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7857 results in Fluid dynamics and solid mechanics

Page 81 of 393

  • Preface

  • Arshad Noor Siddiquee, Zahid A. Khan, Pankul Goel
  • Book:
    Engineering Mechanics
    Published online:
    04 April 2019
    Print publication:
    16 March 2018, pp xiii-xiv

  • Summary

    Proper design and analysis of the elements of a structure, machine or installation is critical to its rigidity, safety, cost and reliability. With methods and materials of fabrication, construction and manufacturing changing rapidly, a lot of attention to design and analysis is required so that the system is robust yet cost effective. Further, ‘principles of mechanics’ is a foundation subject and its importance to several engineering disciplines cannot be overemphasized. A sound understanding of this subject is extremely useful during the analysis of complex problems in core engineering subjects. The subject deals with a variety of materials, in different geometries and loading configurations subjected to various types of loads. During this course, the learner needs to be presented cases similar to those encountered in real engineering problem-situations. This helps the student develop faculties to choose the right approach to analyze problems, situations and arrive at a correct solution.

    Due to the importance of engineering mechanics and its applications in many engineering disciplines, it is a part of common engineering curricula. The contents of this volume have been developed to match the syllabi of major universities. This treatise is organized to provide the basic concepts in the initial chapters; advancing to subsequent application of these concepts to a variety of situations encountered in engineering problem solving. The architecture of the volume makes it a self-sufficient introduction to the subject. The book begins with an introduction to basic building blocks of this subject, such as units, system of units of force and force systems. Representation, interaction and concatenation of forces in the Cartesian space are also dealt with. Concept of planar forces is developed through concurrent and non-concurrent forces in chapters 2 and 3. These chapters demonstrate articulation of forces and force systems to resolve forces, to work out resultants, and equilibrium conditions through free body diagrams. The concept and articulation of moments and couples is developed through forces and force systems. Forces and moments are further related to real applications by introducing beams and loading of beams.

    Apart from applied and incident forces as dealt with in the beginning, friction and related aspects are introduced in chapters 4 and 5. Forces induced due to friction, their estimation and articulation is presented in these chapters.

  • 15 - Kinematics of Rigid Bodies

  • Arshad Noor Siddiquee, Zahid A. Khan, Pankul Goel
  • Book:
    Engineering Mechanics
    Published online:
    04 April 2019
    Print publication:
    16 March 2018, pp 661-707

  • Summary

    Introduction

    So far, the motion of particles has been analyzed under kinematics and kinetics. Earlier, the rectilinear and curvilinear motion of a particle was studied in the chapter 10 and 11, respectively, where a body was idealized as a particle and does not have any rotational motion. However, in some cases we cannot make such assumptions where a body consists considerable rotary motion. In this chapter, we will analyse motion of rigid bodies having rotary and general plane motion for parameters like displacement, time, velocity and acceleration without cause of motion (force).

    Rotational Motion

    In this motion all the particles of a rigid body continuously rotate about a fixed axis. Here all the particles have parallel path in the plane of rotation. The examples are moving fan, pump, rotating shaft in a lathe machine and drilling operation, etc.

    Angular Displacement, Angular Velocity and Angular Acceleration

    Angular displacement is the displacement of a body on the plane of rotation about a fixed axis. It is a vector quantity and expressed in radians. For example, consider a link rotates clockwise about a fixed axis as shown in Fig. 15.1. If the link turns by angle θ during time t from OX-axis, the angular displacement of all particles on the link will be θ in clockwise direction. In one revolution the angular displacement of link will be equal to 2π radians.

    Angular Velocity is the rate by which angular displacement varies with respect to time. It is represented by ω. If a rotating body turns by angle dθ in time dt then angular velocity will be given by

    It is a vector quantity. The unit of angular velocity is rad/sec, however in engineering devices; it is expressed in r.p.m. (revolutions per minute).

    If the angular velocity is expressed in r.p.m. then it can be converted into rad/sec as follows:

    Consider a shaft rotating with N r.p.m.

    Then number of revolutions per second will be

    The angular displacement in one revolution of shaft will be 2π radians

    Thus total angular displacement per second will be

    Angular Acceleration is the rate at which angular velocity varies with respect to time. It is represented by α.

  • 10 - Kinematics: Rectilinear Motion of Particles

  • Arshad Noor Siddiquee, Zahid A. Khan, Pankul Goel
  • Book:
    Engineering Mechanics
    Published online:
    04 April 2019
    Print publication:
    16 March 2018, pp 498-528

  • Summary

    Introduction

    Previous chapters were concerned with the forces and reactions under which a body was held stationary; that branch of mechanics is called Statics. However, if the forces remained unbalanced, the body moves; this branch of mechanics is called Dynamics. It is further divided into two branches:

  • a. Kinematics that deals with the analysis of displacement, time, velocity and acceleration of a motion without reason of motion i.e., forces.

