How to Calculate Pressure Difference in Aorta with Ideal Fluid Model

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SUMMARY

The discussion focuses on calculating the pressure difference in the aorta due to an aneurysm using the ideal fluid model. The cross-sectional area of the aorta increases from A1 to A2, where A2 is 1.7 times A1. Given the blood density of 1060 kg/m³ and velocities of v1 = 0.40 m/s and v2 = 0.24 m/s, Bernoulli's equation is essential for deriving the pressure difference between the normal and enlarged regions of the aorta.

PREREQUISITES
  • Understanding of Bernoulli's equation
  • Knowledge of fluid dynamics principles
  • Familiarity with the concept of cross-sectional area in fluid flow
  • Basic understanding of blood properties, including density
NEXT STEPS
  • Study Bernoulli's equation in detail for fluid dynamics applications
  • Explore the implications of aneurysms on blood flow and pressure
  • Learn about the continuity equation in fluid mechanics
  • Investigate the effects of varying cross-sectional areas on fluid velocity and pressure
USEFUL FOR

Medical students, biomedical engineers, and anyone studying cardiovascular fluid dynamics will benefit from this discussion, particularly those interested in the mechanics of blood flow in relation to aneurysms.

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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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