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```Date : (1C) 6 Feb
(1D) 4 Feb
(1E) 4 Feb
(1F) 5 Feb
Can you identify a
common relation
between Figure
(a) & (b).
 The common properties between them is
their ability to flow and can't take a fixed
shape, but take the shape of the container
Materials that exhibit these properties are
called Fluids.
 Fluids are a subset of the phases of
matter and include liquids, gases,
plasmas and, to some extent, plastic
solids.
 Difference between liquids and gases
Gases can be compressed, but liquids
are incompressible.
Fluid Mechanics
(Hydrostatics)
Fluid At rest
Fluid Dynamics
(Hydrodynamics)
Fluid in motion
Students will be able to use
pressure difference between
two points of a fluid and
Newton's laws to analyze
behavior of that fluid.
Concepts
A. Fluids
B. Pressure
C. Manometer
D. Pressure gauge
E. Units of pressure
F. Effect of atmospheric pressure on boiling point of water
G. Change in atmospheric pressure with altitude
H. Pressure difference and force
I. Archimedes Principle
Skills
A. Determine pressure change as function of height in columns of
fluid
B. Explain how a mercury barometer measures atmospheric
pressure
C. Determine atmospheric pressure as a function of altitude
D. Convert between different pressure units
(such as: kPa, atm,mm Hg)
E. Explain how a straw works
F. Explain how a manometer works
G. Measure the gauge pressure of a trapped gas
H. Use manometers & barometers
I. Explain different boiling points of water at different altitudes
J. Measure the apparent weight of an immersed object.
K. Determine the Buoyant force on a submerged, or floating object
L. Use Archimedes principle to explain why large ships do not sink
•
Density
•
Pressure
•
Viscosity
•
Specific weight (unit weight)
•
Specific gravity (relative density)
•
Specific volume
Density ‘𝝆’
•
It is the ratio between mass (m) and
volume (V). It’s unit is kg/m3
• If a fluid has more atoms/molecules
and particles are placed close to each
other, it is going to have a higher
density.
• The density of water
𝝆w= 1 g/cm3= 1000 Kg/m3
• The density of air
𝝆air= 1.21 Kg/m3
Specific Gravity
(Relative Density)
A) Pressure at a point:
• When object is submerged in a fluid, fluid
exerts a force on the object.
• The force is perpendicular to the surface of the
object at each point of the surface.
• The magnitude of the perpendicular force
on a surface per unit area is called the
pressure of the fluid:
F
F
P
or P 
A
A
where
P is the pressure of the fluid,
F is the force exerted by the fluid on the object,
A is the area of the object.
The SI unit of pressure is
Pascal (Pa) =1 N/m2.
The Pascal is a small unit of pressure.
• If the force acts at an angle, the force
component along the direction perpendicular
to the surface must be used to calculate
pressure.
F sin 𝛉
F
F cos 𝛉
F
𝜃
𝜃
A
A
P=
𝐹 𝑠𝑖𝑛 𝜃
𝐴
P=
𝐹 𝑐𝑜𝑠 𝜃
𝐴
Factors affecting the
pressure at a point
Why do snowshoes
keep you from sinking
into the snow?
Atmospheric (air)
Pressure
•
The weight of air column over unit
area of earth surface at sea level.
1 atm ≈1.01325×105 Pa.
• It exerted due to collisions
between the mixture of gases
found in the air
Fluids pays a pressure in every direction
If air pressure always push us from outside,
how come we keep balanced?!
Unit
Weight
Length
Conversion
Newton/𝒎𝟐
1 atm = 101,325 = 1.013 x 𝟏𝟎𝟓 𝑵/𝒎𝟐
Pascal (Pa)
1 atm = 1.013 x 𝟏𝟎𝟓 𝑵/𝒎𝟐
1 𝑵/𝒎𝟐 = 1 Pascal
Psi (lb/in2)
1 atm = 14.7 psi
(Pound per square inch)
Bar
1 atm = 1.013 bar
1 bar = 𝟏𝟎𝟓 𝑵/𝒎𝟐
cm Hg
1 atm = 76 cm Hg = 760 mm Hg = 29.92
inHg
Torr
1 atm = 760 torr
1 torr = 1 mm Hg
1 Torr = 101325/760 Pascal (≈ 133.3 Pa)
I. Converting between atmospheres and
millimeters of mercury.
1 atm. = 760.0 mm Hg
• Example 1: Convert 0.875 atm to mmHg.
0.875 atm x 760.0 mmHg / atm = 665 mmHg
• Example 2: Convert 745.0 mmHg to atm.
745.0 mmHg x atm / 760.0 mmHg = 0.980 atm
II. Converting between atmospheres and
kilopascals.
1 atm. = 101.325 kPa
• Example 3: Convert 0.955 atm to kPa.
