Fluid mechanics and equipments

1. 1
FLUID MECHANICS AND
EQUIPMENTS
(CHE 241)
CHAPTER 1
FLUID PROPERTIES

2. 2
OBJECTIVE
To acquire fundamental concepts of fluid properties
LEARNING OUTCOMES
At the end of this chapter, student should be able to:
i. Define fluid
ii. State the differences between solid and fluid
iii. Calculate common fluid properties when
appropriate information are given.
iv. Define Newton’s Law of viscosity; relationship
between shear stress and rate of shear strain

3. 3
1.1 FLUIDS
• We normally recognize 3 states of matter : Solid, Liquid and Gas.
• Although differ in many respects, liquids and gases have common
characteristics in which they are differ from solids.
• Liquid and gas are fluids: in contrast to solids, they (fluid) lack the ability to
resist deformation. Because a fluid cannot resist the deformation force, it
moves, it flows under the action of the force. Its shape will change
continuously as long as the force is applied.
• A solid can resist a deformation force while at rest, this force may cause
some displacement but the solid does not continue to move indefinitely
FLUID
Deforming continuously
for as long as the force
applied
Flow under the action
of such forces
Unable to retain any
unsupported shape

4. What is a fluid?
• A fluid is a substance in the gaseous or liquid form
• Distinction between solid and fluid?
– Solid: can resist an applied shear by deforming. Stress is proportional
to strain
– Fluid: deforms continuously under applied shear. Stress is proportional
to strain rate
F
A
 
 
F V
A h
 
 
Solid Fluid
1.1 FLUIDS

5. • Stress is defined as the force per
unit area.
• Normal component: normal stress
– In a fluid at rest, the normal
stress is called pressure
• Tangential component: shear stress
1.1 FLUIDS

6. • A liquid takes the shape of the
container it is in and forms a free
surface in the presence of gravity
• A gas expands until it encounters
the walls of the container and fills
the entire available space.
Gases cannot form a free surface
• Gas and vapor are often used as
synonymous words
1.1 FLUIDS

7. solid liquid gas
1.1 FLUIDS

8. No-slip condition
• No-slip condition: A fluid in direct contact with a solid
``sticks'‘ to the surface due to viscous effects
• Responsible for generation of wall shear stress w,
• surface drag D= ∫w dA, and the development of the
boundary layer
• The fluid property responsible for the no-slip condition is
viscosity

9. 9
1.1 FLUIDS
• Deforming is caused by shearing forces, i.e. forces such as F (refer Figure
1.1), which act tangentially to the surfaces to which they are applied and
causes the material originally occupying the space ABCD to deform AB’C’D.
F
D
A
B’
B C’
C
y
x
E
ø
Figure 1.1: Deformation caused by shearing forces
We can then say:
A fluid is a substance which deforms continuously, or flows,
when subjected to shearing forces.
On the other hand, this definition means the very important
point that:
If a fluid is at rest, there are no shearing forces acting. All
forces must be perpendicular to the planes which they are
acting.

10. 10
1.2 SHEAR STRESS IN A MOVING FLUID
• Shear stresses are developed when the fluid is in motion. If
the particles of the fluid move relative to each other so they
have different velocities, causing the original shape of fluid
to become distorted.
• If the velocity of fluid is the same at every point, no shear
stresses will be produced, since the fluid particles are at
rest relative to each other.
• If ABCD (refer Figure 1.1) represents an element in a fluid
with thickness s perpendicular to the diagram, the force F
will act over an area A equal to BC x s.
• The force per unit area, F/A is the shear stress τ and the
deformation, measured by angle ø (the shear strain), will be
proportional to the shear stress.
• The shear strain ø will continue to increase with time and
the fluid will flow.
• The rate of shear strain (or shear strain per unit time) is
directly proportional to the shear stress.

11. 11
• Suppose that in time t, a particle at E (refer Figure 1.1) moves through a
distance x.
• If E is a distance y from AD then, for a small angles,
• Revise that shear stress is proportional to shear strain, then
E
at
particle
the
of
velocity
the
is
t
/
x
u
where
y
u
y
)
t
/
x
(
yt
x
strain
shear
of
Rate
y
x
,
strain
Shear






u
constant x
y
 
1.2 SHEAR STRESS IN A MOVING FLUID
Equation 1.1

12. 12
• The term u/y is the change of velocity with y and may be written in differential
form du/dy.
• The constant of proportionality is known as the dynamic viscosity μ of the fluid.
Substitute to Equation 1.1,
Equation 1.2 is Newton’s law of viscosity
du
τ=μ
dy
1.2 SHEAR STRESS IN A MOVING FLUID
Equation 1.2

13. 13
• Fluids obeying Newton’s law
of viscosity and for which μ
has a constant value are
known as Newtonian fluids.
• Most common fluids fall into
this category, for which shear
stress is linearly related to
velocity gradient (refer Figure
1.2)
1.3 NEWTONIAN AND NON-NEWTONIAN FLUIDS
Figure 1.2: Variation of shear stress with velocity gradient
Rate of shear strain, du/dy

