Answered: Consider steady flow in the closed…

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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$### Flow in a Closed Cavity Consider steady flow in the closed cavity shown in the figure. The bottom and side walls are fixed, while the top surface slides to the right at speed $ U $. The fluid-filled space is relatively narrow, such that $ H/L \ll 1 $. This allows the flow in the central part of the cavity (away from the end walls) to be fully developed. #### Diagram Explanation - **Coordinate System**: The $ y $-axis is marked vertically, and the $ x $-axis is marked horizontally. - **Flow Description**: The fluid is contained within a rectangular cavity. The height of the cavity is denoted by $ H $ and the length by $ L $. - **Boundary Conditions**: The top surface moves to the right at speed $ U $, inducing flow within the fluid, while side and bottom walls remain stationary. #### Objective Determine the fully developed velocity profile, $ v_x(y) $.$

Transcribed Image Text:### Flow in a Closed Cavity Consider steady flow in the closed cavity shown in the figure. The bottom and side walls are fixed, while the top surface slides to the right at speed $ U $. The fluid-filled space is relatively narrow, such that $ H/L \ll 1 $. This allows the flow in the central part of the cavity (away from the end walls) to be fully developed. #### Diagram Explanation - **Coordinate System**: The $ y $-axis is marked vertically, and the $ x $-axis is marked horizontally. - **Flow Description**: The fluid is contained within a rectangular cavity. The height of the cavity is denoted by $ H $ and the length by $ L $. - **Boundary Conditions**: The top surface moves to the right at speed $ U $, inducing flow within the fluid, while side and bottom walls remain stationary. #### Objective Determine the fully developed velocity profile, $ v_x(y) $.

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