0.955 atm x 101.325 kPa / atm = 96.76 kPa
• Example 4: Convert 98.35 kPa to atm.
98.35 kPa x atm / 101.325 kPa = 0.970 atm
III. Converting between millimeters of
mercury and kilopascals.
760.0 mmHg = 101.325 kPa
• Example 5: Convert 740.0 mmHg to kPa.
740.0 mmHg x 101.325 kPa / 760.0 mmHg = 9.609 x 10-3 kPa
• Example 6: Convert 99.25 kPa to mmHg.
99.25 kPa x 760.0 mmHg / 101.325 kPa = 744.436 mmHg
Absolute Pressure
• A pressure measured relative to a perfect
vacuum.
• Explain the relationship among absolute
pressure, gauge pressure, and atmospheric
pressure
Pabs  Patm  Pgage
where
Pabs : Absolute pressure
Patm : Atmospheric pressure
Pgage : Gage pressure = ρ g h
Gauge Pressure
• A pressure measured using a pressure
measuring instrument .
• Is the difference between the absolute
pressure and the current atmospheric
pressure.
• It can be either positive or negative
depending on whether the pressure is
above or bellow the atmospheric
pressure.
Work with your group and try to deduce
the main parameters that affecting the
pressure of fluid Using this simulation
• Static Fluid pressure:
• Atmospheric pressure is a good
example of static pressure as its
ultimate source is gravity.
• The pressure exerted by a static fluid
depends only upon
1) The depth of the fluid (h)
2) The density of the fluid (ρ)
3) The acceleration of gravity (g)
• Imagine a horizontal plate (x)
of area (A) at depth (h) inside
a liquid of density (ρ).
• This plate acts as the base of
a column of the liquid.
• The force acting on the plate
(x) is the weight of the
column of the liquid whose
height (h) and cross section
area (A).
• The force resulting from the liquid pressure
balances with the weight of the column of the
liquid.
 PL   g h
 Pt  Pa   g h
where: (Pa ) is the atmospheric pressure.
• For a fluid whose density remains
approximately constant throughout, the
pressure increases linearly with depth:
P = P0 + ρFg h
where
P is the pressure at the bottom of the
column of the fluid,
P0 is the pressure at the top of the column,
g is the acceleration due to gravity,
ρF is the density of the fluid = m/V
h is the height of the column of the fluid.
▪ If you are in a car that is
submerged in a flood,
how hard will it be to
Because water pushes
immersed foam with
upward force due to
pressure difference across
piece of foam.
the
an
the
the
1. Change in atmospheric
pressure with density
 Density of a fluid decreases with increase in
temperature.
 It increases with increase in pressure.
Effect of atmospheric pressure on
boiling point of water
Is it easier or harder to boil water when
on top of a very high mountain?
• As altitude increases, atmospheric pressure
and boiling point decrease because air is less
dense at higher altitudes.
• If the atmospheric pressure is exactly 1 atm, the
boiling point of water is 100.0 degrees Celsius. This is
because the vapor pressure of water is 1 atm at this
temperature.
• The boiling point decreases to 80.0 degrees at higher
altitudes.
• If you increase the pressure, the boiling point
will increase because more energy will be
needed to raise the vapor pressure to the
increased atmospheric pressure. Likewise, if
you decrease the pressure, the boiling point
will decrease.
• If you want water to stay a liquid,
just pressurize it a lot. This is done
in pressure cookers to allow food
to cook more quickly in water at a
temperature of several hundred
degrees.
2. Change in atmospheric pressure
with altitude/ depth
Pressure increases with
increase in depth .
Pressure decreases with
increase in altitude .
The higher you go up
above sea surface level,
the lower the pressure.
Pressure is equal at all the
points that lie on the same level
A
B
C
Pressure is equal at point A,
B and is smaller than that at
point C
What is the reason of building
water tanks very height?
• When a liquid is put in a Ushaped tube, the level of the
liquid in the two branches is
the same.
• When another liquid is
added in one branch of the
tube (both liquids don’t
mix).
A
B
The pressure at point B = The pressure at point A
(at the same level).
 Pa  1 g h1  Pa   2 g h 2
 1 h1  2 h 2
2
h1

1
h2
If the 1st liquid is water, then the ratio (ρ2 / ρ1)
represents the relative density of the 2nd liquid.
How could you use
the U-shaped tube to
determine the
specific density of
some liquids?
 Specific gravity (relative density):
Is the ratio of density of a fluid to density of
water at 4ºC
SG = ρ / ρw
Unitless
The relative density of oil
•
Oils relative density ranging from 0.7
to 0.98 g/cm3 so most are less dense
than water .
• For Petroleum ≅ 800 Kg/m3 or 0.8
g/cm3
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