3. (Problem 2.6) A stenosis is a narrowing of a blood vessel or valve. Stenosis of a blood vessel arises during atherosclerosis and could occlude an artery, depriving the tissue downstream of oxygen. Further, the fluid shear stresses acting on the endothelial cells lining blood vessels may affect the expression of genes that regulate endothelial cell function. Such gene expression can influence whether the stenosis grows or not. Consider a symmetric stenosis as shown in Figure 2.36 (p. 112). Assume the velocity profile within the stenosis of radius Ri(z) has the same shape as the profile outside the stenosis and is represented as Vz(r) = Vmax 1- R2 Outside the stenosis, the radius equals Ro and the maximum velocity is constant. Within the stenosis, the radius of the fluid channel R(z) equals Ro{1–0.5 [1-4(+)³]"} R(z) = Ro The origin of the z axis is the midpoint of the stenosis. (a) Develop an express for Vmax in a stenosis in terms of the volumetric flow rate Q, cylindrical tube of radius Ro, and distance along the stenosis z/L. (b) Compute the shear stress acting on the surface of the stenosis (r = R₁) at z = 0 relative to the value outside the stenosis.
3. (Problem 2.6) A stenosis is a narrowing of a blood vessel or valve. Stenosis of a blood vessel arises during atherosclerosis and could occlude an artery, depriving the tissue downstream of oxygen. Further, the fluid shear stresses acting on the endothelial cells lining blood vessels may affect the expression of genes that regulate endothelial cell function. Such gene expression can influence whether the stenosis grows or not. Consider a symmetric stenosis as shown in Figure 2.36 (p. 112). Assume the velocity profile within the stenosis of radius Ri(z) has the same shape as the profile outside the stenosis and is represented as Vz(r) = Vmax 1- R2 Outside the stenosis, the radius equals Ro and the maximum velocity is constant. Within the stenosis, the radius of the fluid channel R(z) equals Ro{1–0.5 [1-4(+)³]"} R(z) = Ro The origin of the z axis is the midpoint of the stenosis. (a) Develop an express for Vmax in a stenosis in terms of the volumetric flow rate Q, cylindrical tube of radius Ro, and distance along the stenosis z/L. (b) Compute the shear stress acting on the surface of the stenosis (r = R₁) at z = 0 relative to the value outside the stenosis.
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter1: Basic Modes Of Heat Transfer
Section: Chapter Questions
Problem 1.2DP
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![3. (Problem 2.6) A stenosis is a narrowing of a blood vessel or valve. Stenosis of a blood vessel arises
during atherosclerosis and could occlude an artery, depriving the tissue downstream of oxygen. Further,
the fluid shear stresses acting on the endothelial cells lining blood vessels may affect the expression of
genes that regulate endothelial cell function. Such gene expression can influence whether the stenosis
grows or not.
Consider a symmetric stenosis as shown in Figure 2.36 (p. 112). Assume the velocity profile
within the stenosis of radius Ri(z) has the same shape as the profile outside the stenosis and is
represented as
Vz(r) = Vmax
1-
R2
Outside the stenosis, the radius equals Ro and the maximum velocity is constant. Within the stenosis,
the radius of the fluid channel R(z) equals
Ro{1–0.5 [1-4(+)³]"}
R(z) = Ro
The origin of the z axis is the midpoint of the stenosis.
(a) Develop an express for Vmax in a stenosis in terms of the volumetric flow rate Q, cylindrical
tube of radius Ro, and distance along the stenosis z/L.
(b) Compute the shear stress acting on the surface of the stenosis (r = R₁) at z = 0 relative to the
value outside the stenosis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7884aebb-abc9-4ae2-aee8-88ec2e400645%2Fe2526ea7-eb8b-4ac8-8f84-38100dd23862%2Fbuq7dr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. (Problem 2.6) A stenosis is a narrowing of a blood vessel or valve. Stenosis of a blood vessel arises
during atherosclerosis and could occlude an artery, depriving the tissue downstream of oxygen. Further,
the fluid shear stresses acting on the endothelial cells lining blood vessels may affect the expression of
genes that regulate endothelial cell function. Such gene expression can influence whether the stenosis
grows or not.
Consider a symmetric stenosis as shown in Figure 2.36 (p. 112). Assume the velocity profile
within the stenosis of radius Ri(z) has the same shape as the profile outside the stenosis and is
represented as
Vz(r) = Vmax
1-
R2
Outside the stenosis, the radius equals Ro and the maximum velocity is constant. Within the stenosis,
the radius of the fluid channel R(z) equals
Ro{1–0.5 [1-4(+)³]"}
R(z) = Ro
The origin of the z axis is the midpoint of the stenosis.
(a) Develop an express for Vmax in a stenosis in terms of the volumetric flow rate Q, cylindrical
tube of radius Ro, and distance along the stenosis z/L.
(b) Compute the shear stress acting on the surface of the stenosis (r = R₁) at z = 0 relative to the
value outside the stenosis.
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