FINAL: Fundamentals Flashcards
How does pressure change with water depth?
for every 10 m increase in water depth, pressure increases by around 1 atm (101.3 kPa)
How does work scale with body mass?
- force is proportional to number of muscle fibres, which is proportional to cross-sectional area of muscle (M^0.67)
- displacement is proportional to muscle length (while a muscle can only contract by 20% of its relaxed length, the longer a muscle is the longer this 20% becomes) (M^0.33)
- work scales with body mass as M^0.67 x M^0.33 = M^1
Why is surface area to volume so
important?
- SA/V is the ratio of an animal’s inside to its
outside - animal’s surface area is the interface between it and its environment
- this determines how it exchanges oxygen, carbon dioxide, heat, nutrients, wastes, etc.
- if every aspect of an animal was to increase geometrically with its body mass (∝ volume), functions requiring large S.A. would progressively become limited
How can you avoid decreasing SA/V ratio?
get bigger in only one dimension
How does dynamic viscosity change with shear strain rate if the fluid is shear thickening?
if a fluid is shear thickening, as the applied stress increases, the dynamic viscosity of the fluid increases
because the viscosity has increased, a greater increase in shear stress is required to increase the shear strain rate of the fluid
In what way is a prairie dog burrow like a Venturi meter?
A venturi meter is a device used to measure the velocity of a fluid by passing it from a tube with a large cross-sectional area into a constriction: a tube with a smaller cross-sectional area. A manometer filled with liquid is placed with one arm connected to the large tube and the other to the small tube. When the fluid flows from the large to the small tube its velocity increases and its pressure drops, causing a pressure differential across the manometer which draws fluid up towards the lower pressure in the small tube. A prairie dog burrow has two openings, one at the top of a raised mound of earth, one flush with the ground. As air flowing over the ground hits the mound, it is forced to flow up and over the top. This causes the flow to be constricted, forcing it to accelerate and drop in pressure. Thus the burrow is like the manometer, while the raised mound of earth acts like the constriction of the smaller tube in the venturi meter. But unlike the manometer, the burrow isn’t filled with liquid, so the low pressure at the opening of the raised burrow draws air through the burrow, down a pressure gradient, from the higher pressure at the other burrow entrance flush with the ground.
What does a pitot tube measure?
A pitot tube measures the dynamic pressure of a fluid, which is proportional to the velocity of the fluid. It can therefore be used to measure fluid velocity (or airspeed). It consists of a tube with an opening that faces directly into the oncoming fluid flow. The moving fluid hits the opening of the tube and stagnates (stops) converting its dynamic pressure into static pressure. The stagnation pressure at this point is therefore the sum of the static and dynamic pressures of the fluid flow. A second opening in the tube parallel to the fluid’s flow is called the static port, and is used to measure the static pressure of the fluid. A pressure gauge (manometer) placed between these two ports will measure the dynamic pressure only.
What is Reynold’s number?
ratio of inertial forces in a fluid (related to fluid density, velocity, and characteristic length) and viscous forces in a fluid (dynamic viscosity)
dimensionless number used to predict whether flow is laminar (low Re) or turbulent (high Re)
What are features of laminar flow (low Re)?
- ordered movement of fluids along streamlines
- reversible in time
- no mixing
What are features of turbulent flow (high Re)?
- disordered flow
- non-reversible in time
- mixing
- vorticity
What is dynamic viscosity?
measure of relationship between shear stress applied to a fluid, and the resulting shear strain rate
units: Pa s
What is kinematic viscosity?
ratio of dynamic viscosity of a fluid to its density
units: Stokes (St)
Swimming at low Reynolds number is a challenging prospect. Explain what type of
motion is required to move in this environment.
requires motion in which power stroke to push animal forward and recovery stroke to re-set position of structure for next power stroke are not exact opposites of each other (ie. not time reversible)
ie. beating flagellum moving like a cork-screw or cilia bending during recovery stroke can both provide non-time reversible motion
The force a contracting pennate muscle can produce is determined by…
- length of its sarcomeres
- physiological cross-sectional area
- pennation angle of muscle fibres
any animals, particularly arthropods, use power amplifiers in their limbs because…
they generate a movement faster than muscle that activates them
A shallow tray is filled with a shear thickening liquid. You float a flat card on the surface of the fluid and then proceed to push the card horizontally across the surface of the fluid at a constant velocity by applying a force with your finger. If you double the force that you are exerting on the card, what happens to the speed of the card?
increases, but does not quite double
What is dE of a lever system?
perpendicular distance from axis of rotation to line of action of the force
What happens to material where stress begins to level out with increasing strain?
material reaches its yield point – this is when the material is strained beyond its elastic region, and begins to deform (begins to strain with little increase in stress)
Assume that sauropods (long-necked dinosaurs) held their necks vertically and grew in size from a juvenile to adult with geometric similarity. How would you predict the blood pressure in their heart would scale with body mass as they grow? Give the predicted allometric exponent (b) and briefly explain why this would be so.
