, Chapter 1 Introduction and Basic Concepts
Introduction, Classification, and System
1-1C
Solution We are to define a fluid and how it differs between a solid and a gas.
Analysis A substance in the liquid or gas phase is referred to as a fluid. A fluid differs from a solid in that a
solid can resist an applied shear stress by deforming, whereas a fluid deforms continuously under the influence of shear
stress, no matter how small. A liquid takes the shape of the container it is in, and a liquid forms a free surface in a larger
container in a gravitational field. A gas, on the other hand, expands until it encounters the walls of the container and fills
the entire available space.
Discussion The subject of fluid mechanics deals with ball fluids, both gases and liquids.
1-2C
Solution We are to determine whether the flow of air over the wings of an aircraft and the flow of gases through a jet
engine is internal or external.
Analysis The flow of air over the wings of an aircraft is external since this is an unbounded fluid flow over a
surface. The flow of gases through a jet engine is internal flow since the fluid is completely bounded by the solid surfaces
of the engine.
Discussion If we consider the entire airplane, the flow is both internal (through the jet engines) and external (over the
body and wings).
1-3C
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.
1-4C
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, different approximations are used in the analysis of fluid flows based on
their classification.
1-2
PROPRIETARY MATERIAL. © 2013 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 the Mach number of a flow and the meaning for a Mach number of 2.
Analysis The Mach number of a flow is defined as the ratio of the speed of flow to the speed of sound in the
flowing fluid. A Mach number of 2 indicate a flow speed that is twice the speed of sound in that fluid.
Discussion Mach number is an example of a dimensionless (or nondimensional) parameter.
1-6C
Solution We are to discuss if the Mach number of a constant-speed airplane is constant.
Analysis No. The speed of sound, and thus the Mach number, changes with temperature which may change
considerably from point to point in the atmosphere.
1-7C
Solution We are to determine if the flow of air with a Mach number of 0.12 should be approximated as
incompressible.
Analysis Gas flows can often be approximated as incompressible if the density changes are under about 5 percent,
which is usually the case when Ma < 0.3. Therefore, air flow with a Mach number of 0.12 may be approximated as being
incompressible.
Discussion Air is of course a compressible fluid, but at low Mach numbers, compressibility effects are insignificant.
1-8C
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.
1-9C
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.
1-3
PROPRIETARY MATERIAL. © 2013 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 define a boundary layer, and discuss its cause.
Analysis The region of flow (usually near a wall) in which the velocity gradients are significant and frictional
effects are important is called the boundary layer. 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 some larger value
sufficiently far from the surface. 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).
1-11C
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.
1-12C
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.
1-13C
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 both shear stresses and additional normal stresses besides pressure, but when a
fluid is at rest, the only normal stress is the pressure, and there are no shear stresses.
1-14C
Solution We are to discuss how to select system when analyzing the acceleration of gases as they flow through a
nozzle.
Analysis When analyzing the acceleration of gases as they flow through a nozzle, a wise choice for the system is the
volume within the nozzle, bounded by the entire inner surface of the nozzle and the inlet and outlet cross-sections. This is a
control volume (or open system) since mass crosses the boundary.
Discussion It would be much more difficult to follow a chunk of air as a closed system as it flows through the nozzle.
1-4
PROPRIETARY MATERIAL. © 2013 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.
Introduction, Classification, and System
1-1C
Solution We are to define a fluid and how it differs between a solid and a gas.
Analysis A substance in the liquid or gas phase is referred to as a fluid. A fluid differs from a solid in that a
solid can resist an applied shear stress by deforming, whereas a fluid deforms continuously under the influence of shear
stress, no matter how small. A liquid takes the shape of the container it is in, and a liquid forms a free surface in a larger
container in a gravitational field. A gas, on the other hand, expands until it encounters the walls of the container and fills
the entire available space.
Discussion The subject of fluid mechanics deals with ball fluids, both gases and liquids.
1-2C
Solution We are to determine whether the flow of air over the wings of an aircraft and the flow of gases through a jet
engine is internal or external.
Analysis The flow of air over the wings of an aircraft is external since this is an unbounded fluid flow over a
surface. The flow of gases through a jet engine is internal flow since the fluid is completely bounded by the solid surfaces
of the engine.
Discussion If we consider the entire airplane, the flow is both internal (through the jet engines) and external (over the
body and wings).
1-3C
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.
1-4C
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, different approximations are used in the analysis of fluid flows based on
their classification.
1-2
PROPRIETARY MATERIAL. © 2013 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 the Mach number of a flow and the meaning for a Mach number of 2.
Analysis The Mach number of a flow is defined as the ratio of the speed of flow to the speed of sound in the
flowing fluid. A Mach number of 2 indicate a flow speed that is twice the speed of sound in that fluid.
Discussion Mach number is an example of a dimensionless (or nondimensional) parameter.
1-6C
Solution We are to discuss if the Mach number of a constant-speed airplane is constant.
Analysis No. The speed of sound, and thus the Mach number, changes with temperature which may change
considerably from point to point in the atmosphere.
1-7C
Solution We are to determine if the flow of air with a Mach number of 0.12 should be approximated as
incompressible.
Analysis Gas flows can often be approximated as incompressible if the density changes are under about 5 percent,
which is usually the case when Ma < 0.3. Therefore, air flow with a Mach number of 0.12 may be approximated as being
incompressible.
Discussion Air is of course a compressible fluid, but at low Mach numbers, compressibility effects are insignificant.
1-8C
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.
1-9C
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.
1-3
PROPRIETARY MATERIAL. © 2013 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 define a boundary layer, and discuss its cause.
Analysis The region of flow (usually near a wall) in which the velocity gradients are significant and frictional
effects are important is called the boundary layer. 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 some larger value
sufficiently far from the surface. 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).
1-11C
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.
1-12C
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.
1-13C
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 both shear stresses and additional normal stresses besides pressure, but when a
fluid is at rest, the only normal stress is the pressure, and there are no shear stresses.
1-14C
Solution We are to discuss how to select system when analyzing the acceleration of gases as they flow through a
nozzle.
Analysis When analyzing the acceleration of gases as they flow through a nozzle, a wise choice for the system is the
volume within the nozzle, bounded by the entire inner surface of the nozzle and the inlet and outlet cross-sections. This is a
control volume (or open system) since mass crosses the boundary.
Discussion It would be much more difficult to follow a chunk of air as a closed system as it flows through the nozzle.
1-4
PROPRIETARY MATERIAL. © 2013 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.
