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PHYSICS II (PHY 121):
FLUID MECHANICS
KONDWANI CHAFULUMIRA CHUMACHIYENDA MWALE
Basic Sciences Department
Faculty Of Agriculture
Bunda /City Campus
Lilongwe University Of Agriculture And Natural Resources (LUANAR)
1
TOPIC
HYDROSTATICS (FLUIDS AT REST)
FLUID MECHANICS
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
HDROSTATICS, FLUID AT REST
Hydrostatics is the branch of physics that deals with the
study of properties of fluids at rest.
Fluids at rest: the forces produced in a fluid at rest is
always perpendicular to the surface in contact with the
liquid.
Ideal fluids are incompressible.
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
PROPERTIES OF FLUIDS AT REST
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
THRUST
Thrust is total perpendicular force exerted
by the liquid at rest on a surface in contact
with it
It is also known as buoyant force
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
SPECIFIC WEIGHT (𝜸)
Specific weight is the ratio of the weight to the
volume of a substance
𝜸 =
𝒎𝒈
𝒗
but 𝝆 =
𝒎
𝒗
then 𝜸 = 𝝆𝒈
For liquids,  may be taken as constant for practical
changes of pressure.
The specific weight of water for ordinary temperature
variations is 9.79 kN/m3. NB:𝟏𝑵 = 𝟏𝒌𝒈. 𝒎𝒔−𝟐
SPECIFIC WEIGHT (𝜸)
The specific weight of a gas can be calculated using its
equation of state
Where pressure p is absolute pressure, v is the volume per
unit weight, temperature T is the absolute temperature,
and R is the gas constant of that particular species:
𝑷𝑽
𝑻
= 𝒏𝑹
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
SPECIFIC WEIGHT (𝜸)
And the gas constant R is given as:
Since 𝜸 = 1/v, then:
weight
molar
t
n
a
t
s
n
o
c
s
a
g
l
a
s
r
e
v
i
n
u
Mg
R
R 
 0
RT
P


PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
DENSITY OF A BODY
Density is the mass per unit volume.
It can be expressed in terms of specific weight
𝜌 =
𝛾
𝑔
, and
𝛾 = 𝜌𝑔
In SI units, the density of water is 1000kg/m3 at 4°C.
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
SPECIFIC GRAVITY
The specific gravity of a body is the dimensionless ratio of
the weight of the body to the weight of an equal volume
of a substance taken as a standard.
Solids and liquids are referred to water (20°C) as standard,
while gases are often referred to air free of carbon dioxide
or hydrogen (0°C) as standard.
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
SPECIFIC GRAVITY
The following equations are used to calculate specific
gravity.
water
of
volume
equal
of
weight
e
c
n
a
t
s
b
u
s
of
t
h
g
i
e
w
gravity
Specific 
water
of
weight
specific
e
c
n
a
t
s
b
u
s
of
t
h
g
i
e
w
specific

water
of
density
e
c
n
a
t
s
b
u
s
of
density

PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
VISCOCITY OF A FLUID
Viscosity is the internal friction of a fluid which opposes the motion
of one layer of fluid past one another. NB: A fluid moves in form of
layers
Viscosity is the property of any moving fluid (liquid or gas) to
oppose the relative motion between its layers.
The greater the viscosity of a fluid, the greater is the force required
to cause one layer of a fluid to slide past another.
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
CONT.….
The viscosity of a fluid not only retards its own motion but
also retards the motion of a solid through it. The greater the
viscosity of a fluid, the harder it is for a solid to move through
it. Imagine the difference between swimming in water and
honey.
The forces of attraction between the molecules of a moving
fluid determine the viscosity of the fluid.
The viscosity of a liquid will increase as its temperature is
reduced. However the coefficient of viscosity of gases
increase with the increase in temperature.
VISCOCITY OF A FLUID
Consider Figure 1 in table 1 ,two large, parallel plates are at a
small distance y apart, the space between the plates being filled
with a fluid.
To keep the upper plate moving at a constant velocity U, it is
found that a constant force F must be applied.
Thus there must exist a viscous interaction between plate and
fluid, manifested in a drag on the former and a shear force on
the latter.
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
FIGURE 1
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
VISCOCITY OF A FLUID
The fluid in contact with the upper plate will adhere to it and
will move at velocity U, and the fluid in contact with the fixed
plate will have velocity zero. If distance y and velocity U are not
too great, the velocity profile will be a straight line.
Experiments have shown that shear force F varies with the area
of the plate A, with velocity U, and inversely with distance y.
Since by similar triangles, U/y = dV/dy, we have
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
VISCOCITY OF A FLUID
𝐹𝛼(𝐴
𝑈
𝑦
= A
𝑑𝑉
𝑑𝑦
) Or
(
𝐹
𝐴
= τ) 𝛼
𝑑𝑉
𝑑𝑦
Where  = F/A = shear stress.
If a proportionality constant, , called the absolute
(dynamic) viscosity, is introduced,
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
VISCOCITY OF A FLUID
strain
shear
of
rate
stress
shear
dy
dV
or
dy
dV



