Chapter 1 Introduction and Basic Concepts
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 property 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 restrictions, the Manual should be promptly returned
unopened to McGraw-Hill: This Manual is being provided only to authorized
professors and instructors for use in preparing 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 distributed to or used by any student or other
third party. No part of this Manual may be reproduced, displayed or distributed
in any form or by any means, electronic or otherwise, without the prior written
permission of McGraw-Hill.
1-1
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to
teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.
, Chapter 1 Introduction and Basic Concepts
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 liquid 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 approximations 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 nearly constant during flow – especially flow at low speeds.
Discussion It turns out that the Mach number is the critical parameter 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 difference between forced and natural 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 natural 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 depend on your frame of reference.
1-2
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to
teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.
, Chapter 1 Introduction and Basic Concepts
1-5C
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 freestream value sufficiently far 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 much 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 the 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 stress, 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 system. This has been a source of confusion for students for
many years. [See the next question for further discussion about this.]
1-3
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to
teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.
, Chapter 1 Introduction and Basic Concepts
1-10C
Solution We are to discuss when a system is considered closed or open.
Analysis Systems may be considered to be closed or open, depending on whether a fixed mass or a volume in space
is chosen for study. A closed system (also known as a control mass or simply a system) consists of a fixed amount of
mass, and no mass can cross its boundary. An open system, or a control volume, is a properly selected region in space.
Discussion In thermodynamics, it is more common to use the terms open system and closed system, but in fluid
mechanics, it is more common to use the terms system and control volume to mean the same things, respectively.
Mass, Force, and Units
1-11C
Solution We are to discuss the difference between pound-mass and pound-force.
Analysis Pound-mass lbm is the mass unit in English system whereas pound-force lbf is the force unit in the
English system. One pound-force is the force required to accelerate a mass of 32.174 lbm by 1 ft/s2. In other words, the
weight of a 1-lbm mass at sea level on earth is 1 lbf.
Discussion It is not proper to say that one lbm is equal to one lbf since the two units have different dimensions.
1-12C
Solution We are to discuss the difference between kg-mass and kg-force.
Analysis The unit kilogram (kg) is the mass unit in the SI system, and it is sometimes called kg-mass, whereas kg-
force (kgf) is a force unit. One kg-force is the force required to accelerate a 1-kg mass by 9.807 m/s2. In other words, the
weight of 1-kg mass at sea level on earth is 1 kg-force.
Discussion It is not proper to say that one kg-mass is equal to one kg-force since the two units have different
dimensions.
1-13C
Solution We are to calculate the net force on a car cruising at constant velocity.
Analysis There is no acceleration, thus the net force is zero in both cases.
Discussion By Newton’s second law, the force on an object is directly proportional to its acceleration. If there is zero
acceleration, there must be zero net force.
1-4
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to
teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.
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 property 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 restrictions, the Manual should be promptly returned
unopened to McGraw-Hill: This Manual is being provided only to authorized
professors and instructors for use in preparing 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 distributed to or used by any student or other
third party. No part of this Manual may be reproduced, displayed or distributed
in any form or by any means, electronic or otherwise, without the prior written
permission of McGraw-Hill.
1-1
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to
teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.
, Chapter 1 Introduction and Basic Concepts
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 liquid 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 approximations 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 nearly constant during flow – especially flow at low speeds.
Discussion It turns out that the Mach number is the critical parameter 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 difference between forced and natural 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 natural 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 depend on your frame of reference.
1-2
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to
teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.
, Chapter 1 Introduction and Basic Concepts
1-5C
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 freestream value sufficiently far 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 much 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 the 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 stress, 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 system. This has been a source of confusion for students for
many years. [See the next question for further discussion about this.]
1-3
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to
teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.
, Chapter 1 Introduction and Basic Concepts
1-10C
Solution We are to discuss when a system is considered closed or open.
Analysis Systems may be considered to be closed or open, depending on whether a fixed mass or a volume in space
is chosen for study. A closed system (also known as a control mass or simply a system) consists of a fixed amount of
mass, and no mass can cross its boundary. An open system, or a control volume, is a properly selected region in space.
Discussion In thermodynamics, it is more common to use the terms open system and closed system, but in fluid
mechanics, it is more common to use the terms system and control volume to mean the same things, respectively.
Mass, Force, and Units
1-11C
Solution We are to discuss the difference between pound-mass and pound-force.
Analysis Pound-mass lbm is the mass unit in English system whereas pound-force lbf is the force unit in the
English system. One pound-force is the force required to accelerate a mass of 32.174 lbm by 1 ft/s2. In other words, the
weight of a 1-lbm mass at sea level on earth is 1 lbf.
Discussion It is not proper to say that one lbm is equal to one lbf since the two units have different dimensions.
1-12C
Solution We are to discuss the difference between kg-mass and kg-force.
Analysis The unit kilogram (kg) is the mass unit in the SI system, and it is sometimes called kg-mass, whereas kg-
force (kgf) is a force unit. One kg-force is the force required to accelerate a 1-kg mass by 9.807 m/s2. In other words, the
weight of 1-kg mass at sea level on earth is 1 kg-force.
Discussion It is not proper to say that one kg-mass is equal to one kg-force since the two units have different
dimensions.
1-13C
Solution We are to calculate the net force on a car cruising at constant velocity.
Analysis There is no acceleration, thus the net force is zero in both cases.
Discussion By Newton’s second law, the force on an object is directly proportional to its acceleration. If there is zero
acceleration, there must be zero net force.
1-4
PROPRIETARY MATERIAL. © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to
teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.
