Round your final answer to three significant figures. In an aortic aneurysm, a b

Question

Round your final answer to three significant figures. In an aortic aneurysm, a bulge forms where the walls of the aorta are weakened. If blood flowing through the aorta (radius 1.20 cm) enters an aneurysm with a radius of 3.00 cm. how much on average is the blood pressure higher inside the aneurysm than the pressure in the unenlarged part of the aorta? The average flow rate through the aorta is 120 cm^3/s. Assume the blood is non-viscous and the patient is lying down so there is no change in height. (Take the density of blood to be 1060 kg/m^3). Pa

Explanation / Answer

bernoulli equation states that:

P1+0.5*pho*v1^2+pho*g*h1=P2+0.5*pho*v2^2+pho*g*h2

where P1=pressure at first point

pho=density of the fluid

v1=speed of the fluid at first point

v2=speed of the fluid at the second point

g=acceleration due to gravity=9.8 m/s^2

h1=height at first point

h2=height at second point

as per given information:

at first point, radius =1.2 cm

speed =v1=flow rate/cross section area

=120/(pi*1.2^2)=26.5258 cm/s=0.265258 m/s

at second point , radius=3 cm

speed=v2=120/(pi*3^2)=4.244 cm/s=0.04244 cm/s

h1=h2

pho=1060 kg/m^3

using the values in bernoulli principle equation:

P1+0.5*1060*0.265258^2=P2+0.5*1060*0.04244^2

==>P2-P1=36.337 Pa

so pressure difference in 3 significant figures is given by

36.3 Pa

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