### Problem StatementA cylindrical container of radius \( R = 1 \, ft \), and height of \( 3 \, ft \) rotates at an angular velocity \( \omega = 100 \, rpm \). The tank contains \( 2 \, ft \) of water at rest.#### Tasks:(a) Determine the force acting at the bottom of the tank.(b) What angular velocity is needed for the free surface to just reach the center of the bottom of the tank.### Diagram ExplanationThe image shows a cylindrical container depicted with the following annotations:- **z-axis**: Oriented vertically, indicating direction along the cylinder's height.- **r-axis**: Showing radial direction from the center of the cylinder.- **R**: The radius of the cylinder (1 ft).- **g**: Gravity acting downwards.- **\(\omega\)**: Angular velocity, shown as circular arrows at the base, indicating the direction of rotation.- **\(z_0\)**: Height of the free surface from the bottom of the tank when the tank is rotating.- Dashed lines indicate the initial water level and the parabolic shape of the water surface due to rotation.This setup is used to analyze the effects of rotation on the fluid's behavior and calculate the necessary conditions for specific surface positioning.

The resulting force created by the pressure loading of a liquid acting on submerged surfaces is…

Answered: A cylindrical container of radius R = 1…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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