  • b. Kinetics that deals with the analysis of displacement, time, velocity, acceleration of a motion along with the forces causing motion. It also deals with the mass of the body and relationships between the forces acting on a body.

    • A body under motion can be idealized as a particle which is concentrated about its centre of gravity. It is assumed that a particle does not have rotational movement. However, if rotational movement of the body cannot be neglected then such body cannot be treated as particle.

    Displacement, Velocity and Acceleration

    Displacement is the minimum distance or smallest route travelled by a body from a starting point to the destination point along a straight line. It is a vector quantity as it is concerned with both magnitude and direction of motion.

    Consider a particle moves from origin point A to destination point B via different paths A-1-2-B, A-B and A-3-4-B as shown in Fig. 10.1. Here the smallest route A-B travelled along a straight line will be displacement. However the other route traversed by the body will be called distance which depends upon magnitude only and called a scalar quantity. Being vector quantity, the displacement can have positive or negative value but distance always has a positive quantity.

    Velocity of a body is described as the rate of change of displacement with respect to time. Velocity can be average velocity, instantaneous velocity and uniform velocity depending upon the variation of displacement and time.

    Average velocity: In the previous example if body travels displacement Δs during time interval Δt via path A-B then the average velocity is given by

    Instantaneous velocity: At a particular instant, the velocity of a body is known as Instantaneous velocity.

  • 11 - Kinematics: Curvilinear Motion of Particles

  • Arshad Noor Siddiquee, Zahid A. Khan, Pankul Goel
  • Book:
    Engineering Mechanics
    Published online:
    04 April 2019
    Print publication:
    16 March 2018, pp 529-559

  • Summary

    Introduction

    When the motion of a body takes place along a curved path, it is called curvilinear motion. The curvilinear motion is known as a two-dimensional motion as it takes place in the X–Y plane. The basic difference between rectilinear and curvilinear motion is that in a rectilinear motion, all particles of a body move parallel to each other along a straight line but in a curvilinear motion all particles move parallel to each other along a curved path in a common plane. Some common examples of curvilinear motion are as follows:

  • a. A vehicle passing over a speed breaker.

  • b. Turning of a vehicle along a curved path.

  • c. Motion of a ball during lofted six in cricket.

  • d. Motion of missile fired from a fighter plane.

  • e. Oscillatory motion of a pendulum.

    • Rectangular Coordinates

    This system is used to analyse the curvilinear motion of a particle moving in X–Y plane. Here the velocity and acceleration are resolved in two perpendicular components along X and Y axis. The resultant value of velocity and acceleration can be determined by using vector approach or combining its components as discussed below:

    Velocity: Consider a ball during lofted six, it consists two types of motions, one rotary motion and another curvilinear motion. Here the rotary motion is neglected and assumed that all particles of ball will travel with same displacement, velocity and acceleration. Consider a displacement-time graph where a particle is moving along a curved path in X–Y plane. Let at any instant t, particle has position A. If particle moves from point A to B by displacement Δs during time interval Δt as shown in Fig. 11.1.

    We know that the instantaneous velocity is given by

    The above equation provides instantaneous velocity by using vector approach. It can also obtained from its components,

    Acceleration: Consider velocity–time graph where a particle is moving along a curved path in the X–Y plane. Let at any instant t, particle has velocity v. During motion from point A to B, if velocity of particle increases by Δv in time interval Δt as shown in Fig. 11.2.

Engineering Mechanics
  • Problems and Solutions
  • Arshad Noor Siddiquee, Zahid A. Khan, Pankul Goel
  • Published online:
    04 April 2019
    Print publication:
    16 March 2018
  • This comprehensive and self-contained textbook will help students in acquiring an understanding of fundamental concepts and applications of engineering mechanics. With basic prior knowledge, the readers are guided through important concepts of engineering mechanics such as free body diagrams, principles of the transmissibility of forces, Coulomb's law of friction, analysis of forces in members of truss and rectilinear motion in horizontal direction. Important theorems including Lami's theorem, Varignon's theorem, parallel axis theorem and perpendicular axis theorem are discussed in a step-by-step manner for better clarity. Applications of ladder friction, wedge friction, screw friction and belt friction are discussed in detail. The textbook is primarily written for undergraduate engineering students in India. Numerous theoretical questions, unsolved numerical problems and solved problems are included throughout the text to develop a clear understanding of the key principles of engineering mechanics. This text is the ideal resource for first year engineering undergraduates taking an introductory, single-semester course in engineering mechanics.

Page 81 of 393