FLUID MECHANICS MC/EL/RN/ES/GL/MN/MR/PE 264
CHAPTER 1
BASIC CONCEPTS AND FLUID PROPERTIES
1.1 Why Study Fluid Mechanics?
Fluid mechanics is highly relevant to our daily life. We live in the world full of fluids.
Fluid mechanics covers many areas such as meteorology, oceanography,
aerodynamics, biomechanics, hydraulics, mechanical engineering, civil engineering,
naval architecture engineering, etc. It does not only explain scientific phenomena but
also leads industrial applications. To fully understand the importance of fluid
mechanics, consider the following examples:
We are often challenged with problems involving water. Design of aqueducts to
transport water from one place to another is possible through the knowledge of
fluid mechanics. Removal of waste water from towns for the purpose of ensuring
cleanliness can be achieved through the study of fluid mechanics. Finally,
engineers developed water treatment technologies to get rid of waterborne
diseases to remove other forms of hazards.
To come up with other means of transport, the Wright brothers applied the
knowledge from engineering fluid mechanics to develop the world’s first airplane
(flying machine). Later (1940s), engineers designed practical jet engines to make
this means of transport more possible.
By way of ensuring that homes get access to electrical power, engineers
developed technologies including the water turbine, the wind turbine, the
electric generator, the motor and the electric grid system.
Most of our farming activities demand that we keep supplying water to keep
them alive. For instance, engineers designed the irrigation system to supply to
our vegetables and other plants of interest.
It can be seen from above that with knowledge in fluid mechanics, engineers can solve
problems and come up with innovative ideas that can lead to development or
improvement of technology.
1.2 What then is Fluid Mechanics?
It is the science that deals with the action of forces on fluids either at rest (fluid statics)
or in motion (fluid dynamics) and their effects on boundaries such as solid surfaces or
interfaces with other fluids.
The subject of fluid mechanics can be subdivided into two (2) broad categories:
Hydrodynamics
INSTRUCTORS: E. ADAZE/ DR. M. OSMAN 1
,FLUID MECHANICS MC/EL/RN/ES/GL/MN/MR/PE 264
Gas dynamics
Hydrodynamics deals with the flow of fluids for which there is virtually no density
change. Examples include flow of liquids and flow of gases at low speeds. Gas dynamics
deals with fluid that undergo significant density changes. Examples are high-speed flows
of a gas through a nozzles and the movement of a body through the low density air of
the upper atmosphere.
Another area of fluid mechanics is aerodynamics which deals with the flow of air past
aircraft or rockets.
1.3 What is a Fluid?
A fluid is defined as a substance that will continuously deform – that is, flow under the
action of a shear stress (no matter how small that stress may be) causing its constituent
particles to continuously change their positions relative to one another. The rate of
deformation (strain) of a fluid is related to the applied shear stress by a property called
viscosity.
A fluid can be either a gas or a liquid. The differences in behaviour of solids, liquids
and gases are due to the differences in their molecular structures.
In solids, the molecules have definite spacing. Their movement is restricted. As a result,
solids have definite volume and shape. In liquids, the spacing between the molecules is
essentially constant but the molecules can move with respect to each other when a
shearing force is applied. Therefore, liquids have definite volume but no definite shape.
Finally, in gases, the spacing between the molecules is much wider than that of either
solids or liquids. The spacing is also variable (keeps changing). Therefore, gases have
neither definite shape nor definite volume. Table 1.1 gives a summary on the
comparison of solids, liquids and gases.
INSTRUCTORS: E. ADAZE/ DR. M. OSMAN 2
,FLUID MECHANICS MC/EL/RN/ES/GL/MN/MR/PE 264
Table 1.1 Differences between Solids, Liquids and Gases
From Table 1.1, it can be seen that a liquid is difficult to compress because the
molecules will repulsive forces if they are brought close together. It changes its shape
according to the shape of its container with an upper free surface. However, a gas is
easy to compress because there are no forces (on average) between the molecules and
expands to fill its container. There is thus no free surface.
Consequently, an important characteristic of a fluid from the viewpoint of fluid
mechanics is its compressibility. Another characteristic is its velocity. Whereas a solid
shows its elasticity in tension, compression or shear stress, a fluid does so only for
compression. In other words, a fluid increases its pressure against compression, trying
to retain its original volume. This characteristic is called compressibility. Furthermore,
a fluid shows resistance whenever two layers slide over each other. The characteristic
is called viscosity.
