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# (answered) – 1) An aorta has a constriction that reduces its diameter to 1/3

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(answered) – 1) An aorta has a constriction that reduces its diameter to 1/3DescriptionSolution downloadThe Question1) An aorta has a constriction that reduces its diameter to 1/3 of its normal diameter. The velocity of the blood as it enters the large region of the aorta is 11.0 cm/s. Assuming the blood has zero viscosity and a density of 1.00×10^3 kg/m3, calculate the pressure difference (?P=PL-PS) in the fluid at the large and small regions of this aorta.?2) Blood pressure at the exit of the heart is 100mmHg and upon return it is zero at the entrance to the heart. If the pressure drop along the constriction in the diagram for question 1 is approximately 450Pa, what fraction of the total available blood pressure would this represent?-Attached is a formula sheet. The answer to question 1 is 445Pa and the question to answer 2 is 3%. But I need to know how to get to those answers, and what 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 c

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