/




PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
VISCOCITY AND NEWTONIAN FLUIDS
 is measured in Pa/s (Decapoise)
Fluids for which the proportionality of the above equation holds are
called Newtonian fluids. Viscosity remains constant for all shear rates
The above expression was postulated by Newton and is known as
Newton’s equation of viscosity.
An Ideal or perfect fluid is one which there are no tangential or shear
stresses between the fluid particles.
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
VISCOCITY AND NEWTONIAN FLUIDS
No real fluid in practice fully complies with this
concept, and for all fluids in motion there are
tangential stresses present which have a
dampening effect on the motion.
However, some liquids, including water, are near
to an ideal fluid, and this simplifying assumption
enables mathematical or graphical methods to be
adopted in the solution of certain flow problems.
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
A GRAPH OF NEWTONIAN FLUIDS
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
A GRAPH OF NEWTONIAN FLUIDS
• Another viscosity coefficient, the coefficient of kinematic
viscosity, is defined as


density
mass
osity
c
vis
absolute
sity
o
c
vis
kinematic 
,









g
h
gh
p
gh
gh
p





/
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
EXAMPLE 1
•
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
SOLUTION
•
PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
EXAMPLE 2
Calculate the horizontal force required to move a metal plate of area 𝟐 ×
𝟏𝟎−𝟐𝒎−𝟐 With a velocity of 𝟒. 𝟓 × 𝟏𝟎−𝟐𝒎𝒔−𝟏 when it rests on a layer of
oil 𝟏. 𝟓 × 𝟏𝟎−𝟑𝒎 thick. Coefficient of viscosity of oil = 𝟐𝑵𝒔𝒎−𝟐.
𝑺𝒐𝒍𝒖𝒕𝒊𝒐𝒏
𝑭 = 𝝁𝑨
𝒅𝒗
𝒅𝒚
Here 𝝁 = 𝟐𝑵𝒔𝒎−𝟐
. : 𝑨 = 𝟐 × 𝟏𝟎−𝟐
𝒎−𝟐
;
𝒅𝒗
𝒅𝒚
=
𝟒.𝟓×𝟏𝟎−𝟐𝒎𝒔−𝟏
𝟏.𝟓×𝟏𝟎−𝟑𝒎
= 𝟑𝟎𝒔−𝟏
𝑭 = 𝟐 × 𝟐 × 𝟏𝟎−𝟐 × 𝟑𝟎 = 𝟏. 𝟐𝑵