In general, liquids are called incompressible fluids and gases compressible fluids.
Nevertheless, for liquids, compressibility must be taken into account whenever they are
highly pressurized, and for gases, compressibility may be disregarded whenever the
INSTRUCTORS: E. ADAZE/ DR. M. OSMAN 3
, FLUID MECHANICS MC/EL/RN/ES/GL/MN/MR/PE 264
changes in pressure is small. Although a fluid is an aggregate of molecules in constant
motion, it is treated as a continuous isotropic substance.
Meanwhile, a non-existent, assumed fluid without either viscosity or compressibility is
called an ideal fluid or perfect fluid. A fluid with compressibility but without viscosity is
occasionally discriminated and called a perfect fluid, too. Furthermore, a gas subject to
Boyle’s-Charles’ law is called a perfect or ideal gas.
1.4 The Ideal Gas Law (IGL)
Application of the ideal gas law (IGL) is very common in fluid mechanics. For instance,
in the design of products like air bags, shock absorbers, combustion systems and
aircraft. The IGL is the result of combining three empirical equations previously
developed by Boyle, Charles and Avogadro. These empirical equations are respectively
known as Boyles’s law, Charles law and Avogadro’s law. The equation of state of IGL
is of the form:
p RT (1.1)
where, p is absolute pressure; T is absolute temperature; is fluid density; R is gas
constant which is related to the universal gas constant Ru as follows:
R
R u (1.2)
M
where, M is molar mass (molecular weight). The universal gas constant ( Ru) is usually
taken as 8.314 kJ/kmol K.
1.5 Pascal’s Law
For a given closed system, a pressure change produced at one point in the system will
be transmitted throughout the entire system. This is known as Pascal’s law. See Figure
1.1 for illustration.
Figure 1.1 Concept of Pascal’s Law
Pressures applied to point 1 and point 2 are equal in terms of Pascal’s law. Therefore,
applying force F1 to the smaller area at point 1 will produce a larger force F2 on the
INSTRUCTORS: E. ADAZE/ DR. M. OSMAN 4
CHAPTER 1
BASIC CONCEPTS AND FLUID PROPERTIES
1.1 Why Study Fluid Mechanics?
Fluid mechanics is highly relevant to our daily life. We live in the world full of fluids.
Fluid mechanics covers many areas such as meteorology, oceanography,
aerodynamics, biomechanics, hydraulics, mechanical engineering, civil engineering,
naval architecture engineering, etc. It does not only explain scientific phenomena but
also leads industrial applications. To fully understand the importance of fluid
mechanics, consider the following examples:
We are often challenged with problems involving water. Design of aqueducts to
transport water from one place to another is possible through the knowledge of
fluid mechanics. Removal of waste water from towns for the purpose of ensuring
cleanliness can be achieved through the study of fluid mechanics. Finally,
engineers developed water treatment technologies to get rid of waterborne
diseases to remove other forms of hazards.
To come up with other means of transport, the Wright brothers applied the
knowledge from engineering fluid mechanics to develop the world’s first airplane
(flying machine). Later (1940s), engineers designed practical jet engines to make
this means of transport more possible.
By way of ensuring that homes get access to electrical power, engineers
developed technologies including the water turbine, the wind turbine, the
electric generator, the motor and the electric grid system.
Most of our farming activities demand that we keep supplying water to keep
them alive. For instance, engineers designed the irrigation system to supply to
our vegetables and other plants of interest.
It can be seen from above that with knowledge in fluid mechanics, engineers can solve
problems and come up with innovative ideas that can lead to development or
improvement of technology.
1.2 What then is Fluid Mechanics?
It is the science that deals with the action of forces on fluids either at rest (fluid statics)
or in motion (fluid dynamics) and their effects on boundaries such as solid surfaces or
interfaces with other fluids.
The subject of fluid mechanics can be subdivided into two (2) broad categories:
Hydrodynamics
INSTRUCTORS: E. ADAZE/ DR. M. OSMAN 1
,FLUID MECHANICS MC/EL/RN/ES/GL/MN/MR/PE 264
Gas dynamics
Hydrodynamics deals with the flow of fluids for which there is virtually no density
change. Examples include flow of liquids and flow of gases at low speeds. Gas dynamics
deals with fluid that undergo significant density changes. Examples are high-speed flows
of a gas through a nozzles and the movement of a body through the low density air of
the upper atmosphere.
