Answered: In an experiment to determine the force…

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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$**Experiment Overview** In an experimental setup, we aim to determine the force acting on an oval-shaped body. A model is mounted in the test section of a wind tunnel, which features a rectangular cross-section with height $2h$ and width $\ell$ (into the page). The model occupies the entire width of the test section and is subjected to a steady, uniform, incompressible flow with velocity $V_1$. **Pressure and Velocity Conditions** A pressure gauge measures the pressure difference $\Delta p$ between the test section's exit (location 2) and entrance (location 1). The velocity profile downstream of the model is depicted, showing variations in the flow. **Control Volume Analysis** The diagram illustrates a control volume that spans the entire test section. It highlights different flow parameters: - Velocity $V_1$ at the inlet - Height $h$ indicating the modeled area - A maximum velocity $V_{\text{max}}$ at the exit - Pressure difference $\Delta p$ **Objective** The goal is to calculate the force acting on the model using the given quantities: $V_1$, $h$, $\ell$, $\Delta p$, and density $\rho$. **Graph/Diagram Explanation** - A cross-section of the wind tunnel is illustrated, showing a rectangular test section. - The flow enters at velocity $V_1$ from the left. - The model (oval shape) is placed centrally. - The control volume encloses the section where the model is located, capturing the velocity and pressure signatures before and after the model. - The schematic emphasizes the flow continuity and momentum principles necessary for evaluating the aerodynamic forces.$

Transcribed Image Text:**Experiment Overview** In an experimental setup, we aim to determine the force acting on an oval-shaped body. A model is mounted in the test section of a wind tunnel, which features a rectangular cross-section with height $2h$ and width $\ell$ (into the page). The model occupies the entire width of the test section and is subjected to a steady, uniform, incompressible flow with velocity $V_1$. **Pressure and Velocity Conditions** A pressure gauge measures the pressure difference $\Delta p$ between the test section's exit (location 2) and entrance (location 1). The velocity profile downstream of the model is depicted, showing variations in the flow. **Control Volume Analysis** The diagram illustrates a control volume that spans the entire test section. It highlights different flow parameters: - Velocity $V_1$ at the inlet - Height $h$ indicating the modeled area - A maximum velocity $V_{\text{max}}$ at the exit - Pressure difference $\Delta p$ **Objective** The goal is to calculate the force acting on the model using the given quantities: $V_1$, $h$, $\ell$, $\Delta p$, and density $\rho$. **Graph/Diagram Explanation** - A cross-section of the wind tunnel is illustrated, showing a rectangular test section. - The flow enters at velocity $V_1$ from the left. - The model (oval shape) is placed centrally. - The control volume encloses the section where the model is located, capturing the velocity and pressure signatures before and after the model. - The schematic emphasizes the flow continuity and momentum principles necessary for evaluating the aerodynamic forces.

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