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Model the valve and the heart chambers as shown in the figure below. Aorta -Valve Ventricle (a) Assume that the cross-sections of the ventricle and the aorta are both about 5 cm². The area of a healthy, open aortic valve is 4.1 cm². In a healthy body, the average velocity of blood in the left ventricle and in the aorta is about 48 cm . Determine the velocity across the valve. S Think: What equations dictating the flow through the valve are valid: the equation of continuity, Bernoulli's equation or Poiseuille's equation? What simplifications should you make regarding the blood flow. V = valve ст ✓ S (b) Determine the pressure gradient across the aortic valve. Think: What equations dictating the flow through the valve are valid: the equation of continuity, Bernoulli's equation or Poiseuille's equation? Are the radii of the different regions the same? Can you apply Poiseuille's equation? Can you apply Bernoulli's equation? What simplifications should you make regarding the blood flow, if you plan to use Bernoulli's equation? AP= ✓ mmHg Blood is ejected from the left ventricle of the heart into the aorta through the aortic valve. Aortic stenosis is a stiffening of this valve which leads to faulty fluid mechanics. This problem explores the how the different models of fluid motion can be used to study an unhealthy valve. The density and viscosity of blood are 1060 and 0.004 Pa·s, respectively. kg m³ Aortic Stenosis Aortic Valve with Stenosis Normal Aortic Valve Aorta Mount Sinai Medical Center New York All Rights Reserved Restricted Blood Flow Normal Blood Flow Model the valve and the heart chambers as shown in the figure below. Aorta -Valve Ventricle Mount Sinai

Model the valve and the heart chambers as shown in the figure below. Aorta -Valve Ventricle (a) Assume that the cross-sections of the ventricle and the aorta are both about 5 cm². The area of a healthy, open aortic valve is 4.1 cm². In a healthy body, the average velocity of blood in the left ventricle and in the aorta is about 48 cm . Determine the velocity across the valve. S Think: What equations dictating the flow through the valve are valid: the equation of continuity, Bernoulli's equation or Poiseuille's equation? What simplifications should you make regarding the blood flow. V = valve ст ✓ S (b) Determine the pressure gradient across the aortic valve. Think: What equations dictating the flow through the valve are valid: the equation of continuity, Bernoulli's equation or Poiseuille's equation? Are the radii of the different regions the same? Can you apply Poiseuille's equation? Can you apply Bernoulli's equation? What simplifications should you make regarding the blood flow, if you plan to use Bernoulli's equation? AP= ✓ mmHg Blood is ejected from the left ventricle of the heart into the aorta through the aortic valve. Aortic stenosis is a stiffening of this valve which leads to faulty fluid mechanics. This problem explores the how the different models of fluid motion can be used to study an unhealthy valve. The density and viscosity of blood are 1060 and 0.004 Pa·s, respectively. kg m³ Aortic Stenosis Aortic Valve with Stenosis Normal Aortic Valve Aorta Mount Sinai Medical Center New York All Rights Reserved Restricted Blood Flow Normal Blood Flow Model the valve and the heart chambers as shown in the figure below. Aorta -Valve Ventricle Mount Sinai

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter15: Fluid Mechanics
Section: Chapter Questions
Problem 52P
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Model the valve and the heart chambers as shown in the figure below. Aorta -Valve Ventricle (a) Assume that the cross-sections of the ventricle and the aorta are both about 5 cm². The area of a healthy, open aortic valve is 4.1 cm². In a healthy body, the average velocity of blood in the left ventricle and in the aorta is about 48 cm . Determine the velocity across the valve. S Think: What equations dictating the flow through the valve are valid: the equation of continuity, Bernoulli's equation or Poiseuille's equation? What simplifications should you make regarding the blood flow. V = valve ст ✓ S (b) Determine the pressure gradient across the aortic valve. Think: What equations dictating the flow through the valve are valid: the equation of continuity, Bernoulli's equation or Poiseuille's equation? Are the radii of the different regions the same? Can you apply Poiseuille's equation? Can you apply Bernoulli's equation? What simplifications should you make regarding the blood flow, if you plan to use Bernoulli's equation? AP= ✓ mmHg
Transcribed Image Text:Model the valve and the heart chambers as shown in the figure below. Aorta -Valve Ventricle (a) Assume that the cross-sections of the ventricle and the aorta are both about 5 cm². The area of a healthy, open aortic valve is 4.1 cm². In a healthy body, the average velocity of blood in the left ventricle and in the aorta is about 48 cm . Determine the velocity across the valve. S Think: What equations dictating the flow through the valve are valid: the equation of continuity, Bernoulli's equation or Poiseuille's equation? What simplifications should you make regarding the blood flow. V = valve ст ✓ S (b) Determine the pressure gradient across the aortic valve. Think: What equations dictating the flow through the valve are valid: the equation of continuity, Bernoulli's equation or Poiseuille's equation? Are the radii of the different regions the same? Can you apply Poiseuille's equation? Can you apply Bernoulli's equation? What simplifications should you make regarding the blood flow, if you plan to use Bernoulli's equation? AP= ✓ mmHg
Blood is ejected from the left ventricle of the heart into the aorta through the aortic valve. Aortic stenosis is a stiffening of this valve which leads to faulty fluid mechanics. This problem explores the how the different models of fluid motion can be used to study an unhealthy valve. The density and viscosity of blood are 1060 and 0.004 Pa·s, respectively. kg m³ Aortic Stenosis Aortic Valve with Stenosis Normal Aortic Valve Aorta Mount Sinai Medical Center New York All Rights Reserved Restricted Blood Flow Normal Blood Flow Model the valve and the heart chambers as shown in the figure below. Aorta -Valve Ventricle Mount Sinai
Transcribed Image Text:Blood is ejected from the left ventricle of the heart into the aorta through the aortic valve. Aortic stenosis is a stiffening of this valve which leads to faulty fluid mechanics. This problem explores the how the different models of fluid motion can be used to study an unhealthy valve. The density and viscosity of blood are 1060 and 0.004 Pa·s, respectively. kg m³ Aortic Stenosis Aortic Valve with Stenosis Normal Aortic Valve Aorta Mount Sinai Medical Center New York All Rights Reserved Restricted Blood Flow Normal Blood Flow Model the valve and the heart chambers as shown in the figure below. Aorta -Valve Ventricle Mount Sinai
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