Another area of fluid mechanics is aerodynamics which deals with the flow of air past
aircraft or rockets.
1.3 What is a Fluid?
A fluid is defined as a substance that will continuously deform – that is, flow under the
action of a shear stress (no matter how small that stress may be) causing its constituent
particles to continuously change their positions relative to one another. The rate of
deformation (strain) of a fluid is related to the applied shear stress by a property called
viscosity.
A fluid can be either a gas or a liquid. The differences in behaviour of solids, liquids
and gases are due to the differences in their molecular structures.
In solids, the molecules have definite spacing. Their movement is restricted. As a result,
solids have definite volume and shape. In liquids, the spacing between the molecules is
essentially constant but the molecules can move with respect to each other when a
shearing force is applied. Therefore, liquids have definite volume but no definite shape.
Finally, in gases, the spacing between the molecules is much wider than that of either
solids or liquids. The spacing is also variable (keeps changing). Therefore, gases have
neither definite shape nor definite volume. Table 1.1 gives a summary on the
comparison of solids, liquids and gases.
INSTRUCTORS: E. ADAZE/ DR. M. OSMAN 2
,FLUID MECHANICS MC/EL/RN/ES/GL/MN/MR/PE 264
Table 1.1 Differences between Solids, Liquids and Gases
From Table 1.1, it can be seen that a liquid is difficult to compress because the
molecules will repulsive forces if they are brought close together. It changes its shape
according to the shape of its container with an upper free surface. However, a gas is
easy to compress because there are no forces (on average) between the molecules and
expands to fill its container. There is thus no free surface.
Consequently, an important characteristic of a fluid from the viewpoint of fluid
mechanics is its compressibility. Another characteristic is its velocity. Whereas a solid
shows its elasticity in tension, compression or shear stress, a fluid does so only for
compression. In other words, a fluid increases its pressure against compression, trying
to retain its original volume. This characteristic is called compressibility. Furthermore,
a fluid shows resistance whenever two layers slide over each other. The characteristic
is called viscosity.
In general, liquids are called incompressible fluids and gases compressible fluids.
Nevertheless, for liquids, compressibility must be taken into account whenever they are
highly pressurized, and for gases, compressibility may be disregarded whenever the
INSTRUCTORS: E. ADAZE/ DR. M. OSMAN 3
, FLUID MECHANICS MC/EL/RN/ES/GL/MN/MR/PE 264
changes in pressure is small. Although a fluid is an aggregate of molecules in constant
motion, it is treated as a continuous isotropic substance.
Meanwhile, a non-existent, assumed fluid without either viscosity or compressibility is
called an ideal fluid or perfect fluid. A fluid with compressibility but without viscosity is
occasionally discriminated and called a perfect fluid, too. Furthermore, a gas subject to
Boyle’s-Charles’ law is called a perfect or ideal gas.
1.4 The Ideal Gas Law (IGL)
Application of the ideal gas law (IGL) is very common in fluid mechanics. For instance,
in the design of products like air bags, shock absorbers, combustion systems and
aircraft. The IGL is the result of combining three empirical equations previously
developed by Boyle, Charles and Avogadro. These empirical equations are respectively
known as Boyles’s law, Charles law and Avogadro’s law. The equation of state of IGL
is of the form:
p RT (1.1)
where, p is absolute pressure; T is absolute temperature; is fluid density; R is gas
constant which is related to the universal gas constant Ru as follows:
R
R u (1.2)
M
where, M is molar mass (molecular weight). The universal gas constant ( Ru) is usually
taken as 8.314 kJ/kmol K.
1.5 Pascal’s Law
For a given closed system, a pressure change produced at one point in the system will
be transmitted throughout the entire system. This is known as Pascal’s law. See Figure
1.1 for illustration.
Figure 1.1 Concept of Pascal’s Law
Pressures applied to point 1 and point 2 are equal in terms of Pascal’s law. Therefore,
applying force F1 to the smaller area at point 1 will produce a larger force F2 on the
INSTRUCTORS: E. ADAZE/ DR. M. OSMAN 4
