Chapter 1 Introduction and Basic Concepts PROPRIETARY MATERIAL . © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparati on. If you are a student using this Manual, you are using it wit hout permission. 1-1 Solutions Manual for Fluid Mechanics: Fundamentals and Applications by Çengel & Cimbala CHAPTER 1 INTRODUCTION AND BASIC CONCEPTS PROPRIETARY AND CONFIDENTIAL This Manual is the proprietary propert y of The McGraw-Hill Companies, Inc. (“McGraw-Hill”) and protected by copyright and other state and federal laws. By opening and using this Manual the user agrees to the following restrictions, and if the recipient does not agree to these restricti ons, the Manual should be promptly returned unopened to McGraw-Hill: This Manual is being provided only to authorized professors and instructors for use in prep aring for the classes using the affiliated textbook. No other use or distribution of this Manual is permitted. This Manual may not be sold and may not be distribute d to or used by any student or other third party. No part of this Manual m ay be reproduced, displayed or distributed in any form or by any means, electroni c or otherwise, without the prior written permission of McGraw-Hill. Chapter 1 Introduction and Basic Concepts PROPRIETARY MATERIAL Introduction, Classification, and System 1-1C Solution We are to define internal, external, and open-channel flows. Analysis External flow is the flow of an unbounded fluid over a surface such as a plate, a wire, or a pipe. The flow in a pipe or duct is internal flow if the fluid is completely bounded by solid surfaces . The flow of liquids in a pipe is called open-channel flow if the pipe is partially filled with the liqui d and there is a free surface , such as the flow of water in rivers and irrigation ditches. Discussion As we shall see in later chapters, there different appr oximations are used in the analysis of fluid flows based on their classification. 1-2C Solution We are to define incompressible and compressible flow, and discuss fluid compressibility. Analysis A fluid flow during which the density of the fluid remains nearly constant is called incompressible flow . A flow in which density varies significantly is called compressible flow . A fluid whose density is practically independent of pressure (such as a liquid) is commonly referred to as an “incompressible fluid,” although it is more proper to refer to incompressible flow. The flow of compressible fluid (such as air) does not necessarily need to be treated as compressible since the density of a compressible fluid may still remain near ly constant during flow – especially flow at low speeds. Discussion It turns out that the Mach number is the critical para meter to determine whether the flow of a gas can be approximated as an incompressible flow. If Ma is less than about 0.3, the incompressible approximation yields results that are in error by less than a couple percent. 1-3C Solution We are to define the no-slip condition and its cause. Analysis A fluid in direct contact with a solid surface sticks to the surface and there is no slip . This is known as the no-slip condition , and it is due to the viscosity of the fluid. Discussion There is no such thing as an inviscid fluid, since all fluids have viscosity. 1-4C Solution We are to define forced flow and discuss the differe nce between forced and natu ral flow. We are also to discuss whether wind-driven flows are forced or natural. Analysis In forced flow, the fluid is forced to flow over a surface or in a tube by external means such as a pump or a fan. In natural flow , any fluid motion is caused by natural means such as the buoyancy effect that manifests itself as the rise of the warmer fluid and the fall of the cooler fluid. The flow caused by winds is natura l flow for the earth, but it is forced flow for bodies subjected to the winds since for the body it makes no difference whether the air motion is caused by a fan or by the winds. Discussion As seen here, the classification of forced vs. natural flow may de pend on your frame of reference. . © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparati on. If you are a student using this Manual, you are using it wit hout permission. 1-2 Chapter 1 Introduction and Basic Concepts PROPRIETARY MATERIAL . © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparati on. If you are a student using this Manual, you are using it wit hout permission. 1-31-5C Solution We are to define a boundary layer, and discuss its cause. Analysis When a fluid stream encounters a solid surface that is at rest, the fluid velocity assumes a value of zero at that surface. The velocity then varies from zero at the surface to the freestr eam value sufficiently fa r from the surface. The region of flow in which the velocity gradients are significant and frictional effects are important is called the boundary layer . The development of a boundary layer is caused by the no-slip condition . Discussion As we shall see later, flow within a boundary layer is rotational (individual fluid particles rotate), while that outside the boundary layer is typically irrotational (individual fluid particles move, but do not rotate). 1-6C Solution We are to discuss the differences between classical and statistical approaches. Analysis The classical approach is a macroscopic approach , based on experiments or analysis of the gross behavior of a fluid, without knowledge of individual molecules, whereas the statistical approach is a microscopic approach based on the average behavior of large groups of individual molecules. Discussion The classical approach is easier and mu ch more common in fluid flow analysis. 1-7C Solution We are to define a steady-flow process. Analysis A process is said to be steady if it involves no changes with time anywhere within th e system or at the system boundaries. Discussion The opposite of steady flow is unsteady flow , which involves changes with time. 1-8C Solution We are to define stress, normal st ress, shear stress, and pressure. Analysis Stress is defined as force per unit area , and is determined by dividing the force by the area upon which it acts. The normal component of a force acting on a surface per unit area is called the normal stress , and the tangential component of a force acting on a surface per unit area is called shear stress . In a fluid at rest, the normal stress is called pressure . Discussion Fluids in motion may have additional normal stresses, but when a fluid is at rest, the only normal stress is the pressure. 1-9C Solution We are to define system, surroundings, and boundary. Analysis A system is defined as a quantity of matter or a region in space chosen for study . The mass or region outside the system is called the surroundings . The real or imaginary surface that separates the system from its surroundings is called the boundary . Discussion Some authors like to define closed systems and open systems , while others use the notation “system” to mean a closed system and “control volume” to mean an open sy stem. This has been a source of confusion for students for many years. [See the next question for further discussion about this.]
