Problem on buoyant force - 1.6 | 7. Basics of fluid mechanics-I(Cont.) | Hydraulic Engineering - Vol 1
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Introduction to Buoyant Force

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Teacher
Teacher

Today, we will delve into buoyant force, defined as the upward force exerted by a fluid on an object that is submerged. Can anyone tell me what influences this force?

Student 1
Student 1

I think it depends on the weight of the fluid displaced.

Teacher
Teacher

Exactly! The buoyant force is equal to the weight of the fluid displaced, as stated in Archimedes' principle. Can anyone remind me how we calculate the weight of the displaced fluid?

Student 2
Student 2

It’s the volume times the density of the fluid, right?

Teacher
Teacher

Correct! We use the formula: Buoyant Force = Volume Displaced × Fluid Density × g. Remember the acronym **VDFg** for this formula!

Student 3
Student 3

Can you give us an example of this?

Teacher
Teacher

Sure! If we have a block submerged in water, we calculate how much water it displaces to find the buoyant force acting on it.

Application of Buoyant Force

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Teacher
Teacher

Now, let’s consider a practical application of buoyant force in hydraulic engineering. Why do engineers need to understand buoyant forces?

Student 4
Student 4

To design bridges and boats to ensure they float!

Teacher
Teacher

Exactly! Understanding buoyant forces helps ensure structures can withstand their weight in water. If we have a vessel, how do we ensure it remains stable?

Student 3
Student 3

By making sure their center of gravity is below the center of buoyancy.

Teacher
Teacher

Right! Stability ensures that the vessel does not capsize. Remember the phrase **CG below CB** to help you recall this concept.

Solving Buoyancy Problems

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Teacher
Teacher

Let’s solve a problem! A block of wood weighs 10 N when submerged in a fluid. What information can we gather?

Student 2
Student 2

We can determine its volume and the density of the fluid based on its buoyant force.

Teacher
Teacher

Correct! If the buoyant force equals the weight of the fluid displaced, we can figure out its volume. How would we express that?

Student 1
Student 1

Using the formula for buoyant force.

Teacher
Teacher

Exactly! Let's calculate it. If we know the fluid density is 800 kg/m³, what’s the volume of the block?

Student 4
Student 4

We find the volume by rearranging the equation: V = F / (ρg).

Teacher
Teacher

Excellent! Now let’s input the values and solve for volume!

Introduction & Overview

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Quick Overview

This section discusses buoyant force, including its definition, practical examples, and underlying principles.

Standard

In this section, we explore the concept of buoyant force, defined as the upward force exerted by a fluid on a submerged body, and examine problems related to buoyancy, including practical applications in engineering.

Detailed

Detailed Summary

In this section, we investigate the concept of buoyant force, which is the upward force exerted by a static fluid on an object that is partially or fully submerged. The principles underlying buoyancy are fundamental to fluid mechanics, particularly in applications related to hydraulic engineering. The section outlines the calculation of buoyant force as the weight of the fluid displaced by the submerged object, encapsulated by Archimedes' principle. Key problems and examples illustrate how to apply these ideas in real-life situations, emphasizing the relationship between fluid density, object volume, and submerged weight. The section concludes with exercises to solidify understanding, encouraging problem-solving skills in hydraulics.

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Understanding Buoyant Force

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The buoyant force exerted on a body by a static fluid, which is fully or partially submerged, is always equal to the weight of the fluid displaced by the body. This force acts in the opposite direction of gravity.

Detailed Explanation

The buoyant force is the upward force exerted by a fluid on an object that is immersed in it. When an object is submerged, it displaces a volume of fluid. The weight of this displaced fluid equates to the buoyant force acting on the object. It’s important to note that this force acts upward, counteracting the downward force of gravity. Thus, if the buoyant force equals the weight of the object, it will float; if it is less, the object will sink.

Examples & Analogies

Imagine a beach ball submerged underwater. As you push it down, it pushes up against your hand with equal force. This upward force is the buoyant force, and it’s trying to return the ball to the surface. It’s like if you try to hold a ball underwater; the water pushes it back up to the surface to where it can float.

Deriving Buoyant Force for Floating Objects

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In equilibrium, the weight of the body supports the weight of the displaced liquids. For a block of wood, density ρ1 floating at the interface of two liquids, ρ2 and ρ3, the relationship can be stated as: ρ1 V1 g = ρ2 V2 g + ρ3 V3 g.

Detailed Explanation

When an object like a block of wood is floating at the interface of two liquids, we can analyze the forces acting on it. The weight of the wood (determined by its density and total volume) must balance the weights of the volumes of the two displaced liquids. In mathematical terms, this is expressed as the weight of the wood (ρ1 V1 g) being equal to the sum of the weights of the liquids above (ρ2 V2 g) and below (ρ3 V3 g) the block. By understanding these relationships, you can solve problems involving floating objects in different fluid environments.

Examples & Analogies

Think of a sponge sitting on water. The sponge is soaked with water (density ρ1) and it floats because the weight of the water it displaces (which is still much lighter than itself) pushes it upwards. If you try adding too many heavy things on the sponge, it will sink because it can’t displace enough weight in water to remain afloat.

Problem Statement and Resolution

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A block of wood with density ρ1 is floating completely submerged. We can calculate the weights and volumes through the relationship of their densities, resulting in a series of equations to balance the forces.

Detailed Explanation

To solve problems involving buoyancy, first, visualize the situation, then identify the forces acting on the body. By establishing equilibrium (where the total upward buoyant force equals the total downward weight), you can derive relationships between the volumes and densities of the different fluids and the object. The calculations will often involve substituting known physics values and then simplifying equations to find unknowns, such as volume or density of the block.

Examples & Analogies

Consider a rubber duck in a bathtub. It displaces a certain amount of water equal to its own weight. If you add a weight to the rubber duck – say a paperclip – it still floats, but if you add too many paperclips, it will sink. The rubber duck's buoyant force can only support a certain amount of weight; beyond that, it can no longer equal the downward gravitational forces.

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Buoyant Force: The force acting upwards on a submerged object, equal to the weight of the displaced fluid.

  • Archimedes' Principle: The concept that the buoyant force is equal to the weight of the fluid displaced.

  • Density: The measure of mass per unit volume, significant in determining buoyant forces.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • Example of a boat floating on water demonstrates how buoyant forces keep it afloat.

  • A balloon in water displacing a certain volume of water while determining the buoyant force acting on it.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎵 Rhymes Time

  • If it's heavy and in water, but does not sink, It’s buoyant, just think before you blink!

📖 Fascinating Stories

  • Once there was a boat named Bob, no matter how much weight he bore, he always floated because he knew how to displace the right amount of water!

🧠 Other Memory Gems

  • Remember B.F. = VDVg for Buoyant Force = Volume * Density of Fluid * g!

🎯 Super Acronyms

Use **BAP** to recall

  • Buoyancy Acts Proportional - to the weight of the fluid displaced.

Flash Cards

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Glossary of Terms

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  • Term: Buoyant Force

    Definition:

    The upward force exerted on an object submerged in a fluid, equal to the weight of the fluid displaced by the object.

  • Term: Archimedes' Principle

    Definition:

    A principle stating that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid displaced.

  • Term: Density

    Definition:

    The mass per unit volume of a substance, commonly expressed in kg/m³.