselves in the flow. They can also increase the effect of the flow by moving themselves: increasing the relative velocities acting on their surfaces and increasing the pressure differences produced.
Induced Movement of Solids.
The most important application of Bernoulli’s principle on solids is the process called lift described above. Lift can act both on immobile and mobile organisms.
The Action of Lift on Immobile Organisms:
Many seeds utilise lift to slow their descent to the ground, increasing the dispersion range. Maple seeds, for example, reduce their sinking speed through the action of a lift-generating airfoil like a helicopter caused by the difference between the upstream and downstream edges of the seed. The mechanism is effective regardless of the direction of the wind: this is necessary because the seed is unable to align itself with the wind. Other seeds such as ash samara use a different mechanism. In these cases the seed is symmetrical so there is no difference between the edges of the seed: instead the spinning motion of the seed itself produces lift. The seed spins not only horizontally but vertically as well. When the wind is blowing this results in a velocity difference above and below the seed. Above the seed the velocities of the wind and spinning motion unite whilst below the seed the velocities oppose each other. Lift is produced because of the pressure difference created. This mechanism is similar to that of Flettner rotors and again it is effective regardless of the side from which the wind is blowing.
The Action of Lift on Mobile Organisms:
Mobile organisms are able to move to face the direction of the wind and therefore they have evolved highly specialised structures to produce lift. Coupled with their own ability to produce momentum this enables various organisms to fly. Birds are, of course, the best example of this. Birds’ wings produce the same circulatory flow pattern (and hence lift) as the ash samaras but without themselves rotating. Either as a result of their own asymmetry or by facing the flow at a slight inclination (or both), they cause the flow to be more rapid on the above side than on the other, producing lift. The lift caused is proportional to the area of the wing, so birds use the broadest expanse possible when taking off, landing, or moving slowly. Certain birds also practise what is known as dynamic soaring, in which they are able to stay aloft without beating their wings or being in an upward current of air. By alternately diving and climbing they expose themselves to different wind speeds and from the difference can extract the energy to remain aloft (this is why many birds have an undulating flight).
Induced Flow of Fluids.
Use of Induced Flow by Immobile Structures: Capturing Currents:
Some organisms are either immobile or produce structures which are immobile. In order to induce a flow of a fluid in these organic or inorganic structures they have developed features that are effective regardless of the direction of the fluid flow. These can be recognised as belonging to two distinct groups of geometric systems, called Types I and II. They function primarily by capturing the current and manipulating its energy to fulfil a purpose. It will be noted that this fluid is predominantly water because the low density of air and its low pressure (compared to water) means that the affect of Bernoulli’s Principle is much greater in the aquatic environment.
Type I systems consist of a U-shaped pipe through the earth with openings at either end. For a fluid to move through the system the openings must differ in shape, size or elevation above the ground (to expose the opening to different wind or water currents). “Internal flow will travel from the smaller, blunter, lower or more sheltered opening (where the fluid pressure is much higher) to the larger, sharper, higher or less sheltered opening (where the velocity of the current is greater, fluid pressure is lower and viscous entrainment is promoted by the larger size of the opening or the greater current)” (Vogel, 1978).
The burrows of prairie dogs are excellent examples of a Type I system. The burrows appear complicated, however further examination reveals that they are usually simple two-ended tunnels with a few side-chambers. Burrows can be up to 50 feet long and 10 feet deep. Obviously in such large structures some form of ventilation is required – free diffusion of oxygen through the soil or tunnel is insufficient to meet the needs of even a single animal sitting at the bottom of the burrow – and the prairie dogs do this by means of induced flow. The tunnels exit in the centre of a mound of dirt, once regarded as a lookout post. Close examination of these exits reveals that one is a low-rounded dome while the other is a higher, sharper-edged crater mound.
The dogs work hard to maintain this difference: the shapes are not accidental. Calculations have shown that even at low wind speeds of one mile an hour the air in the burrow is replaced about once every ten minutes. Both the difference in height and the difference in shape contribute to the effect. Worms living on mudflats (such as lugworms) also construct burrows with two openings, one raised above the other, inducing the flow of fluids (water and air) through the burrow.
