1- property of matter

introduction

States of MatterMatter comes in a variety of states: solid, liquid, gas, and plasma.

• The molecules of solid are locked in a rigid structure and can only vibrate. (Add thermal energy and the vibrations increase.) .

•Some solids are crystalline, like table salt, in which the atoms are arranged in a repeating pattern.

•Some solids are amorphous, like glass, in which the atoms have no orderly arrangement.

•Either way, a solid has definite volume and shape.

• A liquid is virtually incompressible and has definite volume but no definite shape.

• A gas is easily compressed. It has neither definite shape nor definite volume.

• A plasma is an ionized gas and is the most common form of matter in the universe, since the insides of stars are plasmas.

Phase Changes of the matter

Evaporation: Liquid Gas

Condensation: Gas Liquid

Melting: Solid Liquid

Freezing: Liquid Solid

Sublimation: Solid Gas

FluidsThe term fluid refers to gases and liquids.

Gases and liquids have more in common with each other than they do with solids, since gases and liquids both have atoms/molecules that are free to move around.

They are not locked in place as they are in a solid. The hotter the fluid, the faster its molecules move on average, and the more space the fluid will occupy (if its container allows for expansion.)

Also, unlike solids, fluids can flow.

The mass density of a substance is the mass of a substance divided by its volume:

V

m

SI Unit of Mass Density: kg/m3

DEFINITION OF MASS DENSITY

Pressure

A

FP

Pressure is simply force per unit area.

Pressure is often measured in pounds per square inch (psi), atmospheres (atm), or torr (which is a millimeter of mercury).

The S.I. unit for pressure is the pascal, which is a Newton per square meter: 1 Pa = 1 N / m

2. Atmospheric pressure is at sea level is normally:

1 atm = 1.01 ·10 5 Pa = 760 torr = 14.7 psi.

At the deepest ocean trench the pressure is about 110 million pascals.

Pressure in a Fluid

Pressure in a fluid is the result of the forces exerted by molecules as they bounce off each other in all directions.

Therefore, at a given depth in a liquid or gas, the pressure is the same and acts in every direction.

Pressure and Depth in a Static Fluid

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mgAPAP 12

Vm

Pressure and Depth in a Static Fluid

VgAPAP 12

AhV

AhgAPAP 12

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Pressure GaugesghPP 12

ghPatm

mm 760m 760.0

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Pa 1001.1233

5

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Ph atm

Pressure Gauges

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ghPP atm pressure gauge

2

absolute pressure

Pressure Gauges

Pascal’s Principle

PASCAL’S PRINCIPLE

Any change in the pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and enclosing walls.

Pascal’s Principle

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1

1

2

2

A

F

A

F

1

212 A

AFF

Pascal’s Principle

Example : A Car Lift

The input piston has a radius of 0.0120 mand the output plunger has a radius of 0.150 m.

The combined weight of the car and the plunger is 20500 N. Suppose that the input piston has a negligible weight and the bottom surfaces of the piston and plunger are at the same level. What is the required input force?

Pascal’s Principle

N 131m 150.0

m 0120.0N 20500 2

2

2

F

1

212 A

AFF

Mass Density

Example 2 Blood as a Fraction of Body Weight

The body of a man whose weight is 690 N contains about5.2x10-3 m3 of blood.

(a)Find the blood’s weight and (b)express it as apercentage of the body weight.

Mass Density

N 54sm80.9kg 5.5 2 mgW(a)

%8.7%100N 690

N 54Percentage

kg 5.5mkg1060m102.5 333 Vm

(b)

Fluids in Motion

In steady flow the velocity of the fluid particles at any point is constant as time passes.

Unsteady flow exists whenever the velocity of the fluid particles at a point changes as time passes.

Turbulent flow is an extreme kind of unsteady flow in which the velocity of the fluid particles at a point change erratically in both magnitude and direction.

Fluids in Motion

Fluid flow can be compressible or incompressible. Most liquids are nearly incompressible.

Fluid flow can be viscous or nonviscous.

