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# (answered) – 1) Air moves through the human trachea at 3 m/s during

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(answered) – 1) Air moves through the human trachea at 3 m/s duringDescriptionSolution downloadThe Question1) Air moves through the human trachea at 3 m/s during inhalation. A constriction in thetrachea leads to a doubling in the air speed. Find (approximate) the pressure change at theconstriction (versus that in an unconstructed trachea). Use a density for air of 1.2 kg/m3.Comment on the significance of this pressure change.2)?Determine the Reynolds number associated with the swimming motion of aTuna in water at 20C if it has an effective diameter of 33 cm. The swimming speed of the tuna is 18 m/s (65 km/h!)-Attached is a formula sheet. The answer to question 1 is??P ? 17 Pa; a negligible drop, compared to 101,000 pa available!. The answer to question 2 is 10^6. I need to know how to get to the answer i.e. the process and the formulas to use.?Trent University: PHYS-BIOL 1060HFormula Sheet?x= tan ?lstress ? shearG?=strain ? shearShear Strain:? shear ?1. GeneralWeight:Fg ? W = mg (SI units: newtons, N)GM 1 M 2r2Newton?s 2nd Law: F = ma (SI: N)2Kinetic Energy: E = 1 / 2mv (SI: joules, J)1 22Circle: Area= ?r = ?D4perimeter= 2?r = ?D2cylinder: Area= 2?rl + (2 ? ?r ) (shaft + bases)2volume= ?r lRectangle:Area= L ? Wperimeter= 2( L + W )22Sphere: Surface Area= 4?r = ?D4?r 3Volume=332Cube: Surface Area= 6L Volume= LGravitational Law:F=?2/3-law? surface area to mass relationship:A ? M 2/3?1/4-law? surface area to mass relationship:A? M5/8massmDensity: ? ==volume V?=F?l=Y= Y?Al0Breaking Stress:? max? shear =solid cylinder twist:Fshear?x=G= G?Al0G?r 3? twistFtngnt =2lhollow cylinder twist:Ftngnt =Elastic Energy stored in strain:22G?trave? twistlU elast ? Yl? 2 ? Y (?l ) 2122F?v=?A?yF?vfor Viscoelastic fluids:= G? shear + ?A?yliquid shear & viscosity:P1 ? P2 2(R ? r 2 )4?L?R 4 ?PFlow Rate: Q = Av ave =8?L?v ave DReynold?s number of flow: Re =Flow profile in a tube:v=?Stoke?s law for drag at high viscosity (for sphere):Fd = 6? ? r v2. FluidsPressure:FP?AGauge Pressure:Pgauge = Pabs ? PatmHydrostatic pressure:Pabs = Patm + ?ghTerminal speed of spherical sinking/floating objects:F= ? fluidVdisplaced gbuoyancyForce Surface EnergySurface Tension: ? ==LengthAreaBuoyant Force:Transmural pressure in a bubble with inner and outer?P = Pin ? Pout = 4?R2r 2 gvt =( ? obj ? ? fluid )9?Terminal velocity of objects under centrifugation:vt =8? 2 Rf 2 r 2( ? obj ? ? fluid )9?3. Atomic Motion, Heat and DiffusionPV = n R T = N k B Tparticles moving in n-dimensions:1nm v 2 = k BT22Transmural pressure in a bubble with gas on only onestress ?Y?=strain ?Tensile Stress:Shear Stress:surface:2. ElasticityElastic modulus:Shear Modulus:v1 A1 = v2 A2p + ? v + ? g y = constant at any pointmass conservation in a fluid:(?l )maxF? max = YAlside:?P = Pin ? Pout = 2Capillary rise of liquid:hliquid?R2? liquid ? air cos?=? liquid grContact angle and surface tension:? glass / air ? ? glass / liquid ? ? liquid / air cos? = 01Diffusion coefficient:D=v2 ?3Diffusion in n-dimensions:R 2 = 2nDtTrent University: PHYS-BIOL 1060HStokes-Einstein Eqn (for diffusing spherical particles):k TD= B6??r?L = ?L?T22 k BTSedimentation parameter in centrifuge:s=vt4? f 2 RHeat conduction:2r 2

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