FLUID MECHANICS 2..pptx

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.

PROPERTIES OF FLUIDS AT REST

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

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

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

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



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.

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.

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


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.

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.

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.

FIGURE 1

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

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,

strain
shear
of
rate
stress
shear
dy
dV
or
dy
dV



/





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.

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.

A GRAPH OF NEWTONIAN FLUIDS

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





/

EXAMPLE 1
•

SOLUTION
•

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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