An incompressible, nonviscous fluid is called an ideal fluid.

When the flow is steady, streamlines are often used to represent the trajectories of the fluid particles.

The Equation of Continuity

The mass of fluid per second that flows through a tube is called the mass flow rate.

distance

tvAVm

2222 vA

t

m

111

1 vAt

m

The Equation of Continuity

222111 vAvA

The mass flow rate has the same value at every position along a tube that has a single entry and a single exit for fluid flow.

SI Unit of Mass Flow Rate: kg/s

Incompressible fluid: 2211 vAvA

Volume flow rate Q: AvQ

The Equation of Continuity

Example : A Garden Hose

A garden hose has an unobstructed openingwith a cross sectional area of 2.85x10-4m2. It fills a bucket with a volume of 8.00x10-3m3

in 30 seconds.

Find the speed of the water that leaves the hose through (a)the unobstructed opening and (b) an obstructed opening with half as much area.

The Equation of Continuity

AvQ

sm936.0

m102.85

s 30.0m1000.824-

33

A

Qv

(a)

(b) 2211 vAvA

sm87.1sm936.0212

12 v

A

Av

Bernoulli’s Equation

If frictional losses are neglected, the flow of an incompressible fluid is governed by Bernoulli’s equation.

Bernoulli’s equation states that at any point in the channel of a flowing fluid the the following relationship holds:

Constant2

1 2 ρvρghP

P: the pressure in the fluidh: the heightρ: the densityv: the velocity at any point in the flow channel

Constant2

1 2 ρvρghP

Bernoulli’s Equation

The first term (P) is the potential energy per unit volume of the fluid due to the pressure in the fluid. The second term (ρgh) is the gravitational potential energy per unit volume.The third term (0.5ρv2) is the kinetic energy per unit volume.

It is an expression of conservation of energy in an incompressible fluid.

Viscosity

Different kinds of fluids flow more easily than others.

Oil, for example, flows more easily than molasses. This is because molasses has a higher viscosity, which is a measure of resistance to fluid flow.

Inside a pipe or tube a very thin layer of fluid right near the walls of the tube are motionless because they get caught up in the microscopic ridges of the tube.

Layers closer to the center move faster and the fluid sheers.

The middle layer moves the fastest.

The more viscous a fluid is, the more the layers want to cling together, and the more it resists this shearing.

The resistance is due the frictional forces between the layers as the slides past one another.

Note, there is no friction occurring at the tube’s surface since the fluid there is essentially still.

The friction happens in the fluid and generates heat.

The Bernoulli equation applies to fluids with negligible viscosity.

Viscous Flow

Flow of an ideal fluid.

Flow of a viscous fluid.

The magnitude of the tangential force required to move a fluid layer at a constant speed is given by:

y

AvF

coefficient of viscosity

SI Unit of Viscosity: Pa·s

Common Unit of Viscosity: poise (P)

1 poise (P) = 0.1 Pa·s

FORCE NEEDED TO MOVE A LAYER OF VISCOUS FLUID WITH CONSTANT VELOCITY

Viscosity and Poiseuille’s Law

In a real fluid, the molecules attract to each other; consequently, relative motion between the fluid molecules is opposed by a frictional force, which is called viscous friction.

Viscous friction is proportional to the velocity of flow and to the coefficient of viscosity for the given fluid.

The velocity is highest at the center and decreases toward the walls; at the walls of the pipe, the fluid is stationary.

Laminar flow. The length of the arrows indicates the magnitude of the velocity of the fluid.

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ηL

PPπRQ

If viscosity is taken into account, it can be shown that the rate of laminar flow Q through a cylindrical tube of radius R and length L is given by Poiseuille’s law; which is

Viscosity and Poiseuille’s Law

P1 - P2: the difference between the fluid pressures at the two end of the cylinder.η: the coefficient of viscosity measured in units of dyn·sec/cm2, which is called a poise.

