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Consider an annular fluid flow created by two concentric cylinders spinning. The cylinders are long, and you consider the cross-section at mid-height, such that the flow may be considered two-dimensional. The outer cylinder has radius ro=0.4 m and is rotating with angular velocity w,-0.55 s-1, while the inner cylinder has radius r=0.1 m and is rotating with angular velocity wi=2.8 s-1-1. The flow field is given by Ur = Uz = = 0; uo W= = k (rue) (²) r Ər 1 p2. curl(u) i (due) + j 1 = [ (wir? -w [(w₁r ² —w₂r² ) p² Note that when considering three-dimensional polar coordinates, i.e., u(r, 0, z, t) (ur, uo, uz), the vorticity is written explicitly as: = dr² ) + 1 дur r 20 + :) + j ( dur Which of the following statements is true: 1. The vorticity is maximum at r=0.1 m 2. None of the above 3. The vorticity is maximum at r=0.4 m 4. The vorticity is zero 5. The vorticity is maximum at r=0.25 m r²r² (W₁-W₂) r

Consider an annular fluid flow created by two concentric cylinders spinning. The cylinders are long, and you consider the cross-section at mid-height, such that the flow may be considered two-dimensional. The outer cylinder has radius ro=0.4 m and is rotating with angular velocity w,-0.55 s-1, while the inner cylinder has radius r=0.1 m and is rotating with angular velocity wi=2.8 s-1-1. The flow field is given by Ur = Uz = = 0; uo W= = k (rue) (²) r Ər 1 p2. curl(u) i (due) + j 1 = [ (wir? -w [(w₁r ² —w₂r² ) p² Note that when considering three-dimensional polar coordinates, i.e., u(r, 0, z, t) (ur, uo, uz), the vorticity is written explicitly as: = dr² ) + 1 дur r 20 + :) + j ( dur Which of the following statements is true: 1. The vorticity is maximum at r=0.1 m 2. None of the above 3. The vorticity is maximum at r=0.4 m 4. The vorticity is zero 5. The vorticity is maximum at r=0.25 m r²r² (W₁-W₂) r

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
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Consider an annular fluid flow created by two concentric cylinders spinning. The cylinders are long, and you consider the cross-section at mid-height, such that the flow may be considered two-dimensional. The outer cylinder has radius ro=0.4 m and is rotating with angular velocity w.=0.55 s-1, while the inner cylinder has radius ri=0.1 m and is rotating with angular velocity wi=2.8 s-1-1. The flow field is given by 1 Ur = Uz = 0; U = „2¹7/ [(W₂0² _w p2 r W = Note that when considering three-dimensional polar coordinates, i.e., u(r, 0, z, t) = (ur, uo, uz), the vorticity is written explicitly as: k curl(u) ( 1 0 (rus) - i (w₁r ² — w₂r² ) r² [(wir? + 1 Jur r 20 1 Juz r 20 r²r² (W1-W₂) r due) + j (du - du.) - + Which of the following statements is true: 1. The vorticity is maximum at r=0.1 m 2. None of the above 3. The vorticity is maximum at r=0.4 m 4. The vorticity is zero 5. The vorticity is maximum at r=0.25 m
Transcribed Image Text:Consider an annular fluid flow created by two concentric cylinders spinning. The cylinders are long, and you consider the cross-section at mid-height, such that the flow may be considered two-dimensional. The outer cylinder has radius ro=0.4 m and is rotating with angular velocity w.=0.55 s-1, while the inner cylinder has radius ri=0.1 m and is rotating with angular velocity wi=2.8 s-1-1. The flow field is given by 1 Ur = Uz = 0; U = „2¹7/ [(W₂0² _w p2 r W = Note that when considering three-dimensional polar coordinates, i.e., u(r, 0, z, t) = (ur, uo, uz), the vorticity is written explicitly as: k curl(u) ( 1 0 (rus) - i (w₁r ² — w₂r² ) r² [(wir? + 1 Jur r 20 1 Juz r 20 r²r² (W1-W₂) r due) + j (du - du.) - + Which of the following statements is true: 1. The vorticity is maximum at r=0.1 m 2. None of the above 3. The vorticity is maximum at r=0.4 m 4. The vorticity is zero 5. The vorticity is maximum at r=0.25 m
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