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FLUID MECHANICS 2..pptx

  • 1. PHYSICS II (PHY 121): FLUID MECHANICS KONDWANI CHAFULUMIRA CHUMACHIYENDA MWALE Basic Sciences Department Faculty Of Agriculture Bunda /City Campus Lilongwe University Of Agriculture And Natural Resources (LUANAR) 1 TOPIC
  • 2. HYDROSTATICS (FLUIDS AT REST) FLUID MECHANICS PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 3. HDROSTATICS, FLUID AT REST Hydrostatics is the branch of physics that deals with the study of properties of fluids at rest. Fluids at rest: the forces produced in a fluid at rest is always perpendicular to the surface in contact with the liquid. Ideal fluids are incompressible. PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 4. PROPERTIES OF FLUIDS AT REST PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 5. THRUST Thrust is total perpendicular force exerted by the liquid at rest on a surface in contact with it It is also known as buoyant force PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 6. SPECIFIC WEIGHT (𝜸) Specific weight is the ratio of the weight to the volume of a substance 𝜸 = 𝒎𝒈 𝒗 but 𝝆 = 𝒎 𝒗 then 𝜸 = 𝝆𝒈 For liquids,  may be taken as constant for practical changes of pressure. The specific weight of water for ordinary temperature variations is 9.79 kN/m3. NB:𝟏𝑵 = 𝟏𝒌𝒈. 𝒎𝒔−𝟐
  • 7. SPECIFIC WEIGHT (𝜸) The specific weight of a gas can be calculated using its equation of state Where pressure p is absolute pressure, v is the volume per unit weight, temperature T is the absolute temperature, and R is the gas constant of that particular species: 𝑷𝑽 𝑻 = 𝒏𝑹 PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 8. SPECIFIC WEIGHT (𝜸) And the gas constant R is given as: Since 𝜸 = 1/v, then: weight molar t n a t s n o c s a g l a s r e v i n u Mg R R   0 RT P   PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 9. DENSITY OF A BODY Density is the mass per unit volume. It can be expressed in terms of specific weight 𝜌 = 𝛾 𝑔 , and 𝛾 = 𝜌𝑔 In SI units, the density of water is 1000kg/m3 at 4°C. PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 10. SPECIFIC GRAVITY The specific gravity of a body is the dimensionless ratio of the weight of the body to the weight of an equal volume of a substance taken as a standard. Solids and liquids are referred to water (20°C) as standard, while gases are often referred to air free of carbon dioxide or hydrogen (0°C) as standard. PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 11. SPECIFIC GRAVITY The following equations are used to calculate specific gravity. water of volume equal of weight e c n a t s b u s of t h g i e w gravity Specific  water of weight specific e c n a t s b u s of t h g i e w specific  water of density e c n a t s b u s of density  PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 12. VISCOCITY OF A FLUID Viscosity is the internal friction of a fluid which opposes the motion of one layer of fluid past one another. NB: A fluid moves in form of layers Viscosity is the property of any moving fluid (liquid or gas) to oppose the relative motion between its layers. The greater the viscosity of a fluid, the greater is the force required to cause one layer of a fluid to slide past another. PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 13. CONT.…. The viscosity of a fluid not only retards its own motion but also retards the motion of a solid through it. The greater the viscosity of a fluid, the harder it is for a solid to move through it. Imagine the difference between swimming in water and honey. The forces of attraction between the molecules of a moving fluid determine the viscosity of the fluid. The viscosity of a liquid will increase as its temperature is reduced. However the coefficient of viscosity of gases increase with the increase in temperature.
  • 14. VISCOCITY OF A FLUID Consider Figure 1 in table 1 ,two large, parallel plates are at a small distance y apart, the space between the plates being filled with a fluid. To keep the upper plate moving at a constant velocity U, it is found that a constant force F must be applied. Thus there must exist a viscous interaction between plate and fluid, manifested in a drag on the former and a shear force on the latter. PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 15. FIGURE 1 PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 16. VISCOCITY OF A FLUID The fluid in contact with the upper plate will adhere to it and will move at velocity U, and the fluid in contact with the fixed plate will have velocity zero. If distance y and velocity U are not too great, the velocity profile will be a straight line. Experiments have shown that shear force F varies with the area of the plate A, with velocity U, and inversely with distance y. Since by similar triangles, U/y = dV/dy, we have PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 17. VISCOCITY OF A FLUID 𝐹𝛼(𝐴 𝑈 𝑦 = A 𝑑𝑉 𝑑𝑦 ) Or ( 𝐹 𝐴 = τ) 𝛼 𝑑𝑉 𝑑𝑦 Where  = F/A = shear stress. If a proportionality constant, , called the absolute (dynamic) viscosity, is introduced, PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 18. VISCOCITY OF A FLUID strain shear of rate stress shear dy dV or dy dV    /     PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 19. VISCOCITY AND NEWTONIAN FLUIDS  is measured in Pa/s (Decapoise) Fluids for which the proportionality of the above equation holds are called Newtonian fluids. Viscosity remains constant for all shear rates The above expression was postulated by Newton and is known as Newton’s equation of viscosity. An Ideal or perfect fluid is one which there are no tangential or shear stresses between the fluid particles. PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 20. VISCOCITY AND NEWTONIAN FLUIDS No real fluid in practice fully complies with this concept, and for all fluids in motion there are tangential stresses present which have a dampening effect on the motion. However, some liquids, including water, are near to an ideal fluid, and this simplifying assumption enables mathematical or graphical methods to be adopted in the solution of certain flow problems. PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 21. A GRAPH OF NEWTONIAN FLUIDS PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 22. A GRAPH OF NEWTONIAN FLUIDS • Another viscosity coefficient, the coefficient of kinematic viscosity, is defined as   density mass osity c vis absolute sity o c vis kinematic  ,          g h gh p gh gh p      / PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 23. EXAMPLE 1 • PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 24. SOLUTION • PHY 121 – Fluid Mechanics Basic Sciences Department LUANAR
  • 25. EXAMPLE 2 Calculate the horizontal force required to move a metal plate of area 𝟐 × 𝟏𝟎−𝟐𝒎−𝟐 With a velocity of 𝟒. 𝟓 × 𝟏𝟎−𝟐𝒎𝒔−𝟏 when it rests on a layer of oil 𝟏. 𝟓 × 𝟏𝟎−𝟑𝒎 thick. Coefficient of viscosity of oil = 𝟐𝑵𝒔𝒎−𝟐. 𝑺𝒐𝒍𝒖𝒕𝒊𝒐𝒏 𝑭 = 𝝁𝑨 𝒅𝒗 𝒅𝒚 Here 𝝁 = 𝟐𝑵𝒔𝒎−𝟐 . : 𝑨 = 𝟐 × 𝟏𝟎−𝟐 𝒎−𝟐 ; 𝒅𝒗 𝒅𝒚 = 𝟒.𝟓×𝟏𝟎−𝟐𝒎𝒔−𝟏 𝟏.𝟓×𝟏𝟎−𝟑𝒎 = 𝟑𝟎𝒔−𝟏 𝑭 = 𝟐 × 𝟐 × 𝟏𝟎−𝟐 × 𝟑𝟎 = 𝟏. 𝟐𝑵