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Determine the two-dimensional stream function corresponding to p = Aln(r/ro), A is a constant. What is the flow pattern? Plot the velocity field, potential field, and alines ||

Determine the two-dimensional stream function corresponding to p = Aln(r/ro), A is a constant. What is the flow pattern? Plot the velocity field, potential field, and alines ||

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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**Problem Statement:** 3. Determine the two-dimensional stream function corresponding to \(\phi = A \ln(r/r_0)\), where \(A\) is a constant. What is the flow pattern? Plot the velocity field, potential field, and streamlines. **Explanation:** This problem involves finding the stream function for a given potential function \(\phi\) in a two-dimensional flow. The function \(\phi = A \ln(r/r_0)\) is given, where \(A\) is a constant and \(r_0\) is a reference radius. **Tasks:** 1. **Determine the Stream Function**: Calculate the stream function corresponding to the given potential function in polar coordinates. 2. **Flow Pattern**: Identify the characteristics of the flow pattern based on the computed stream function. 3. **Plot Graphics**: - **Velocity Field**: Visual representation of the velocity vectors at various points. - **Potential Field**: Examine how the potential function varies across the plane. - **Streamlines**: Plot the lines that represent the trajectory of fluid particles in the flow. Further analysis of these components will help in understanding how the fluid behaves in this configuration.
Transcribed Image Text:**Problem Statement:** 3. Determine the two-dimensional stream function corresponding to \(\phi = A \ln(r/r_0)\), where \(A\) is a constant. What is the flow pattern? Plot the velocity field, potential field, and streamlines. **Explanation:** This problem involves finding the stream function for a given potential function \(\phi\) in a two-dimensional flow. The function \(\phi = A \ln(r/r_0)\) is given, where \(A\) is a constant and \(r_0\) is a reference radius. **Tasks:** 1. **Determine the Stream Function**: Calculate the stream function corresponding to the given potential function in polar coordinates. 2. **Flow Pattern**: Identify the characteristics of the flow pattern based on the computed stream function. 3. **Plot Graphics**: - **Velocity Field**: Visual representation of the velocity vectors at various points. - **Potential Field**: Examine how the potential function varies across the plane. - **Streamlines**: Plot the lines that represent the trajectory of fluid particles in the flow. Further analysis of these components will help in understanding how the fluid behaves in this configuration.
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