solids, liquids & gases

SOLID, LIQUID & GAS

INTRODUCTION

An understanding of fundamental properties of different states of mater is important in all science, engineering, and in a medicine. Force put stresses on solids, stress can strain, deform, and break those solids, whether they are steel beams or bones. Fluids under pressure can perform work, or they carry nutrient and essentials solutes, like the blood flowing through our arteries and veins. Flowing gases cause pressure differences that can lift a massive cargo plane or the roof off a house in hurricane.

Matter?Matter?

▪ ▪ solidsolid

▪ ▪ liquidliquid

▪ ▪ gasgas

What are their characteristics?What are their characteristics?

SOLIDSOLID

General types of solids : General types of solids :

▪ ▪ amorphousamorphous

▪ ▪ polycrystallinepolycrystalline

▪ ▪ crystallinecrystalline

Each type is characteristic by the Each type is characteristic by the size of an order region within the size of an order region within the materialmaterial

a)Amorphous – atoms not arranged in any orderly & repetitive array

b) Polycrystalline – High degree of order within limited regions which vary in size and orientation to each other.

c) Crystalline – High degree of order throughout the entire volume of the material.

LIQUID

▪ weaker binding▪ able to flow ▪ definite volume but no definite

shape▪ density higher than the density of

gases

GAS

▪ fills container▪ compressible ▪ flows easily ▪ very low density – each particles

are well separated

disorder short range order long range order

How the forces between atoms/molecules react?▪ Frepulsive= Fattractive (at equilibrium r )

▪ atoms repel each other due to repulsive forces (compressed)

▪ atoms attract each other corresponding to attractive force (stretched)

prepulsive r

AF

qattractive r

BF

INTERMOLECULAR FORCESINTERMOLECULAR FORCES

Graph of intermolecular force, Fresultant vs. the distance between atoms, r

r0

r = r0 ;

|Frepulsive| = |Fattractive|

r < r0;

|Frepulsive| > |Fattractive|

r > r0

|Frepulsive| < |Fattractive|

qp r

B

r

AF resultant

At equilibrium state distance between two atoms is stable (no work done) & the potential energy is minimum.If the force exists, r is change and net of work is done then change the potential energy.

rFWU

POTENTIAL ENERGY BETWEEN MOLECULESPOTENTIAL ENERGY BETWEEN MOLECULES

Minus sign means the force between the Minus sign means the force between the atoms is the same but with the opposite to atoms is the same but with the opposite to the applied forcethe applied force

DENSITYDENSITY

V

M

SI unit : kg/m3

an object having uniform composition is defined as its mass M divided by its volume V

defined as the scalar value of the force acting perpendicular to, and distributed over, a space, divided by the area of the surface :

A

FP

PRESSUREPRESSURE

unit : N/m2 / Pascal

Fluid at the rest (static)

Variation of pressure with depth

AA

HH

WW

FFTOPTOP

FFBOTTOMBOTTOM

●● For this volume For this volume not to movenot to move (static (static fluid) we must have thatfluid) we must have that

FBOTTOM = FTOP + mg

FFBOTTOMBOTTOM - F - FTOP TOP = mg = (density x Vol) x g = mg = (density x Vol) x g

FFBOTTOMBOTTOM - F - FTOP TOP = = A H g A H g

Since Force = P x ASince Force = P x A

PPBottom Bottom A – PA – PTop Top A = A = A H g, A H g, oror

PPBottomBottom – P – PTopTop = = H g H g

The pressure below is greaterThe pressure below is greater than the pressure abovethan the pressure above. .

Variation of pressure with depth

Pressure in a fluid increases with depth h

P(h)

Po = Patm

h

Pressure at depth h

P(h) = Po + ρgh

ρ = density (kg/m3) = 1000 kg/m3 for water

The pressure at the surface is The pressure at the surface is atmospheric pressure, 10atmospheric pressure, 1055 N/m N/m22

Pressure increases Pressure increases with depth, so the with depth, so the speed of water speed of water leakingleakingfrom the bottom hole from the bottom hole isislarger than that from larger than that from the the higher ones.higher ones.

● All points at the same depth must be at the same pressure

Pressure in a ContainerPressure in a Container

Example:

What pressure (due to the only water) will a swimmer 20 m below the surface of the ocean experience?

Solution:

Given h = 20 m ρsea water = 1.025 x 103 kg/m3

Thus, P= ρgh =(1.025 x 103 kg/m3)(9.8 m/s2)(20m) = 2.0 x 105 N

A water bed is 2.00 m on a side and 30.0 cm deep. Find:

a) its weightb) pressure that the water bed exerts on the

floor. Assume that the entire lower surface of the bed makes contact with the floor.

