Download Topic11.Presentation.ICAM

NAZARIN B. NORDIN
[email protected]
What you will learn:
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Pascal’s law
Incompressibility of fluids
Pressure, force ratio
Archimedes principle
Density and relative density
Introduction to fluids
A fluid is a substance that can flow and
c onfor m t o the boundaries of a n y
container in which we put them.
e.g. water, air, glass.
• A fluid is any substance that can flow such as
a liquid or a gas.
• Fluids don’t have well defined shapes.
• A fluid takes on any shape to fit a container.
• The study of fluids can be divided into two
categories : hydrostatics and hydrodynamics
or fluid dynamics.
Basic properties of fluids
Density (mass per
unit volume) -   m / V
Pressure (force per
unit area) - P  F / A
Basic properties of fluids
Pressure (force per
unit area) - P  F / A
Notice that from
definition, pressure may
depend on direction.
However, this is not the
case for static fluids.
(why?).
Basic properties of fluids
Pressure (force per
unit area) - P  F / A
Unit of pressure:
1 pascal (Pa) = 1
Newton per square
meter.
1 atm. = 1.01 x 105 Pa
Fluids at rest
Pressure increases when we go “deeper”
into water – why?
F2  F1  mg,
F1  p1 A,
F2  p2 A,
m  A( y1  y2 )
Fluids at rest
Pressure of a fluid in static equilibrium
depends on depth only
p2  p1  g ( y1  y2 ),
or
p  p0  gh
Example
Which one of the four container + fluid has
highest pressure at depth h?
How about if (d) is move up (down)
by distance h?
Pascal’s Princple
• A change in the pressure applied to an
enclosed incompressible fluid is transmitted
undiminished to every portion of the fluid and
to the walls of the container as a direct
consequence of Newton’s Law.
Example: Hydraulic level
• Applied force Fi 
change in pressure
p=Fi/Ai=Fo/Ao.
• Therefore output force
is Fo=FiAo/Ai.
• Therefore
• Fo > Fi if Ao > Ai
• How about work done?
Archimedes’ Principle
• Buoyant force – upward
force in liquid because of
increasing pressure in
liquid as one goes down
below the surface.
• (a) a hole in water.
Notice that the hole is in
static equilibrium if it is
filled with water.
Archimedes’ Principle
• (a) a hole in water.
Notice that the hole is in
static equilibrium if it is
filled with water.
• Therefore the upward
force = mfg, mf = mass of
displaced water.
Archimedes’ Principle
• (b) The hole in water is
replaced by a solid with
the same shape.
• Since nothing changes in
water, therefore the
upward force = mfg, mf =
mass of displaced water
= buoyant force
Archimedes’ Principle
• (c) The solid in water is
replaced by a piece of
wood with mw < mf..
• In this case the wood
float on the surface with
Fb=mwg.
Archimedes’ Principle
• When a body is fully or partially submerged
in a fluid, a buoyant force Fb from the
surrounding fluid acts on the body. The force
is directed upward and has a magnitude
equal to the weight mfg of the fluid that has
been displaced by the body.
Archimedes’ Principle
• Question: Imagine a large sphere of water
floating in outer space. The sphere of water
is formed under its own gravity. Is there any
buoyant force if an object enters this sphere
of fluid?
PRESSURE
• Pressure is the quantity that is related to the force acting on
the walls of the balloon and is defined as the normal force per
unit area.
• If F is the force perpendicular to the surface area A, the
pressure P is therefore
F
P
A
• The pressure at a point in a fluid depends on the depth.
Greater depths result in greater pressures
• Pascal’s Law:
For a confined fluid in a container, the change in pressure will
be transmitted without loss to every point of the liquid and
to the walls of the container
• Archimedes’ Principle:
Any body that is completely or partially submerged
in a fluid will experience an upthrust that is equal
to the weight of the fluid displaced by the body
Fluids in Motion
• An ideal fluid is one that
(i) flows smoothly,
(ii) is non-viscuous,
(iii) is incompressible,
(iv) is irrotational.
• The path of steady flow can be visualized using streamlines.
• Under steady-state flow conditions, for a given time interval,
the volume of liquid flowing into the tube must equal the
volume of liquid flowing out of a tube.This is known as the
Continuity Equation.
Flowing liquids
• The continuity equation – conservation of
mass in a incompressible liquid flow.
V  A1v1t  A2 v2 t
or
A1v1  A2 v2
v = velocity of fluid
flowing through
area A in the tube
Example
• What is the volume flow rate of water if
Ao=1.2cm2, A=0.35cm2 and h=45mm.
A0v0  Av
v 2  v02  2 gh
2 ghA2
 v0 
 28.6cm / s.
2
2
A0  A
RV  A0v0  34cm3 / s.
Bernoulli’s Equation
• Bernoulli’s Equation relates the elevation y,
speed v and pressure P of a fluid at any point
in a tube.
• According to Bernoulli’s Equation:
1 2
P  v  gy  constant
2
• However, Bernoulli’s Equation is not
applicable to viscous fluids .
Bernoulli’s Equation
• Bernoulli’s Equation is
a consequence of
conservation of
energy in steady flow.
W  K ;
1
1
2
K  mv2  mv12
2
2
1
 V (v22  v12 )
2
Bernoulli’s Equation
• Bernoulli’s Equation is
a consequence of
conservation of
energy in steady flow.
W  Wg  WP ;
Wg  ( V ) g ( y2  y1 )
W p   p2 V  p1V
Bernoulli’s Equation
• Adding together, we
obtain
1 2
1 2
p1  v1  gy1  p2  v2  gy2
2
2
or
1 2
p  v  gy  c
2
(Bernoulli’s
Equation)
Example
• What is the speed v of
the water emerging
from the hole?
• Show that v2=2gh
(same as free fall)
DENSITY
•The density is an important factor that
determines the behaviour of a fluid.
•The density of a fluid  is defined as the
mass m per unit volume V:
m

V
•The SI unit for the density is kg / m
3