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normal pressure drop through the 4 cm long section of artery

normal pressure drop through the 4 cm long section of artery

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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One of your friends has experienced a circulatory problem. A physician has diagnosed this as a problem in fluid mechanics and recommends corrective surgery. You, as an expert in fluid mechanics, are called upon to assess the correctness of the diagnosis: i.e., to provide a "second opinion". The physician believes that a shoulder artery, which is normally required to carry a flow of 1.2 liters/minute of blood has become pinched or constricted by an overgrowth of the adjacent bones. The normal artery has an internal diameter of 0.4 cm at this position. The physician believes that a 4 cm long section has had its cross sectional area reduced by a factor of four. These dimensional data are taken from X-ray negatives and are presumably correct. The stress-strain relationship for blood is described by the Bingham plastic equation. However, let us make the simplifying assumption that blood is a Newtonian fluid with density = 1050 kg/m³ and viscosity = 3.2×10-³ Pa·s. (a) Compute the normal pressure drop through the 4 cm long section of artery with a diameter of 0.4 cm.
Transcribed Image Text:One of your friends has experienced a circulatory problem. A physician has diagnosed this as a problem in fluid mechanics and recommends corrective surgery. You, as an expert in fluid mechanics, are called upon to assess the correctness of the diagnosis: i.e., to provide a "second opinion". The physician believes that a shoulder artery, which is normally required to carry a flow of 1.2 liters/minute of blood has become pinched or constricted by an overgrowth of the adjacent bones. The normal artery has an internal diameter of 0.4 cm at this position. The physician believes that a 4 cm long section has had its cross sectional area reduced by a factor of four. These dimensional data are taken from X-ray negatives and are presumably correct. The stress-strain relationship for blood is described by the Bingham plastic equation. However, let us make the simplifying assumption that blood is a Newtonian fluid with density = 1050 kg/m³ and viscosity = 3.2×10-³ Pa·s. (a) Compute the normal pressure drop through the 4 cm long section of artery with a diameter of 0.4 cm.
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(b) Compute the pressure drop in this 4 cm long section of artery when it is constricted as seen in the X-ray images. Assume that the cross section remains circular, and to keep us all on the same basis, assume that the body has some control mechanism which maintains the same volumetric flow rate through the artery. You may wish to compare these calculations with a normal pressure of 16000 Pa generated by the heart.
Transcribed Image Text:(b) Compute the pressure drop in this 4 cm long section of artery when it is constricted as seen in the X-ray images. Assume that the cross section remains circular, and to keep us all on the same basis, assume that the body has some control mechanism which maintains the same volumetric flow rate through the artery. You may wish to compare these calculations with a normal pressure of 16000 Pa generated by the heart.
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