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Fluid with constant velocity Uo and density p flows past an infinitely long cylinder (see figure). The flow direction coincides with the symmetry axis and the only force on the body is then the drag force FD. Downstream of the body the wake flow generated has a velocity uı less than U. With a given u,/U calculate the drag force FD per unit depth acting on the body. CV vp 0 X,

Fluid with constant velocity Uo and density p flows past an infinitely long cylinder (see figure). The flow direction coincides with the symmetry axis and the only force on the body is then the drag force FD. Downstream of the body the wake flow generated has a velocity uı less than U. With a given u,/U calculate the drag force FD per unit depth acting on the body. CV vp 0 X,

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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**Text:** Fluid with constant velocity \( U_\infty \) and density \( \rho \) flows past an infinitely long cylinder (see figure). The flow direction coincides with the symmetry axis and the only force on the body is then the drag force \( F_D \). Downstream of the body the wake flow generated has a velocity \( u_1 \) less than \( U_\infty \). With a given \( u_1/U_\infty \), calculate the drag force \( F_D \) per unit depth acting on the body. **Diagram Explanation:** The diagram illustrates a control volume (CV) around an infinitely long cylinder. It shows a flow of fluid entering from the left with a uniform velocity \( U_\infty \). The flow lines indicate that the fluid moves parallel to the symmetry axis of the cylinder. The fluid flows past the cylinder, creating a wake with a reduced velocity \( u_1 \) on the downstream side. Key features in the diagram include: - Coordinate axes \( x_1 \) and \( x_2 \) indicating directions. - The condition \( \nabla p = 0 \) indicates that the pressure gradient is zero across the control volume boundary. - The diagram emphasizes the change in velocity downstream of the cylinder, illustrating the formation of a wake. The setup is used to analyze the drag force per unit depth, \( F_D \), acting on the cylinder due to the flow of the fluid.
Transcribed Image Text:**Text:** Fluid with constant velocity \( U_\infty \) and density \( \rho \) flows past an infinitely long cylinder (see figure). The flow direction coincides with the symmetry axis and the only force on the body is then the drag force \( F_D \). Downstream of the body the wake flow generated has a velocity \( u_1 \) less than \( U_\infty \). With a given \( u_1/U_\infty \), calculate the drag force \( F_D \) per unit depth acting on the body. **Diagram Explanation:** The diagram illustrates a control volume (CV) around an infinitely long cylinder. It shows a flow of fluid entering from the left with a uniform velocity \( U_\infty \). The flow lines indicate that the fluid moves parallel to the symmetry axis of the cylinder. The fluid flows past the cylinder, creating a wake with a reduced velocity \( u_1 \) on the downstream side. Key features in the diagram include: - Coordinate axes \( x_1 \) and \( x_2 \) indicating directions. - The condition \( \nabla p = 0 \) indicates that the pressure gradient is zero across the control volume boundary. - The diagram emphasizes the change in velocity downstream of the cylinder, illustrating the formation of a wake. The setup is used to analyze the drag force per unit depth, \( F_D \), acting on the cylinder due to the flow of the fluid.
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