Book cover for Applied Physics

Applied Physics

Dale Ewen, Neil Schurter, P. Erik Gundersen

ISBN #9780134159386

11th Edition

2,119 Questions

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18,063 Students Helped

Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter focuses on the behavior of fluids and the fundamental principles that govern their use in technology and everyday life. Key concepts include hydrostatic pressure, which is calculated using depth and weight density, and the hydraulic principle that underpins many practical applications, from vehicle brake systems to hydroelectric power plants. Understanding how to calculate pressure, force, and buoyancy forms the basis for analyzing more complex fluid dynamics, including fluid flow and Bernoulli’s principle.

Learning Objectives

1

Describe the behavior of fluids and understand their common properties.

2

Determine hydrostatic pressure and calculate pressure at various depths using the formula P = hDw.

3

Differentiate between gauge pressure and absolute pressure in fluid systems.

4

Calculate buoyant force using Archimedes’ principle and analyze fluid flow using Bernoulli’s principle.

5

Apply the hydraulic (Pascal’s) principle to solve real-world problems such as dam design and water supply systems.

Key Concepts

CONCEPT

DEFINITION

Fluid

A substance that flows, which includes both liquids and gases, sharing similar behavior in terms of pressure and flow.

Hydrostatic Pressure

The pressure exerted by a fluid at rest on a submerged object, which depends mainly on the depth and weight density of the fluid.

Weight Density (Dw)

The weight per unit volume of a fluid; it is a key factor in calculating hydrostatic pressure.

Gauge Pressure

Pressure measured relative to the ambient atmospheric pressure.

Absolute Pressure

Pressure measured relative to a perfect vacuum (zero pressure); it is the sum of gauge pressure and atmospheric pressure.

Buoyancy (Archimedes’ Principle)

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

Bernoulli’s Principle

A principle stating that in a steady flow, an increase in the fluid’s speed occurs simultaneously with a decrease in pressure or potential energy.

Hydraulic (Pascal’s) Principle

A principle stating that pressure applied to a confined fluid is transmitted undiminished to every portion of the fluid and the walls of the container.

Example Problems

Example 1

Find the pressure (in $\mathrm{lb} / \mathrm{in}^{2}$ ) at the bottom of a tower with water $50.0 \mathrm{ft}$ deep.

Example 2

Find the height of a column of water where the pressure at the bottom of the column is $20.0 \mathrm{lb} / \mathrm{in}^{2}$

Example 3

Find the density of a liquid that exerts a pressure of $0.400 \mathrm{lb} / \mathrm{in}^{2}$ at a depth of 42.0 in.

Example 4

(a) Find the total force on the bottom of a water-filled circular cattle tank $0.750 \mathrm{~m}$ high with radius $1.30 \mathrm{~m}$ where the weight density of water is $98 \overline{0} 0 \mathrm{~N} / \mathrm{m}^{3}$ (b) Find the total force on the side of the tank.

Example 5

What must the water pressure be to supply water to the third floor of a building (35.0 ft up) with a pressure of $40.0 \mathrm{lb} / \mathrm{in}^{2}$ at that level?
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Step-by-Step Explanations

QUESTION

Find the pressure at the bottom of a water-filled drum that is 4.00 ft high with a water weight density of 62.4 lb/ftÂł.

STEP-BY-STEP ANSWER:

Step 1: Identify the formula P = hDw, where h is the height (or depth) and Dw is the weight density.
Step 2: Substitute the given values into the equation: h = 4.00 ft, Dw = 62.4 lb/ftÂł.
Step 3: Calculate the pressure: P = 4.00 ft * 62.4 lb/ft³ = 249.6 lb/ft².
Step 4: Convert the pressure from lb/ft² to lb/in² if desired (1 ft² = 144 in²), then P = 249.6 lb/ft² ÷ 144 ≈ 1.74 lb/in².
Final Answer: The pressure at the bottom is approximately 1.74 lb/in².

Hydrostatic Pressure Calculation

QUESTION

Find the depth in a lake if the pressure is 105 lb/in² given a weight density of 62.4 lb/ft³.

STEP-BY-STEP ANSWER:

Step 1: Write the formula for hydrostatic pressure, P = hDw.
Step 2: Rearrange the formula to solve for depth: h = P / Dw.
Step 3: Ensure units are consistent. Here, convert 105 lb/in² to lb/ft² by multiplying by 144 (since 1 ft² = 144 in²), so P becomes 105 * 144 = 15120 lb/ft².
Step 4: Substitute into the equation: h = 15120 lb/ft² á 62.4 lb/ft³.
Step 5: Calculate h: h ≈ 242 ft.
Final Answer: The depth of the lake is approximately 242 ft.

Determining Depth from Pressure

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Common Mistakes

  • Using the container’s area or width as a variable in pressure calculations, even though pressure depends solely on the depth of the fluid.
  • Forgetting to convert units properly (for instance, mixing up lb/ft² with lb/in² or N/mÂł with other units).
  • Confusing gauge pressure with absolute pressure by neglecting the role of atmospheric pressure.
  • Misapplying the formula for buoyancy or overlooking the principle that force is transmitted undiminished in a confined fluid.