- blood pressure in heart would be same as pressure at depth equal to vertical heigh of blood vessel (pgh)
- rho and g both scale as M0 because they are mass-independent variables
- h would scale with height of dinosaur’s neck
- assuming geometric similarity, neck height is a linear dimension therefore should scale as M0.33
- therefore blood pressure would also increase with neck height and also scale as M0.33
The insect protein resilin has the highest known resilience of any biological material (a resilience of 97%). Explain why you might expect to find resilin incorporated into a power amplifier system in the leg of a jumping insect.
very high resilience indicated that it can return 97% of the energy loaded into it as work of extension can be recovered in work of contraction
this is useful in power amplifier since it ensures almost all energy loaded into resilin by muscle can be released back as mechanical energy to power the insect’s jump
What is resilience?
measure of how efficient the material is at storing and releasing energy
work of contractionn / work of extension
What happens to force produced by pennate muscle as pennation angle increases?
decreases
The work a muscle can do is proportional to…
its volume
A solid material that is ‘anisotropic’ has mechanical properties that are…
dependent on direction of an applied stress
What is extensibility?
strain at failure
Does pennation angle contribute to high force production?
not exactly – any pennation angle > 0 actually reduces how much of the fibre’s force contributes to contraction force of muscle
Why does a lever only amplify either force or displacement, but never both simultaneously?
levers conserve work/energy
W = Fd
lever that amplified both force and distance at the load relative to the effort would mean that more work was done by the load arm than effort arm – this would mean the lever system had created energy from nowhere, which is impossible
What are the units for toughness?
J/m^3
How do you determine stiffness on stress/strain curve?
slope of curve
steeper = stiffer
How do Stress and Strain allow you to determine the general properties of a material, rather than the specific properties of the sample of material being measured?
- stress: convert absolute force to force per unit area
- strain: convert length to % change in length
this removes the effect of the sample’s size, leaving only the size-independent properties of the material
How does a power amplifier allow an animal to increase the power output of its muscle beyond what is possible from muscle contraction alone?
power amplifier is a system that stores the work done by a (slow) muscle contraction in an elastic element as elastic potential energy
this energy can be released rapidly to move a
limb
as power is work/time, a power amplifier allows slow (low power) work done by a contracting muscle to be stored then released rapidly (high power)
What direction is drag in?
always in the direction of incoming flow
In a steady flow above Stokes regime, what happens if there is no energy loss due to viscous effects/friction?
potential energy in the flow will be the same upstream and downstream of the cylinder, resulting in zero drag
In a steady flow above Stokes regime, what happens if you account for viscous effects and energy loss?
there will be a wake downstream of the cylinder, which results in drag
Characteristics of adverse gradients:
- require pressure drop to occur where fluid accelerates, which only occur if the object can divert the flow either with curved surface or with a non-zero angle of attack – therefore, flat plat aligned with flow will NOT cause adverse pressure gradients
- also occur in boundary layer where viscous effects (and energy loss) are important in resulting in the velocity gradient profile
- rough surfaces can move the separation point of the boundary layer towards the trailing edge, but they won’t eliminate them
What is pressure drag dependent on?
cross-sectional area perpendicular to flow direction
larger = larger pressure drag
What is skin friction drag?
a function of viscosity, velocity, length, and surface area
Why does Cd drop during the drag crisis?
because the boundary layer remains attached for longer (further downstream)
this reduces the size of the low pressure wake at the back, and decreases pressure drag
What direction is lift in?
perpendicular to direction of flow
What is Reynold’s number?
ratio of inertial to viscous forces
You discover a microscopic crustacean in a droplet of water that has multiple pairs of
identically hairy legs (same hair widths and hair spacing). You observe that it uses its legs
both to filter particles from the water and to swim. What must the crustacean do with its
legs in order to switch from swimming to filter feeding?
increase the speed that it moves its leg through the water
The drag experienced by an object in flow at low Re (<0.4) is caused by…
friction exerted due to the viscosity of the fluid as it shears past the no-slip surface of the object
At low (Re«1) Reynolds number, what happens to the coefficient of drag (Cd) for an object?
becomes much greater than 1 because skin friction drag dominates, and Cd is the ratio of
the measured total drag divided by the calculated pressure drag
Lobsters have long, hairy antennae covered with receptors which they use to detect odour molecules in the water. They periodically twitch them (rapidly move them backward and forward) when they are ‘smelling’ the water. With reference to Reynolds number and water flow, how does this twitching help them to detect odor molecules?
Re = ρvl/μ
as the lobster is in water, both ρ and μ are constant, and l is a fixed property of the
antennae – therefore if the lobster twitches its antennae (ie. moves them quickly) in the water, the velocity of the water interacting with its antennae will increase, thereby increasing Re
at higher Re, inertial forces increase relative to the viscous forces, allowing the stagnant water between the hairs to be displaced by fresh water, thus bringing odour molecules to the surface of the antennae to be detected/smelled
What does dimpling in a golf ball do?
induces turbulence in the boundary layer
- this increases exchange of momentum between the high momentum free stream fluid and the “no slip” condition fluid
- adds momentum to the surface, delays boundary layer separation
