Data

Equations:

Drag = pU2SCd   high Reynolds number

Lift on a wing = pU2SCl , where S is the planform area

of the wing

Hagen-Poiseuille flow through cylindrical pipe

∆p =几(8) 

1.  4 pts. The thesaurus was thefirst dinosaur to become

extinct, defunct, superseded, disappeared, exterminated,

gone, deceased… Pterosaurs were largest flying animals

ever to inhabit the Earth (see

https://en.wikipedia.org/wiki/Pterosaur_size). Some

pterosaurs, such as Arambourgiania philadelphiae were

estimated to have wingspans exceeding 10 m (~30 ft!).  In

this problem, we will be considering gliding flight. You

will benefit from reviewing the material posted for Lecture

16, in particular the relationship between weight, lift, and

drag when in equilibrium.

a) Using the lift and drag coefficient data above, what is the descent angle (9, in degrees) of a gliding pterosaur?

b) Assume that each wing is triangular in planform shape, with a span s and width at the base b. Calculate the glide velocity (the speed along the path of descent) of a gliding pterosaur.

c) A pterosaur launches off a 30m cliff gliding down to a flat plain below. How far away from the cliff will it land, and how long will it stay aloft? (hint: consider the vertical component of

their gliding velocity).

d) If a pterosaur grabbed a mouthful of prey (as in the movie Jurassic Park) and increased its effective mass before initiating it’s descent, how would your answers to a-c above change.   Qualitative explanations are all that is needed.

2. (3 pts) To get rid of butterflies in your stomach, stop eating

caterpillars. In Lecture 18 on the comparative biomechanics of

nectar feeding in birds, we learned that the volumetric flow rate,

Q, of a fluid through a long cylindrical pipe of constant cross

section follows the Hagen–Poiseuille equation:

∆P =

where ∆P is the pressure difference between the two ends, R is

the radius of the pipe, u is the dynamic viscosity of the fluid,

and L is the length of the pipe.  In this problem, we will explore

how this relationship applies to suction feeding insects, such as

butterflies and moths.

a).  The mouth parts of a butterfly, such as Coleus and Danaus,

are modified into an extensible proboscis through which nectar

is drawn by suction.  Assuming a maximal pressure drop of 105

Pa (= 1 atm), derive a general equation for Q as a function of

nectar viscosity and proboscis dimensions (L and R).

b) Nectar is a concentrated sucrose solution and, as shown in the table provided, the                 concentration of the solution affects viscosity.  Plot Q as a function of nectar concentration for each of two butterfly species.

c) The viscosity of a fluid is notoriously temperature-dependent, as is the case with nectar. If     viscosity decreases with increasing temperature, how would that affect the flow rate through the proboscis? A qualitative answer is appropriate here.

d) Species with broad geographic distributions often show phenotypic variation that reflect local environmental conditions. If butterflies were able to alter their proboscis morphology (e.g. are   phenotypically plastic), what modifications might you expect in colder climates?