**Study of Liquid in a Rotating Cylindrical Tank****Problem Statement:**Consider a liquid in a cylindrical tank where both the tank and the liquid rotate as a rigid body. The free surface of the liquid is exposed to room air, and surface tension effects are negligible. Define the boundary conditions necessary to analyze this system.**Boundary Condition Requirements:**1. **Velocity Boundary Conditions:** - Express the velocity conditions in cylindrical coordinates $(r, \theta, z)$ with velocity components $(u_r, u_\theta, u_z)$. - Apply these conditions at all relevant surfaces, including the tank walls and the free surface.2. **Pressure Boundary Conditions:** - Determine the appropriate pressure boundary conditions for the flow field.**Diagram Explanation:**- **Diagram Description:** - The diagram represents a cross-section of the cylindrical tank. - The tank contains liquid, and both the tank and liquid rotate together.- **Key Features:** - **Free Surface:** The curved shape of the liquid’s free surface indicates rotation, with pressure $P = P_{\text{atm}}$. - **Rotation:** Illustrated with an arrow and angular velocity $\omega$, indicating the direction of rotation. - **Coordinates:** Labeled as $z$ for vertical height, $R$ for the tank’s radius, and $r$ as the radial distance extending from the center. - **Fluid Density ($\rho$):** Denoted within the liquid.The goal is to use these conditions to understand the behavior of the fluid in such a rotating system, taking into account interactions at the surface and other interfaces.

Consider liquid in a cylindrical tank. Both the tank and the liquid rotate as a rigid body. The free surface of the liquid is exposed to room air. Surface tension effects are negligible. Present the boundary conditions required to solve this problem. Specifically, what are the velocity boundary conditions in terms of cylindrical coordinates (r, 0, z) and velocity components (ur, ưo, u:) at all surfaces, including the tank walls and the free surface? What pressure boundary conditions are appropriate for this flow field? Explain. Free surface P-Pan Liquid

Consider liquid in a cylindrical tank. Both the tank and the liquid rotate as a rigid body. The free surface of the liquid is exposed to room air. Surface tension effects are negligible. Present the boundary conditions required to solve this problem. Specifically, what are the velocity boundary conditions in terms of cylindrical coordinates (r, 0, z) and velocity components (ur, ưo, u:) at all surfaces, including the tank walls and the free surface? What pressure boundary conditions are appropriate for this flow field? Explain. Free surface P-Pan Liquid

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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