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6. Newtonian fluid with viscosity μ flows upward at a steady state between two parallel plates that make an angle with the horizontal. The fluid thickness h is much smaller than the width of the channel W. The pressures at each end are known, Po and PL respectively and the pressure variations in the y direction is negligible. Assume that v=v=0, and v, is a function of y alone. Apply conservation principles and shell balance approach to find the following quantities: (a) Shear stress Tyx (y) (b) Wall shear stress Tw (c) Force that needed to be applied to each plate to keep them from moving (d) Fluid velocity profile vx(y) 7. In our body, vasculature has a hierarchical structure such that one large branch bifurcates into two smaller daughter branches. Consider the branching unit in the following figure. The diameter and length of the mother branch and two daughter branches are labeled in the figure, and the pressure drop in each daughter branch is the same. Please calculate the flow rate in two daughter branches in terms of the incoming blood flow rate in the mother branch. Assume blood has constant viscosity μ here. P1 Q1 d₁ 41 P2 23 da P3

6. Newtonian fluid with viscosity μ flows upward at a steady state between two parallel plates that make an angle with the horizontal. The fluid thickness h is much smaller than the width of the channel W. The pressures at each end are known, Po and PL respectively and the pressure variations in the y direction is negligible. Assume that v=v=0, and v, is a function of y alone. Apply conservation principles and shell balance approach to find the following quantities: (a) Shear stress Tyx (y) (b) Wall shear stress Tw (c) Force that needed to be applied to each plate to keep them from moving (d) Fluid velocity profile vx(y) 7. In our body, vasculature has a hierarchical structure such that one large branch bifurcates into two smaller daughter branches. Consider the branching unit in the following figure. The diameter and length of the mother branch and two daughter branches are labeled in the figure, and the pressure drop in each daughter branch is the same. Please calculate the flow rate in two daughter branches in terms of the incoming blood flow rate in the mother branch. Assume blood has constant viscosity μ here. P1 Q1 d₁ 41 P2 23 da P3

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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6. Newtonian fluid with viscosity μ flows upward at a steady state between two parallel plates that make an angle with the horizontal. The fluid thickness h is much smaller than the width of the channel W. The pressures at each end are known, Po and PL respectively and the pressure variations in the y direction is negligible. Assume that v=v=0, and v, is a function of y alone. Apply conservation principles and shell balance approach to find the following quantities:
Transcribed Image Text:6. Newtonian fluid with viscosity μ flows upward at a steady state between two parallel plates that make an angle with the horizontal. The fluid thickness h is much smaller than the width of the channel W. The pressures at each end are known, Po and PL respectively and the pressure variations in the y direction is negligible. Assume that v=v=0, and v, is a function of y alone. Apply conservation principles and shell balance approach to find the following quantities:
(a) Shear stress Tyx (y) (b) Wall shear stress Tw (c) Force that needed to be applied to each plate to keep them from moving (d) Fluid velocity profile vx(y) 7. In our body, vasculature has a hierarchical structure such that one large branch bifurcates into two smaller daughter branches. Consider the branching unit in the following figure. The diameter and length of the mother branch and two daughter branches are labeled in the figure, and the pressure drop in each daughter branch is the same. Please calculate the flow rate in two daughter branches in terms of the incoming blood flow rate in the mother branch. Assume blood has constant viscosity μ here. P1 Q1 d₁ 41 P2 23 da P3
Transcribed Image Text:(a) Shear stress Tyx (y) (b) Wall shear stress Tw (c) Force that needed to be applied to each plate to keep them from moving (d) Fluid velocity profile vx(y) 7. In our body, vasculature has a hierarchical structure such that one large branch bifurcates into two smaller daughter branches. Consider the branching unit in the following figure. The diameter and length of the mother branch and two daughter branches are labeled in the figure, and the pressure drop in each daughter branch is the same. Please calculate the flow rate in two daughter branches in terms of the incoming blood flow rate in the mother branch. Assume blood has constant viscosity μ here. P1 Q1 d₁ 41 P2 23 da P3
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