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Question 1: Consider fully developed two-dimensional Poiseuille flow: flow between two infinite parallel plates separated by distance h, with both the top plate and bottom plate stationary, and a forced pressure gradient dP/dx driving the flow as illustrated in the figure (dP/dx is constant and negative). The flow is steady, incompressible, and two-dimensional in the xy-plane. The velocity components are given by 1 dP u = -(y² - hy); v = 0 2μ αχ h where μ is the fluid's viscosity. Is this flow rotational or irrotational? u(y) a. If it is rotational, calculate the vorticity component in the z-direction. Do fluid particles in this flow rotate clockwise or counterclockwise? b. calculate the linear strain rates in the x- and y-directions, and c. calculate the shear strain rate Exy. d. Combine your results to form the two-dimensional strain rate tensor εij in the xy-plane,

Question 1: Consider fully developed two-dimensional Poiseuille flow: flow between two infinite parallel plates separated by distance h, with both the top plate and bottom plate stationary, and a forced pressure gradient dP/dx driving the flow as illustrated in the figure (dP/dx is constant and negative). The flow is steady, incompressible, and two-dimensional in the xy-plane. The velocity components are given by 1 dP u = -(y² - hy); v = 0 2μ αχ h where μ is the fluid's viscosity. Is this flow rotational or irrotational? u(y) a. If it is rotational, calculate the vorticity component in the z-direction. Do fluid particles in this flow rotate clockwise or counterclockwise? b. calculate the linear strain rates in the x- and y-directions, and c. calculate the shear strain rate Exy. d. Combine your results to form the two-dimensional strain rate tensor εij in the xy-plane,

Elements Of Electromagnetics
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 1: Consider fully developed two-dimensional Poiseuille flow: flow between two infinite parallel plates separated by distance h, with both the top plate and bottom plate stationary, and a forced pressure gradient dP/dx driving the flow as illustrated in the figure (dP/dx is constant and negative). The flow is steady, incompressible, and two-dimensional in the xy-plane. The velocity components are given by 1 dP u = -(y² - hy); v = 0 2μ αχ h where μ is the fluid's viscosity. Is this flow rotational or irrotational? u(y) a. If it is rotational, calculate the vorticity component in the z-direction. Do fluid particles in this flow rotate clockwise or counterclockwise? b. calculate the linear strain rates in the x- and y-directions, and c. calculate the shear strain rate Exy. d. Combine your results to form the two-dimensional strain rate tensor εij in the xy-plane,
Transcribed Image Text:Question 1: Consider fully developed two-dimensional Poiseuille flow: flow between two infinite parallel plates separated by distance h, with both the top plate and bottom plate stationary, and a forced pressure gradient dP/dx driving the flow as illustrated in the figure (dP/dx is constant and negative). The flow is steady, incompressible, and two-dimensional in the xy-plane. The velocity components are given by 1 dP u = -(y² - hy); v = 0 2μ αχ h where μ is the fluid's viscosity. Is this flow rotational or irrotational? u(y) a. If it is rotational, calculate the vorticity component in the z-direction. Do fluid particles in this flow rotate clockwise or counterclockwise? b. calculate the linear strain rates in the x- and y-directions, and c. calculate the shear strain rate Exy. d. Combine your results to form the two-dimensional strain rate tensor εij in the xy-plane,
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