14. 14
• Fluids which do not obey obeying Newton’s law of viscosity are
known as non-Newtonian fluids and fall into one or the following
groups.
1. Plastic: Shear stress must reach a certain minimum before flow
commences. Thereafter, shear stress increases with the rate of
shear according to the relationship in Equation 1.3, where A, B
and n are constants. If n=1, the material is known as Bingham
plastic, e.g. sewage sludge.
2. Pseudo-plastic: Dynamic viscosity decreases as the
rate of shear increases, e.g. colloidial substances like
clay, milk and cement.
1.3 NEWTONIAN AND NON-NEWTONIAN FLUIDS
1.3
n
A B Equation
du
dy
 
 
 
 
 

15. 15
1.3 NEWTONIAN AND NON-NEWTONIAN FLUIDS
3. Dilatant substances: Dynamic viscosity increases as the rate of shear
increase, e.g. quicksand.
4. Thixotropic substances: Dynamic viscosity decreases with the time for
which shearing force is applied, e.g. Thixotropic jelly paints.
5. Rheopectic substances: Dynamic viscosity increases with the time for
which shearing force is applied.
6. Viscoelastic materials: Behave similar to Newtonian fluids but if there
is a sudden large change in shear stress, they behave like plastic.
• The above is a classification of actual fluids.
• There is also one more - which is not real, it does
not exist - known as the ideal fluid. This is a fluid
which is assumed to have no viscosity (τ = 0). This
is a useful concept when theoretical solutions are
being considered - it does help achieve some
practically useful solutions in analyzing some of the
problems arising in fluid mechanics.

16. 16
1.4 DENSITY
The density of a substance is that quantity of matter contained in unit
volume of the substance. It can be expressed in three different ways.
1.4.1 MASS DENSITY
• Mass density ρ is defined as the mass of substance per unit
volume.
• Units: kilogram per cubic meter (kgm-3)
• Dimensions: ML-3
• Typical values at p=1.013 x 105 Nm-2, T=288.15 K, mass
density of water is 1000 kgm-3 and air is 1.23 kgm-3.

17. 17
1.4 DENSITY
1.4.2 SPECIFIC WEIGHT
• Specific weight w is defined as the weight per unit volume.
• Since weight is dependent on gravitational attraction, the specific
weight will vary from point to point, according to the local value of
gravitational acceleration g.
• The relationship between w and ρ can be deduced from Newton’s
second law where,
Weight per unit volume = Mass per unit volume x g
ω = ρg
• Units: newtons per cubic meter (Nm-3)
• Dimensions: ML-2T-2
• Typical values for water is 9.81 x 103 Nm-3
and air is 12.07 Nm-3.

18. 18
1.4 DENSITY
1.4.3 RELATIVE DENSITY
• Relative density or specific gravity (SG) σ is defined as the ratio of
the mass density of a substance to some standard mass density.
• For solids and liquids, the standard mass density chosen is the
maximum density of water (which occur at 4°C at atmospheric
pressure).
• The relationship between is represented by,
C
°
4
at
water
ce
tan
subs
ρ
ρ
=
σ
• For gases, the standard density may be that air or
hydrogen at a specified temperature and pressure,
but the term is not used frequently.
• Units: since relative density is a ratio of two
quantities of the same kind, it is a pure number
having no units.
• Dimensions: as a pure number, its dimension are
M0L0T0=1.
• Typical values for water is 1.0 and oil is 0.9.

19. 19
1.5 VISCOSITY
1.5.1 DYNAMIC VISCOSITY
• The coefficient of dynamic viscosity μ can be defined as the shear
force per unit area (or shear stress τ) required to drag one layer of fluid
with unit velocity past another layer a unit distance away from it in the
fluid.
• Rearranging Equation 1.2,
Time
x
Lenght
Mass
or
Area
Time
x
Force
=
Distance
Velocity
Area
Force
=
dy
du
τ
=
μ
• Unit: newtons seconds per square meter (Nsm-2)
or kilograms per meter per second (kgm-1s-1). But
note that the coefficient of viscosity is often
measures in poise (P) where 10 P = 1 kgm-1s-1.
• Dimension: ML-1T-1
• Typical values for water is 1.14 x 10-3 kgm-1s-1
and air is 1.78 x 10-5 kgm-1s-1.

20. 20
1.5 VISCOSITY
1.5.2 KINEMATIC VISCOSITY
• The kinematic viscosity,  is defined as ratio of dynamic
viscosity, μ to mass density, ρ.
• Unit: square meters per second (m2s-1) but note that the
kinematic viscosity is often measures in stokes (St)
where 10 St = 1 m2s-1.
• Dimension: L2T-1
• Typical values for water is 1.14 x 10-6 m2s-1 and air is
1.46 x 10-5 m2s-1.
ρ
μ
=
ν

21. 21
1.6 UNIT AND CONVERSION FACTORS
• In the United States most measurements use the English system of units
(based on the foot, pound and °F), but most of the world uses the metric
(or SI) units (based on the meter, kilogram and °C).

22. Tutorial
1. Determine the density, specific gravity,
and mass of the air in a room whose
dimensions are 4 m x 5 m x 6 m at 100
kPa and 25oC.