Rectangle Gate AB has length L and width b into the paper is hinged at B and has negligible weight. The liquid level, water, h does not reach the top of the gate for an angle theta. Find an equation for the force P, required to keep the gate in equilibrium. Solve for width, b. In the figure. (hint: draw a free-body diagram for the left and right side of the gate separately) The image illustrates a diagram of a gate system, likely used in a fluid mechanics context. It consists of the following components:- **Line AB**: A solid line inclined from point B to point A. This represents the gate or surface under consideration.- **Point A**: Located at the top of the gate, with an arrow pointing to the right labeled "P," signifying the direction of pressure or force applied horizontally at this point.- **Point B**: The bottom point of the gate, where it rests on a hinge.- **Hinge at B**: Indicates that the gate is hinged at point B, allowing it to pivot around this point.- **Length L**: The length of the gate from B to A, marked along the inclined line.- **Angle θ**: The angle of inclination of the gate with respect to the horizontal, depicted with an arc between the gate and the baseline.- **Baseline**: A horizontal dashed line extending from point B downward.- **Height h**: The vertical distance measured from the baseline upward to a point aligned vertically with point A, indicating the height of fluid above reference level.- **Curved Line**: Represents the fluid level or surface interacting with the gate, varying across its length.This diagram is typically used to analyze the forces and moments acting on submerged or partially submerged surfaces, such as gates or walls in fluid environments.

Givenlength of gate =Llquid level =hangle =θwidth =bforce =P

Answered: Rectangle Gate AB has length L and…

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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Rectangle Gate AB has length L and width b into the paper is hinged at B and has negligible weight. The liquid level, water, h does not reach the top of the gate for an angle theta. Find an equation for the force P, required to keep the gate in equilibrium. Solve for width, b. In the figure. (hint: draw a free-body diagram for the left and right side of the gate separately)

The image illustrates a diagram of a gate system, likely used in a fluid mechanics context. It consists of the following components:

- **Line AB**: A solid line inclined from point B to point A. This represents the gate or surface under consideration.
- **Point A**: Located at the top of the gate, with an arrow pointing to the right labeled "P," signifying the direction of pressure or force applied horizontally at this point.
- **Point B**: The bottom point of the gate, where it rests on a hinge.
- **Hinge at B**: Indicates that the gate is hinged at point B, allowing it to pivot around this point.
- **Length L**: The length of the gate from B to A, marked along the inclined line.
- **Angle θ**: The angle of inclination of the gate with respect to the horizontal, depicted with an arc between the gate and the baseline.
- **Baseline**: A horizontal dashed line extending from point B downward.
- **Height h**: The vertical distance measured from the baseline upward to a point aligned vertically with point A, indicating the height of fluid above reference level.
- **Curved Line**: Represents the fluid level or surface interacting with the gate, varying across its length.

This diagram is typically used to analyze the forces and moments acting on submerged or partially submerged surfaces, such as gates or walls in fluid environments.

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