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Use the method of images to approximate the flow pattern past a cylinder a distance 4a from a single wall. To illustrate the effect of the wall, compute the velocities at corresponding points A,B, C, and D, comparing with a cylinder flow in an infinite expanse of fluid.

Use the method of images to approximate the flow pattern past a cylinder a distance 4a from a single wall. To illustrate the effect of the wall, compute the velocities at corresponding points A,B, C, and D, comparing with a cylinder flow in an infinite expanse of fluid.

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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### Approximation of Flow Pattern Past a Cylinder Near a Wall In this problem, the method of images is employed to approximate the flow pattern around a cylinder positioned at a distance \(4a\) from a single wall. The objective is to understand how the wall affects the flow by calculating the velocities at specific points \(A\), \(B\), \(C\), and \(D\). These values will be compared to those in an ideal scenario where the cylinder flows in an infinite expanse of fluid. #### Diagram Explanation: - **Flow Representation:** The flow is illustrated with parallel arrows denoting the free stream velocity \(U_\infty\). - **Cylinder Position:** The cylinder is illustrated as a circle, situated in proximity to a flat boundary such that the distance from the wall to the center of the cylinder is \(4a\). - **Point Locations:** - **Point \(A\):** Located on the surface of the cylinder at the closest point to the wall. - **Point \(B\):** Positioned on the opposite side of the cylinder from point \(A\). - **Point \(C\):** Situated directly beneath the cylinder at a distance of \(4a\) from its center. - **Point \(D\):** Posited above the cylinder at a distance of \(4a\) from its center and \(2a\) above point \(B\). Understanding the velocity distribution around these points is crucial for evaluating the influence of the nearby wall on the flow pattern.
Transcribed Image Text:### Approximation of Flow Pattern Past a Cylinder Near a Wall In this problem, the method of images is employed to approximate the flow pattern around a cylinder positioned at a distance \(4a\) from a single wall. The objective is to understand how the wall affects the flow by calculating the velocities at specific points \(A\), \(B\), \(C\), and \(D\). These values will be compared to those in an ideal scenario where the cylinder flows in an infinite expanse of fluid. #### Diagram Explanation: - **Flow Representation:** The flow is illustrated with parallel arrows denoting the free stream velocity \(U_\infty\). - **Cylinder Position:** The cylinder is illustrated as a circle, situated in proximity to a flat boundary such that the distance from the wall to the center of the cylinder is \(4a\). - **Point Locations:** - **Point \(A\):** Located on the surface of the cylinder at the closest point to the wall. - **Point \(B\):** Positioned on the opposite side of the cylinder from point \(A\). - **Point \(C\):** Situated directly beneath the cylinder at a distance of \(4a\) from its center. - **Point \(D\):** Posited above the cylinder at a distance of \(4a\) from its center and \(2a\) above point \(B\). Understanding the velocity distribution around these points is crucial for evaluating the influence of the nearby wall on the flow pattern.
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