Excerpt

## Table of Contents

Introduction

Buoyant Force

Archimedes Principle

Buoyant Force Equation

Problem Solving

Summary

References

## Introduction

The eBook discusses the Archimedes principle of buoyancy and the buoyancy equation in general. Application to the field of engineering was also expounded in order to show the relevance of the principle in the engineering context.

Sample problems are presented to understand fully the application of the buoyancy principle of Archimedes. Analysis of whether a certain object will float or sink are then explained based on the buoyancy equation. Therefore stability of objects can be analyzed by applying the mentioned principle.

The principle of buoyancy can be applied in floating objects such as ships and boats, submarines, hydrometer, balloons and airships and so many other real-life applications.

## Buoyant Force

“A buoyant force is defined as an upward force (with respect to gravity) on a body that is totally or partially submerged in fluid, either a liquid or gas. Buoyant forces are caused by the hydrostatic pressure distribution.”^{[1]}

“When a solid object is wholly or partly immersed in a fluid, the fluid molecules are continually striking the submerged surface of the object. The forces due to these impacts can be combined into a single force, the buoyant force.”^{[2]}

“The buoyant force, which always opposes gravity, is nevertheless caused by gravity. Fluid pressure increases with depth because of the (gravitational) weight of the fluid above. This increasing pressure applies a force on a submerged object that increases with depth. The result is buoyancy.”^{[3]}

Figure 1 shows the illustration of the buoyancy principle.

* Figure 1. Bouyancy*

* Source: https://en.wikipedia.org/wiki/Buoyancy/*

## Archimedes Principle

Archimedes principle is the general principle of buoyancy. The *Archimedes principle* states that “*when an object is completely or partially immersed in a fluid, the fluid exerts an upward force on the object equal to the weight of the fluid displaced by the object”*.^{[4]}

“The buoyant force acts at a point called the center of buoyancy, which is located at the center of gravity of the displaced fluid”.^{[5]}

“A completely submerged body displaces a volume of liquid equal to its own volume. Experience also tells us that when an object is submerged, it appears lighter in weight; the water buoys it up, pushes upward, partially supporting it somehow. The buoyancy principle asserts that an object immersed in a fluid will be lighter by an amount equal to the weight of the fluid it displaces. The upward force exerted by the fluid is known as the buoyant force.”^{[6]}

“If the weight of the water displaced is less than the weight of the object, the object will sink. Otherwise the object will float, with the weight of the water displaced equal to the weight of the object.”^{[7]}

As shown in Figure 2, the unloaded ship in “a” floats higher in the water than a loaded ship in “b”.

Abbildung in dieser Leseprobe nicht enthalten

*Figure 2. Illustration of Archimedes principle*

*Source: https://opentextbc.ca/physicstestbook2/chapter/archimedes-principle/*

## Buoyant Force Equation

Consider the illustration shown in Figure 3. Based on the illustration, the equation is derived:^{[8]}

Fup = g (Vb + Va)

**[...]**

^{[1]} Donal F. Elger, et. Al, Engineering Fluid Mechanics, 10th Edition, Wiley, USA, 2013, p 86

^{[2]} Bouyancy: Floating and Sinking, Visual Physics, School of Physics, University of Sydney, Australia, *src.gov.jm/wp-content/uploads/2012/12/buoyancy.pdf*

^{[3]} Archimedes principle, https://www.britannica.com/science/Archimedes-principle

^{[4]} Bouyancy: Floating and Sinking, Visual Physics, School of Physics, University of Sydney, Australia, *src.gov.jm/wp-content/uploads/2012/12/buoyancy.pdf*

^{[5]} Donal F. Elger, et. Al, Engineering Fluid Mechanics, 10th Edition, Wiley, USA, 2013, p 87

^{[6]} Bouyancy: Floating and Sinking, Visual Physics, School of Physics, University of Sydney, Australia, *src.gov.jm/wp-content/uploads/2012/12/buoyancy.pdf*

^{[7]} Archimedes Principle, https://physics.weber.edu/carroll/archimedes/principle.htm

^{[8]} *Donal F. Elger, et. Al, Engineering Fluid Mechanics,10th Edition, Wiley, USA, 2013, p86*

- Quote paper
- Florante Jr Poso (Author), 2015, Bouyancy. The Archimedes Principle, Munich, GRIN Verlag, https://www.grin.com/document/441711

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