POISEUILLE’S LAW

This equation clearly shows that a pressure drop between two ends of a pipe is generated due to fluid viscosity.The pressure drop is inversely proportional to the fourth power of the pipe radius R.This means that for a given flow rate Q the pressure drop required to overcome frictional losses decreases as the fourth power of the pipe radius.

Turbulent Flow

If the velocity of a fluid is increased past a critical point, the smooth laminar flow is disrupted.

The flow becomes turbulent with eddies and whirls disrupting the laminar flow.

In a cylindrical pipe, the flow would be turbulent if its Reynolds number (R) is larger than a few thousands (~3000)

Dv

R ρ: the density of the fluidD: Diameter of the cylinder v: velocity of the flowη: the viscosity

As the flow turns turbulent, it becomes more difficult to force a fluid through a pipe.

Viscous Flow

Example: Giving and Injection

A syringe is filled with a solution whose viscosity is 1.5x10-3 Pa·s. The internal radius of the needle is 4.0x10-4m.The gauge pressure in the vein is 1900 Pa.What force must be applied to the plunger,so that 1.0x10-6m3 of fluid can be injectedin 3.0 s?

Viscous Flow

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s 0.3m100.1m 025.0sPa105.18

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Viscous Flow

Pa 120012 PP

Pa 19001 P

Pa 31002 P

N25.0m100.8Pa 3100 252 APF

Blood flow In humans, blood from the heart into the aorta, from which it

passes into the major arteries. These branch into the small arteries (arterioles), which in turn

branch into myriads of tiny capillaries. The blood returns to the heart via the veins. The radius of the aorta is about 1.2cm, and the blood passing through it has a speed of about 40cm/s. A typical capillary has a radius of about 4x10^-4cm and blood flows though it at a speed of about 5x10^-4m/s. Estimates the number of capillaries that are in the body!

1 1 2 2

2 21 2

291

22

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7 10 (~ 10 )

cap aorta

aorta

cap

A v A v equationof continuity

v N r v r

rvN billions

v r

Circulation of the Blood

The circulation of blood through the body is often compared to a plumbing system with the heart as the pump and the veins, arteries, and capillaries as the pipes through which the blood flows.

This analogy is not entirely correct.

Blood is not a simple fluid; it contains cells that complicate the flow, especially when the passages become narrow.

Furthermore, the veins and arteries are not rigid pipes but are elastic and alter their shape in response to the forces applied by the fluid.

Circulation of the Blood

Blood Pressure

The contraction of the heart chambers is triggered by electrical pulses that are applied simultaneously both to the left and to the right halves of the heart.First the atria contract, forcing the blood into the ventricles; then the ventricles contract, forcing the blood out of the heart.Because of the pumping action of the heart, blood enters the arteries in spurts or pulses.The maximum pressure driving the blood at the peak of the pulse is called the systolic pressure.The lowest blood pressure between the pulses is called the diastolic pressure.

Blood Pressure

In a young healthy individual the systolic pressure is about 120 torr (mm Hg) and the diastolic pressure is about 80 torr.

Therefore the average pressure of the pulsating blood at heart level is 100 torr.

Blood Pressure

Arteries in our bodies are of different size.As the size of the arteries deceases there is an increase of resistance to the blood flow.We can estimate the pressure drop when blood flows through arteries of different size using Poiseuille’s law.

421

8

πR

ηLQPPP

P1 - P2: the difference between the fluid pressures at the two end of the cylinder.η: the coefficient of viscosity measured

4

1

RP

Blood Pressure

Since the pressure drop in the main arteries is small, when the body is horizontal, the average arterial pressure is approximately constant throughout the body.

The arterial blood pressure, which is on the average 100 torr, can support a column of blood 129 cm high.

This means that if a small tube were introduced into the artery, the blood in it would rise to a hight of 129 cm. (The density of human blood is 1.048 to 1.054 g/cm3 at normal body temperature.)

torr61 hearthead gh- PP

• If a person is standing erect, the blood pressure in the arteries is not uniform in the various parts of the body.

• The weight of the blood must be taken into account in calculating the pressure at various locations.