### Problem StatementAn open cylindrical container of radius \( R \) with a thin liquid layer of density \( \rho \) at the bottom is rotating at a constant angular velocity \( \omega \). As a result of the rotation, the liquid is displaced, clearing a circular area at the bottom of the container with a radius \( R/2 \). Determine the height of the liquid, \( H \), on the cylindrical wall.### Diagram ExplanationThe diagram illustrates a cylindrical container viewed in cross-section. The relevant features are:- **Radius \( R \):** The overall radius of the cylindrical container.- **Cleared Area Radius \( R/2 \):** The radius of the circular area at the bottom from which the liquid has been displaced.- **Height \( H \):** This is the height to which the liquid rises on the inner wall of the container due to the rotation.- **Angular Velocity \( \omega \):** Represented by a curved arrow at the base of the diagram, indicating the direction and constancy of rotation.The liquid forms a paraboloidal surface due to rotational forces, causing the central clearance and elevation on the sides. This problem invites the calculation of \( H \) by considering the balance of centrifugal forces and gravitational forces acting on the liquid in rotational equilibrium.

Name: ### Problem StatementAn open cylindrical container of radius \( R \)
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Description: ### Problem StatementAn open cylindrical container of radius \( R \) with a thin liquid layer of density \( \rho \) at the bottom is rotating at a constant angular velocity \( \omega \). As a result of the rotation, the liquid is displaced, clearing

Consider the diagram as shown below for the given system.

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An open cylindrical container of radius R with a thin liquid layer of density p at the bottom, is rotating at a constant angular velocity w. As a result of the rotation, the liquid is displaced clearing a circular area at the bottom of the container or radius R/2. Determine the height of the liquid, H, on the cylindrical wall.

An open cylindrical container of radius R with a thin liquid layer of density p at the bottom, is rotating at a constant angular velocity w. As a result of the rotation, the liquid is displaced clearing a circular area at the bottom of the container or radius R/2. Determine the height of the liquid, H, on the cylindrical wall.

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

An open cylindrical container of radius \( R \) with a thin liquid layer of density \( \rho \) at the bottom is rotating at a constant angular velocity \( \omega \). As a result of the rotation, the liquid is displaced, clearing a circular area at the bottom of the container with a radius \( R/2 \). Determine the height of the liquid, \( H \), on the cylindrical wall.

### Diagram Explanation

The diagram illustrates a cylindrical container viewed in cross-section. The relevant features are:

- **Radius \( R \):** The overall radius of the cylindrical container.
- **Cleared Area Radius \( R/2 \):** The radius of the circular area at the bottom from which the liquid has been displaced.
- **Height \( H \):** This is the height to which the liquid rises on the inner wall of the container due to the rotation.
- **Angular Velocity \( \omega \):** Represented by a curved arrow at the base of the diagram, indicating the direction and constancy of rotation.

The liquid forms a paraboloidal surface due to rotational forces, causing the central clearance and elevation on the sides.

This problem invites the calculation of \( H \) by considering the balance of centrifugal forces and gravitational forces acting on the liquid in rotational equilibrium.

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