/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 26 An ideal fluid flows through a p... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 26

An ideal fluid flows through a pipe of variable cross section without any friction. The fluid completely fills the pipe. At any given point in the pipe, the fluid has a constant A. kinetic energy. B. potential energy. C. total energy. D. velocity. E. pressure.

Short Answer

Expert verified
The correct answer is option C. According to the Bernoulli's principle, the total energy (sum of kinetic energy, potential energy and internal energy) of an ideal fluid flowing in a pipe is constant.

Step by step solution

01

- Understanding Bernoulli's Principle

Bernoulli's principle states that an increase in the speed of the fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. So when the speed of the fluid increases, the pressure decreases and vice versa.
02

- Mapping to the alternatives

Applying Bernoulli's principle with the given options, we will consider the various aspects of a fluid flowing in a pipe. The kinetic energy changes with varying speed as the cross-section changes, so option A is incorrect. The potential energy varies as it is inversely proportional to speed, so option B is incorrect. The velocity changes as per the cross-section of the pipe, so option D is incorrect. Pressure changes based on velocity due to Bernoulli's principle, so option E is incorrect.
03

- Choose the correct answer

The total energy, however, is constant at any given point according to Bernoulli's principle since it is the sum of kinetic, potential and internal energy of the fluid. Therefore, option C is the correct answer as it states that the total energy of the fluid is constant at any given point in the pipe.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fluid Dynamics
Fluid dynamics is a branch of physics concerned with the study of fluids (liquids and gases) in motion. It plays an essential role in understanding how fluids interact with their surroundings.
Several principles help explain fluid motion, including Bernoulli's Principle and the continuity equation. Fluid dynamics allows us to predict how fluids flow through pipes, over surfaces, and around obstacles.
Key concepts in fluid dynamics include:
  • Flow Rate: The quantity of fluid that passes a point per unit time.
  • Velocity Fields: Describe how fluid speed and direction vary in space.
  • Pressure Distribution: How pressure changes in different parts of a fluid.
By understanding these aspects, engineers can design systems like pipelines, irrigation channels, and air ventilation with higher efficiency.
Conservation of Energy
The principle of conservation of energy states that energy in a closed system remains constant over time. In fluid dynamics, this principle is often illustrated through Bernoulli's equation.
Bernoulli's equation expresses conservation of energy for ideal fluid flow, demonstrating that:
  • The kinetic energy per unit volume of a fluid.
  • The potential energy per unit volume due to gravity.
  • The flow work done per unit volume due to pressure.
Together, these energies remain constant, showing how energy transformation occurs without losses in an ideal system.
This means that as fluid moves through a changing cross section, speeds up, or gains height, energy merely shifts from one form to another rather than disappearing.
Ideal Fluid Flow
In fluid dynamics, ideal fluid flow refers to a theoretical concept where the fluid is considered to possess no viscosity and experiences no flow resistance. This simplification allows for easier mathematical analysis of fluid behavior.
An ideal fluid is also incompressible and non-turbulent, meaning:
  • No Viscosity: The fluid's layers shift with no internal friction.
  • Incompressibility: The fluid's density remains constant irrespective of pressure changes.
  • Steady Flow: Fluid properties at a point do not change over time.
This model is useful for applying Bernoulli's Principle and the Continuity Equation, simplifying complex real-world fluid systems for analysis and prediction.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A crown that is supposed to be made of solid gold is under suspicion. When the crown is weighed in air it has a weight of \(5.15 \mathrm{~N}\). When it is suspended from a digital balance and lowered into water, its apparent weight is measured to be \(4.88 \mathrm{~N}\). Given that the specific gravity of gold is \(19.3\), comment on the authenticity of the crown. SSM

A rectangular block of wood, \(10 \mathrm{~cm} \times 15 \mathrm{~cm} \times 40 \mathrm{~cm}\), has a specific gravity of \(0.6\). (a) Determine the buoyant force that acts on the block when it is placed in a pool of freshwater. Hint: Draw a free-body diagram labeling all of the forces on the block. (b) What fraction of the block is submerged? (c) Determine the weight of the water that is displaced by the block.

An elephant that has a mass of \(6000 \mathrm{~kg}\) evenly distributes her weight on all four feet. (a) If her feet are approximately circular and each has a diameter of \(50 \mathrm{~cm}\), estimate the pressure on each foot. (b) Compare the answer in part (a) with the pressure on each of your feet when you are standing up. Make some rough but reasonable assumptions about the area of your feet.

Water flows from a fire truck through a hose that is \(11.7 \mathrm{~cm}\) in diameter and has a nozzle that is \(2 \mathrm{~cm}\) in diameter. The firemen stand on a hill \(5 \mathrm{~m}\) above the level of the truck. When the water leaves the nozzle, it has a speed of \(20 \mathrm{~m} / \mathrm{s}\). Determine the minimum gauge pressure in the truck's water tank.

Medical Usually blood pressure is measured on the arm at the same level as the heart. How would the results differ if the measurement were made on the leg instead?
See all solutions

Recommended explanations on Physics Textbooks

Waves Physics

Read Explanation

Atoms and Radioactivity

Read Explanation

Fluids

Read Explanation

Radiation

Read Explanation

Particle Model of Matter

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.