How to Calculate Pressure Difference in Aorta with Ideal Fluid Model

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To calculate the pressure difference in the aorta due to an aneurysm, apply the principle of conservation of mass, which states that a1v1 = a2v2, where A2 is 1.7 times A1. Given the average blood density of 1060 kg/m3, the velocities are v1 = 0.40 m/s in the normal section and v2 = 0.24 m/s in the enlarged section. Bernoulli's equation is essential for deriving the pressure difference, as it relates pressure, velocity, and height in fluid dynamics. The discussion emphasizes the importance of these equations in solving the problem effectively. Understanding these concepts is crucial for accurately determining the pressure in the aorta.
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Homework Statement


An aneurysm is an abnormal enlargement of a blood vessel such as the aorta.
Suppose that, because of an aneurysm, the cross-sectional area A1 of the aorta
increases to a value A2 = 1,7A1. The speed of blood, with average density of
1060 kg/m3, through a normal portion of the aorta is v1 = 0,40 m/s, and through
the enlarged region is v2 = 0,24 m/s. Using the model of an ideal fluid and
assuming that aorta is horizontal (the person is lying down), determine the
amount by which the pressure P2 in the enlarged region exceeds the pressure
P1 in the normal region!


Homework Equations


a1v1=a2v2
a=surface
v=velocity

The Attempt at a Solution


The only thing is how to get an equation for pressure from this a1v1=a2v2
I guess
 
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