How to Calculate Pressure Difference in Aorta with Ideal Fluid Model

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In summary, an aneurysm is an abnormal enlargement of a blood vessel, specifically the aorta. In this case, the cross-sectional area of the aorta increases to 1.7 times its original value due to the aneurysm. Using the model of an ideal fluid and assuming a horizontal aorta, the pressure in the enlarged region (P2) can be found by Bernoulli's equation, which relates the area and velocity of a fluid. Given the velocity of blood in both the normal (v1) and enlarged (v2) regions, the pressure difference between P2 and P1 can be determined.
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Rron
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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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1. What is an ideal fluid?

An ideal fluid is a theoretical concept in fluid mechanics that has no viscosity or internal friction. It is considered to be incompressible, meaning that its density remains constant regardless of changes in pressure or temperature. Ideal fluids also have uniform flow and do not experience turbulence.

2. What is the ideal fluid problem?

The ideal fluid problem is a mathematical problem in fluid mechanics that involves finding the velocity and pressure distribution of a fluid flow under ideal conditions. This problem assumes that the fluid is inviscid, incompressible, and has a steady, uniform flow.

3. Why is the ideal fluid problem important?

The ideal fluid problem is important because it serves as a basis for understanding and analyzing fluid flow in real-world situations. While ideal fluids do not exist in reality, the solutions to this problem can be used as approximations for real fluid flows in many engineering applications.

4. What are the assumptions made in the ideal fluid problem?

The ideal fluid problem makes several assumptions, including that the fluid is inviscid, incompressible, and has a steady, uniform flow. It also assumes that the flow is irrotational, meaning that the fluid particles do not rotate as they move through the flow field.

5. How is the ideal fluid problem solved?

The ideal fluid problem is solved using mathematical equations that describe the conservation of mass, momentum, and energy in the fluid. These equations can be solved analytically or numerically using computational fluid dynamics methods. The solutions provide information on the velocity and pressure distribution of the fluid flow under ideal conditions.

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