A curved blood vessel has an internal diameter ? = 5 mm and a radius of curvature of ?? = 17 mm. Blood has a density of ρ = 1060 kg/m3 and a viscosity of 3.5 cP, and travels at an average velocity of ? = 1 m/s. a) Comment on the nature of the flow with reference to relevant non-dimensional groups. b) Can the flow be modelled using the Hagen-Poisseuile equation? If not, explain what specific assumptions are invalid. c) The viscosity of blood is measured and is shown in Figure Q2. Consider two long straight blood vessels with steady flow. The diameter of the first vessel is 5 mm and the average velocity is 6 cm/s. The internal diameter of the second vessel is 2.2 mm and the average velocity is 50 cm/s. Which vessel would you expect the Hagen-Poisseiulle equation to be more accurate in? Explain your answer (1-2 sentences).
A curved blood vessel has an internal diameter ? = 5 mm and a radius of curvature of ?? = 17 mm. Blood has a density of ρ = 1060 kg/m3 and a viscosity of 3.5 cP, and travels at an average velocity of ? = 1 m/s. a) Comment on the nature of the flow with reference to relevant non-dimensional groups. b) Can the flow be modelled using the Hagen-Poisseuile equation? If not, explain what specific assumptions are invalid. c) The viscosity of blood is measured and is shown in Figure Q2. Consider two long straight blood vessels with steady flow. The diameter of the first vessel is 5 mm and the average velocity is 6 cm/s. The internal diameter of the second vessel is 2.2 mm and the average velocity is 50 cm/s. Which vessel would you expect the Hagen-Poisseiulle equation to be more accurate in? Explain your answer (1-2 sentences).
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question
100%
A curved blood vessel has an internal diameter ? = 5 mm and a radius of curvature of
?? = 17 mm. Blood has a density of ρ = 1060 kg/m3 and a viscosity of 3.5 cP, and travels
at an average velocity of ? = 1 m/s.
a) Comment on the nature of the flow with reference to relevant non-dimensional
groups.
b) Can the flow be modelled using the Hagen-Poisseuile equation? If not, explain
what specific assumptions are invalid.
c) The viscosity of blood is measured and is shown in Figure Q2. Consider two long
straight blood vessels with steady flow. The diameter of the first vessel is 5 mm and
the average velocity is 6 cm/s. The internal diameter of the second vessel is 2.2
mm and the average velocity is 50 cm/s. Which vessel would you expect the
Hagen-Poisseiulle equation to be more accurate in? Explain your answer (1-2
sentences).
![Viscosity [mPa.s]
10³
%
o
10⁰
10-²
10-1
10⁰ 101
Strain Rate [¹]
Figure Q2: Measurements of the variation of blood viscosity with strain rate.
10² 10³ 104](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a64e81e-0af4-4cb0-8221-b3f2646e3736%2F20c71718-65ec-4237-aec1-56177f64c745%2Flvk8qz8_processed.png&w=3840&q=75)
Transcribed Image Text:Viscosity [mPa.s]
10³
%
o
10⁰
10-²
10-1
10⁰ 101
Strain Rate [¹]
Figure Q2: Measurements of the variation of blood viscosity with strain rate.
10² 10³ 104
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