Download ICNS 132 : Fluid Mechanics

ICNS/PY 132 : Fluid Mechanics
Weerachai Siripunvaraporn
Department of Physics, Faculty of Science
Mahidol University
email&msn : [email protected]
States of Matter
gas
liquid
Solid
 Has a definite volume and shape
Liquid
 Has a definite volume but not a definite shape
solid
Gas – unconfined
 Has neither a definite volume nor shape
All of these definitions are somewhat artificial.
More generally, the time it takes a particular substance to change its shape in response
to an external force determines whether the substance is treated as a solid, liquid or gas.
A fluid is a collection of molecules that are randomly arranged and held
together by weak cohesive forces and by forces exerted by the walls of a
container. Both liquids and gases are fluids.
CH14
Introduction
What do we learn in this chapter?
First, we consider the mechanics
of a fluid at rest—that is,
fluid statics.
We then treat the mechanics of
fluids in motion— that is,
fluid dynamics.
Pressure in a Fluid
How do you feel when you are
under the water?
I feel that there
is a force acting
on me.
Where does the force come from?
Why sharp knife are better cut than dull knife?
when applying same force.
To describe, we need another physics term.
That term is called “Pressure”.
Pressure (P) is defined as the ratio of force to area.
Its unit is N/m2 or another name is pascal (Pa).
Force accelerate.
Pressure cut.
Can you do what I do?
Lying on a bed of nails!
What if she wear a pair of sneaker? Assumed that each sneaker has an
area of 20 cm x 10 cm. What pressure does she exert on the floor?
SI Unit: Kg/m3
CGS Unit: g/cm3
Density Notes
Density is defined as the mass per unit volume of the substance.
The values of density for a substance vary slightly with temperature since volume is
temperature dependent.
The various densities indicate the average molecular spacing in a gas is much greater than
that in a solid or liquid.
CH14
Section 14.2
Consider a small part of fluid,
How many force acting on it?
That is, the pressure P at a depth h below a point in the liquid at which the
pressure is P0 is greater by an amount ρgh. If the liquid is open to the
atmosphere and P0 is the pressure at the surface of the liquid, then P0 is
atmospheric pressure.
Atmospheric Pressure
Everyone is under a pressure!
You are under a pressure due to the
weight of the water.
This woman is also under the
pressure due to the air (has mass).
Atmospheric Pressure
What would happen if you go higher?
weight
of air
What would happen if you go deeper
into the ocean?
Pressure due to
weight of air
Patm  1 atm  1.013  105 Pa
This equation implies that the pressure is the same at all points having the same
depth, independent of the shape of the container.
Compare the pressure at red
marks of all containers?
The water level on both
sides are different. What
would happen next?
The water will flow from one
side to another until both side
has the same pressure at the
same depth.
Why the wall do not collapse?
In view of the fact that the pressure in a fluid depends on depth and on the value of
P0, any increase in pressure at the surface must be transmitted to every other point
in the fluid. This concept was first recognized by the French scientist Blaise Pascal
(1623–1662) and is called Pascal’s law: a change in the pressure applied to a
fluid is transmitted undiminished to every point of the fluid and to the walls of
the container.
Pascal’s Law, Other Applications
Hydraulic brakes
Car lifts
Hydraulic jacks
Forklifts
F1 < F2 when A1 < A2
An important application of Pascal’s law is the hydraulic press illustrated in Figure. A force of
magnitude F1 is applied to a small piston of surface area A1. The pressure is transmitted through
an incompressible liquid to a larger piston of surface area A2. Because the pressure must be the
same on both sides,
P = F1/A1 = F2/A2.
Therefore, the force F2 is greater than the force F1 by a factor A2/A1. By designing a hydraulic
press with appropriate areas A1 and A2, a large output force can be applied by means of a small
input force. Hydraulic brakes, car lifts, hydraulic jacks, and forklifts all make use of this principle.
Absolute vs. Gauge Pressure
P = P0 + r g h
P is the absolute pressure.
The gauge pressure is P – P0.
This is also r g h.
This is what you measure in your tires.
If the pressure inside equal to the
atmosphere pressure, tire will be flat.
Therefore, pressure inside must be
higher than atmospheric pressure.
A and B
PB = PA (at same depth)
0.760 m = 760 mm
Another unit of pressure measurement is mmHg.
sphygmomanometer
Same level as heart
Buoyancy
Object floats when its density less than its
surrounding fluid density and sinks when it’s higher.
Dead Sea, Jordan
Have you ever tried to push a beach ball under water? This is extremely difficult to
do because of the large upward force exerted by the water on the ball. The upward
force exerted by a fluid on any immersed object is called a buoyant force.
You need more
force to push the
ball beneath the
water surface!
And once it’s under
the water, it’s hard
to control it.
Consider portion of “rectangular” fluid.
In equilibrium, B = Fg = Mg
Question: Where is B from?
Higher pressure at bottom than at the top
results in upward (B) force.
Replace portion of fluid with any objects results the same thing.
the direction of motion of an object submerged in a
fluid is determined only by the densities of the
object and the fluid.
This equation tells us that the fraction
of the volume of a floating object that is
below the fluid surface is equal to the
ratio of the density of the object to that
of the fluid.
You have an object that can float in a water on Earth.
Suppose you travel to a remote planet far away from the earth.
This planet has water. But g (gravitational acceleration) is less than the
Earth.
Will your object float in the water at (a) higher, (b) lower, (c) the same
level as what is happening on Earth, or (d) sink?
Answer: Volume = 0.078 m3;
Density = 1.0256 x 103 kg/m3.
Steady or Laminar flow
The flow is said to be steady, or laminar, if each particle of the fluid follows
a smooth path, such that the paths of different particles never cross each
other.
In steady flow, the velocity of fluid particles passing any point remains
constant in time.
Turbulent flow
Above a certain critical speed, fluid flow
becomes turbulent; turbulent flow is
irregular flow characterized by small
whirlpool-like regions.
In turbulent flow, the velocity of fluid
particles passing any point changes
continuously.
Compressible flow
Viscous flow
Rotational flow
Why the cross-section area of the
water tube here is smaller than
that directly beneath the faucet?
Which point fluid has highest (and lowest) velocity?
Which point fluid has highest (and lowest) pressure?
A
B
V1 < V2
P1 > P2
Consider the flow of a segment of an
ideal fluid through a nonuniform pipe
in a time interval t.
(static fluid)
When you are in a stationary car - perhaps waiting in a left-turn lane on a fast
highway - and you are passed by a car or truck traveling at high speed, you find
that your car tends to be "attracted" towards the other vehicle. Why is that?
What happens to the air bubbles in the fluid in this pipe as they
move from the wide diameter pipe, through the narrower region
and emerge into the wider region?
There are two effects to consider here.
The continuity equation tells us that the rate of flow of a fluid increases
(decreases) as it passes from a wider (narrower) pipe to a narrower (wider) pipe.
So, the buoyant air bubbles will speed up as they pass into the narrower region
then slow down again as the emerge into the wider region.
The Bernoulli principle tells us that the pressure in the fluid depends on the
flow rate; a faster (slower) flow rate results in a smaller (larger) pressure. So,
when the bubbles move into the narrower region where the fluid is traveling
faster, they experience a smaller force and so they will expand. When the
bubbles emerge into the wider region, the flow rate is smaller but the pressure
is greater. As a result, they are compressed back to their original size.