• If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.

  • You already know Dokkio is an AI-powered assistant to organize & manage your digital files & messages. Very soon, Dokkio will support Outlook as well as One Drive. Check it out today!

View
 

Fluid flow_External flow (2013)

Page history last edited by Kerstin Nordstrom 10 years, 5 months ago

 Working ContentMacroModels > Fluids > Fluid Flow 

 

            Animals can take advantage of external flows to help them get around.  This is because flow can apply lift to an organism, enabling it to fly or swim.  The classic example of lift is the net force that results perpendicular to an airplane wing, when a fluid flows over that wing.  The argument is made that curvature of the top surface of the wing causes the flow to speed up and hence reduce the pressure relative to the flow over the bottom surface of the wing.  This net pressure difference results in the upward lift that balances the gravitational force and enables an eagle to fly or a penguin to swim.

 

            If we think about a wing, there are a number of forces being applied to the wing (Figure 6).  In the simplest application of lift, an animal will be gliding, without applying any thrust.  In this case, the forces will include the downward gravitational force pulling on the weight of the flyer, the drag force resulting from the friction of the air on the wing (along the direction of the wing), and the lift, perpendicular to the wing. In the steady state, the forces of lift and drag will counterbalance some fraction of the gravitational force, to slow the animal’s descent.  In this case, the glide angle, θ, is equal to the angle defined by the vector sum of the drag and the lift.  The drag and lift are dependent on the characteristics of an animal’s wing.  The ability to generate lift, L, is given by

     Formula

where Cis a shape dependent lift factor, ρ is the density of the fluid, S is the wing’s area (as viewed from on top) and v is velocity.  Therefore, making a wing have a larger area provides greater lift, as does moving faster.  The latter fact will make sense when you think about an aircraft taxiing down a runway does not start to rise up off the ground until it reaches a certain speed.  More speed gives the plane more lift and enables it to become airborne.  Another thing to note from this equation is that a denser fluid will provide more lift.  Therefore there is greater lift in water than in air.  Interestingly, an exactly analogous equation can be written for drag where

     Formula

Therefore, these two factors scale in a similar way with fluid density, wing area and velocity.

 

            The wing needs to provide enough lift that it can compensate for the downward force of gravity on the animal’s weight.  This is sometimes calculated as a wing loading:

     Formula

where m is the animal’s mass, given by its density times its volume, g is gravitational acceleration and S is the animal’s wing area.  Wing loading describes the balance between gravity and lift, with smaller values occurring for those animal’s which can more readily glide (and ultimately fly).  This quantity scales as the animal’s volume to its area.  This scaling is proportional to length3 / length2 which is of the order of magnitude of animal length.  Therefore, smaller animals will have smaller ratios of V/S and have an easier time staying aloft.  Here is a nice video about flying squirrels: http://www.youtube.com/watch?v=_ZgcBUx0Vwg

 

            Many animals will want to do more than just glide, they will want to propel themselves forward through a fluid.  This is possible if the angle at which the lift is generated is tilted forward such that there is a net forward thrust on the animal.  Essentially the resultant of the lift and the drag will apply a rearward force to propel the animal forward.

 

Moving through external flows

 

     Biological organisms make all kinds of adaptations to living in flows.  Both the kind of flow (laminar vs turbulent) and the velocity gradient can impact how an organism interacts with a fluid or a fluid interacts with an organism.  Some small organisms actually live in the boundary layer, and take advantage of the slower flow velocities there. These include larvae of various insects such as mayflies or caddis flies, as well as some beetle larvae and some limpets.  Slower flows cause less drag on the organism, making it easier to hang on and stay put.  Other organisms work to extend at least part of their body outside the boundary layer where they have access to the flow, and therefore more items to eat.  Examples of this include black fly larvae that have feeding fans for gathering plankton out of the flow and barnacles that extend their cirri or limbs.  Check out this video to see barnacles feeding: http://www.youtube.com/watch?v=25F7xMVNt-w

 

     Organisms can also take advantage of flow using the flow for dispersal.  They can send out gametes as a tree does to disperse its pollen or a dandelion does to disperse its seeds.  For the latter, the seeds are carefully designed with a sort of parachute which holds them aloft to travel further from the parent plant.  Animals or plants can also send out olfactory cues to attract others.  A female moth emits pheromones to attract males for mating.  Flowers give off chemicals to attract bees, moths or even hummingbirds to pollinate them.

 

     Some organisms have acquired special adaptations so that they can efficiently move through a fluid.  This occurs for animals that glide or fly in air or that swim through water.  A wide variety of animals can glide, including frogs, lizards, squirrels and fish, by acquiring some extra flaps of tissue to help catch the air.  However, there have been just four kinds of animals that have acquired the ability to fly: extinct pterosaurs, birds, insects and bats.  Of the last three, each has acquired the wings necessary to fly by a separate evolutionary path.  These wings have large surface areas, sufficient to generate enough lift and can be beat up and down frequently enough to generate thrust or forward motion.  Notably, these flying animals are all relatively small.  Large birds, such as the ostrich can no longer generate sufficient lift to get their large bodies off the ground.

 

     For several reasons, swimming is far easier than flying.  First, the lift provided is larger because of the larger density of water versus air.  Second, the animal is somewhat buoyant in water, and certainly much more so than it is in air, due to the fact that its density is so close to that of water.  This buoyancy helps offset a large fraction of the gravitational force in water.  So most of the effort of swimming can be put in to generating thrust.  This is typically done in one of three ways.  First, animals can jet through the water, by expelling fluid behind them to propel themselves forward.  This is common for squid, which are fast jetters, as well as jellyfish, which are very slow jetters.  Second, animals can use drag, using appendages or even cilia to essentially row themselves through the water.  The forward moving stroke extends the cilia out fully to apply a lot of drag to the fluid while the recovery stroke pulls the cilia in to minimize the applied drag.  The net effect is forward motion due to the difference in drag on the fluid.  Third, animals can actually “fly” underwater, generating lift in a direction so as to propel themselves forward.

 

Comments (0)

You don't have permission to comment on this page.