Turret spiders construct only a single-opening vertical burrow, but this is also ventilated by a mechanism similar to that mentioned above. The second ‘opening’ is provided for by the diffusion of air through the soil (the spiders only live in environments where the soil is porous). Over the entrance to the burrow is the “turret”, a craterlike ring of sand maybe half an inch high bound together with silk. Air enters the burrow through the soil and leaves by the turret where even a gentle breeze is enough to induce a flow of air upward in the burrow. This has other practical effects. The spider lives in the bottom of the burrow during the day, a foot below the surface, and risks desiccation because it has no access to water. However the soil is saturated only a few inches below the surface and the flow of air through the soil and burrow draws up moist air from below. It also prevents the hot surface air from penetrating the burrow.
Induced flow of this type is also found in the leaves of plants. The stomatal pores, found on the underside of the leaf, are the sites of gaseous exchange in plants. In some hydrophytes (plants that have lots of water) the stomata are surrounded by small craterlike lips and are connected within the leaf by small air passages. When the wind blows on the leaf the wind speed will be greater at the upwind side of the leaf than at the downwind side. Air will therefore enter the leaf at the stomata farther from the edge and exit at the upwind side. The flow produced is noticeable although the plants run the risk of dehydration (which is probably why this is practised only in hydrophytes). Obviously the effects of this are significant because carbon dioxide (the gas plants require) is very scarce in the atmosphere.
The second geometric system, Type II, involves a conical or cylindrical structure perforated with lots of small holes around the base and sides that open on to a large central cavity that exits through a large hole at the top. Fluids enter through the small holes and leave by the large one. Outside the small holes local flow is zero (the structure is blocking the flow of liquid) and the pressure is very high so fluid enters by the small holes and leaves at the top where the fast moving fluid creates a low pressure. Unlike Type I systems Type II are all above the surface of the substratum.
Marine sponges provide excellent examples of a Type II system. Sponges are filter feeders and therefore it is important to them to maintain a flow of seawater through their bodies. Water enters through the small holes in the animal’s surface and is forcibly expelled through one or more large openings at the top; flow is maintained through the beating of many flagella. However this is energetically very costly so the sponge has evolved to utilise induced flow partly or entirely to account for the movement of water. Depending on the speed of the current it is more or less successful. Closer examination reveals that sponges are highly developed to take maximum advantage of induced flow. Beneath the outer skin there is a space which allows water to enter the filtration system of the organism from all sides regardless of which way the current is flowing (i.e. flow is unidirectional); a set of valves prevents backflow when the internal pressure exceeds the external pressure. In addition sponges grow taller or shorter depending on whether they are living in areas of slow-moving or faster-moving water.
The mounds of some African termites use a Type II system to solve the same ventilation problem as the prairie dogs. There are millions of termites in the 16-foot mounds, so a ventilation system is essential. The mounds have porous sides and a turret at the top. Air enters through the sidewalls and leaves at the top, just like the water in the marine sponges. Other species have two sorts of holes – those without rims round the base and those with around the top. Air enters through the base and again leaves through the top.
Keyhole Limpets use a similar system to ventilate their bodies. The water flows from the lower rim of the shell to exit through the keyhole in the apex of the cone. By using this system the limpet is able to save space within the shell (because it does not need gills).
Some structures do not entirely fit these two categories. The larva of a caddisfly, Macronema, provides an example. It lives in streams and capitalises on the current to drive flow (and hence food) through it filtering system. Water enters through a small upstream-facing orifice and then turns 90 degrees to pass down a tube orientated perpendicularly to the direction of flow to the filtering chamber on the streambed. The exit is a small opening situated behind the entrance tube. The velocity at the entrance is zero: the water stops when it strikes the entrance tube, creating a high pressure. Behind the tube the velocity of the water is considerably greater and the pressure lower. Flow is therefore induced through the organism. This arrangement is similar to the Pitot Tube (on a Pitot tube the exit is upstream of the entrance tube; this is not the case in Macronema because if it were then it would receive water it had already filtered once before).
The thallus of a certain type of red alga Halosaccion glandiforme is one of many bags and cavities found in nature that could be refilled using flow induced pressures. It is an ellipsoidal body of revolution with thin walls used to prevent dehydration and to cool the alga when it is exposed at low tide. Water enters through holes in the distal end of the tube where the pressure is higher than that in the middle of the tube, creating the possibility that flow induced pressure is at least one possible mechanism by which it is refilled.