Answer :a) 1.18 x 104 Nb) 2.95 x 103 Pa

Practice 1:

a change in pressure applied to an enclosed fluids is transmitted undiminished to every point of the fluid and to the walls of the container

2

1

2

1

A

A

F

F

PASCAL’S PRINCIPLEPASCAL’S PRINCIPLE

Hydraulic lifts

Practice 2:

In a car lift used in a service station, compressed air exerts a force on a small piston of circular cross section having a radius of r1=5.00 cm. This pressure is transmitted by an incompressible liquid to a second piston of radius r2=15.0 cm.

a) What force must the compressed air exert on the small piston in order to lift a car weighing 13,300 N? Neglect the weight piston.

b) What air pressure will produce a force of that magnitude?

Answer :a) F1 = 1.48 x 103

N b) P = 1.88 x 105 Pa

ARCHIMEDES’S PRINCIPLEARCHIMEDES’S PRINCIPLEany object completely or partially submerged in a fluid is buoyed up by a force with the magnitude equal to the weight of the fluid displaced by the object.

F

B

gm

gV

hgA

hhgA

FFF

F

F

12F

12

The bouyant force equals the weight of the fluid displaced

SPECIFIC GRAVITYSPECIFIC GRAVITY

The ratio of the mass of a body to the mass of an identical volume of water is equal to the relative density

sp.gr

/

/

r

www

mm

m

m

m

Vm

Vm

mr = reduced mass

* The sp.gr tell how many times more or less dense a material is than water

SURFACE TENSION

The force per unit length exerted by the liquid surface on an object, along its boundary of contact with the object. This force is parallel to the liquid surface and perpendicular to the boundary line of contact.

γ =F / L

The force on the The force on the wire ring is wire ring is measured just measured just before the ring before the ring breaks free of the breaks free of the liquidliquid

γγ =F / 2L =F / 2L

2L = the surface 2L = the surface exerts force both exerts force both the side and the side and outside of the outside of the ringring

FLUID FLOWFLUID FLOW

Laminar or Streamline FlowLaminar or Streamline Flow

▪ ▪ if every particle that passes a particular if every particle that passes a particular points moves along exactly the same smooth points moves along exactly the same smooth path followed by previous particles passing path followed by previous particles passing that pointthat point

Turbulent FlowTurbulent Flow

● ● the flow of a fluid becomes irregular above the flow of a fluid becomes irregular above a certain velocity or under any conditions that a certain velocity or under any conditions that can cause abrupt change in velocitycan cause abrupt change in velocity● ● irregular motion is eddy currentirregular motion is eddy current

▪ The laminar or turbulent behavior of fluids is dependent by:

a) size of the object moving through the fluid, or the size of the vessel in which the fluid is moving.

b) velocity of the object, or the fluid relative to the vessel.

c) viscosity of the fluid.

▪ The relationship between these variables is described by a scaling number, which is dimentionless, called the Reynolds number, Re.

The Continuity EquationThe Continuity Equation

The rate of flow of fluids into a system equals the rate of flow out of the system

2211 vAvA

as the cross-sectional area increases, the speed decreases

Bernoulli’s EquationBernoulli’s Equation

The sum of the pressure P,the kinetic energy per unit volume and the potential energy per unit volume has the same value at all points along the streamlines

constant2

1 211 gyvP

2222

2111 2

1

2

1vgyPvgyP

TORRICELLI’S RESULTTORRICELLI’S RESULT

ghv 22

If a tank filled with fluid and open to the atmosphere has a hole at a depth,h below the surface of the water, then the speed of the fluid leaving the hole is the same as if the liquid had freely fallen through a height,h.

VISCOSITYVISCOSITY

▪ exists in both liquids and gases

▪ a frictional force between adjacent layers of fluid as the layers move past one another.

▪ in liquids – due to the cohesive force

▪ in gases – arises from collisions between the molecules

▪ coefficient of viscosity, η (unit Poiseuille, Pl or Pa.s)

▪ the more viscous the fluid, the greater is the required force.

l

AvF

POISEUILLE’S LAW

L

PPR

t

V

8flow of Rate 21

4

the rate of the flow depends on the pressure difference, the dimensions on the tube and the viscosity of the fluid

L= L= length ; R= ; R=radiusradius; ; ηη== coefficient coefficient of viscosity,of viscosity,

Practice 3:A patient receives a blood transfusion through a needle of radius 0.20mm and length 2.0 cm. The density of blood is 1050 kg/m3.The bottle supplying the blood is 0.50 m above the patient’s arm. What is the rate of flow through the needle? Given the coefficient of viscosity,η of blood is 2.7 x 10-5 N.s/m2

Solution :a)Calculate the pressure difference the level of

the blood and the patient’s arm.b)Substitute the pressure to the Poiseuille’s

equation

▪ Consider a sphere falling through a viscous fluid. As the sphere falls so its velocity increases until it reaches a velocity known as the terminal velocity. At this velocity the frictional drag due to viscous forces is just balanced by the gravitational force and the velocity is constant

▪ the terminal velocity is :

r

mgvt 6

rvFr 6

STOKES LAWSTOKES LAW