Use of Flow Induced Pressures by Mobile Organisms: to fill a Cavity:
Other organisms are able to move to align themselves with the direction of the current flow. They use induced flow not only to provide a flow of fluid through a body but also to fill a bag or cavity. Animals which practise these techniques often use the same principles as the Type I or Type II systems. It will be remembered the theoretical example of the radially symmetrical streamlined form moving through a fluid experienced two forces – a compressive force in front and an expansion force to the sides.
When threatened squid swim rearward at great bursts of speed by a pulsejet mechanism. They use a cavity between the viscera and outer mantle that they alternately fill with seawater through a pair of valves on either side of the head and empty forcefully through a nozzle beneath the head. The mantle muscle is used to expel the liquid but there is no obvious mechanism by which the cavity is refilled, because muscles do not actively expand, although some suggestions have been made. Flow-induced pressure though could be responsible either partially or entirely (depending on the conditions). The high pressure at the head of the squid (where the entrance holes are) coupled with the low pressure on either side of the mantle would cause fluid to enter the cavity.
This process would be increasingly effective at higher speeds. Squids can refill when they are not moving so they clearly are able to do this without any assistance from flow. However experiments have shown that at speed the contribution from induced flow can be very significant (50% at 3 m/s). Similar results have been obtained for other creatures that swim in this manner such as the scallop, which swims by filling the central cavity between its shells with water and expelling it forcefully.
Certain aquatic beetles such as Potamodytes tuberosus use a large air bubble, extending from their forelimbs to behind the tip of the abdomen, as reserve oxygen supply. It has been demonstrated that in rapid moving water the pressure on either side of the beetle is so low that it is close to that of the atmosphere, causing the bubble to refill automatically even though the beetle is submerged. This is the reason some water bubbles exist indefinitely on rocks beneath the surface of the water of fast moving streams. The limitations of this method are, however, severe. If the water stops moving the beetle will drown; and even at quite shallow depths the water pressure is so high that at only very fast water speeds will the bubble continue to refill.
All moving fish are (as might be expected) subjected to the same pressures as swimming squid and they have evolved to take full advantage of this. As has been mentioned, the effects of these pressures are far greater in water so they have more applications. Fish use flow induced pressures to do many things, not only to induce the flow of fluids but also to manipulate physical structures. For example water is forced into the mouth of the fish (situated at the region of highest pressure) and is expelled at the gills (situated at the region of lowest pressure). This is called ram ventilation. So effective is this that many fish stop active pumping at 0.8 m/s and some (like tuna) are unable to actively pump at all, relying instead on continual movement to prevent asphyxiation.
The low subambient pressure on the sides of the fish is transmitted to the heart, located beneath the gills, pulling the heart walls out and increasing the stroke volume (so as the fish swims faster more blood is pumped around its body) and reducing the need to increase the stroke rate (this occurs in other animals). Also the relatively positive pressures fore and aft of the heart aid the return of blood. The eyes of a bluefish (and many others) are located at the point where the pressure coefficient passes through zero (i.e. at the point where the pressure is that of normal water); this is a unique location because here pressure is independent of swimming speed. Focus of an eye depends in large part on the curvature of the cornea; it would be difficult if the later were to vary as a result of swimming speed. Fish compensate for the high pressures induced by having a very bony skull. It appears, therefore, that fish are highly evolved to make the most of their environment.
As has been shown the uses and exploitations of Bernoulli’s principle in nature are wide-ranging and very important to the lifestyles of many organisms, specifically all flying and aquatic life. All organisms, to a greater or lesser extent, are affected by flow induced pressures and many must have adapted to make best use of this source of mechanical energy, such as whales and bats for example. There must also be many other organisms that have adapted to use other physical processes to conserve energy.
Life revolves around the competitive struggle for resources and any organism that can utilise a ‘free’ energy source increases its chances of survival. What can be learnt from this? The biologist should be careful when using explanations of phenomena that require expenditure of chemical energy until simpler physical mechanisms have been ruled out.