class-01-i

8/3/2019 Class-01-i

1/15

Copyright 2011 Cneyt Arslan, All rights reserved.

SYSTEM of UNITS SI (Standard International)

Metric (cgs, mks) British system (foot, pound, mile, yard, ounce,...)

SI units

mass: kg, distance: m, time: s, temp: KForce Newton (N) = kg m / s2

Work Newton-meter = kg m2/ s2

Energy Joule (J) = N m

Pressure Pascal (Pa) = N / m2Gravity g = 9.80665 m / s2

Temp Kelvin (K) = C + 273.15


cgs unitscentimeter (cm) gram (g) second (s)

1 g mass (g) : 10 3 kg mass1 cm : 10 2 m1 dyne (dyn) : 1 g cm / s2 = 10 5 N1 erg : 1 dyn cm = 10 7 Jg = 980.665 cm / s2

British unitsfoot (ft) pound (lb) second (s)

1 pound mass (lbm) : 0.453 kg1 pound force (lbf) : 4.4482 N1 foot (ft) : 30.48 cm1 lbf ft : 1.35582 N m = 1.35582 J1 psia : 6.89476 103 N / m2

g = 32.74 ft / s2

8/3/2019 Class-01-i

2/15


Pressure

1 atm : absolute pressure = 0C, 760 mm Hg: 29.921 inch Hg column = 14.696 lbf/ in2 = psia

1 psia : C, 33.9 ft H2O column1 psig : gauge pressure

Example :21.5 lbf/ in2 gauge pressure (psig) = 21.5 + 14.7 = 36.2 psia

1 psia : 6.89476 103

Pa (N/m2

)1 atm : 1.01325 105 PaBlaise Pascal1623-1662


Temperature

conversion formulae:

F = 32 + 1.8 CR = F + 460K = C + 273.15

C F K R

Boiling water 100 212 373.15 671.7

Melting ice 0 32 273.15 491.7Absolute zero -273.15 -459.7 0 0

Anders Celsius1701-1744

Gabriel Fahrenheit1686-1736

William T. Kelvin1824-1907

William M. Rankine1820-1872
http://www.astro.uu.se/history/images/celsius_face.jpg

8/3/2019 Class-01-i

3/15



Ideal Gas Law (BOYLEs law)

T P V n RK N/m2 m3 kg mol 8314.3 kg m2/ kg mol s2 KR atm ft3 lb mol 0.7302 ft3 atm / lb mol RK atm cm3 g mol 82.057 cm3 atm / g mol K

Robert Boyle1627-1691P V = n R T
http://enlarge%28%27boyle.jpeg%27%29/

8/3/2019 Class-01-i

4/15


1 calorie will raise the temperature of 1 g of water by 1 C.

The dietary calorie is actually 1 kcal.1 cal = 4.184 J

1 BTU (British Thermal Unit) will raise the temperature of

1 lb of water by 1F.1 BTU = 1055 J

The erg is the c.g.s. unit of energy and a very small one; the workdone when a 1-dyne force acts over a distance of 1 cm.

1 J = 107 ergs1 erg = 1 d-cm = 1 g cm2 s2

The electron-volt is even tinier: 1 e-v is the work required to

move a unit electric charge (1 C) through a potential difference of

1 volt.

1 J = 6.24 1018 e-v

The Watt is a unit of power, which measures the rate of energy

flow in J sec1. Thus the Watt-hour is a unit of energy.

An average human consumes energy at a rate of about 100 Watts;

the brain alone runs at about 5 Watts.

1 J = 2.78 104 W-h

1 W-h = 3.6 kJ

The liter-atmosphere is a variant of force-displacement work

associated with volume changes in gases.1 L-atm = 101.325 J

The huge quantities of energy consumed by cities and countries

are expressed in quads; the therm is a similar but smaller unit.1 quad = 1015 Btu = 1.05 1018 J

If the object is to obliterate cities or countries with nuclear

weapons, the energy unit of choice is the ton of TNT equivalent.1 ton of TNT = 4.184 GJ(by definition)

In terms offossil fuels, we have barrel-of-oil equivalent, cubic-

meter-of-natural gas equivalent, and ton-of-coal equivalent.

1 bboe = 6.1 GJ

1 cmge = 37-39 mJ

1 toce = 29 GJ


PROPERTIES of FLUIDS

Liquids Gases

Types of Flow & Reynolds Number

Osborne Reynolds, showed that there are

two different flow patterns exist (1883):

V1 V2 > V1(Laminar) (Turbulent)

Osborne Reynolds1842-1912

8/3/2019 Class-01-i

5/15


Reynolds suggested the following formula to determine theflow characteristics:

where:

Vx : average fluid velocityD : tube diameter

: kinematic viscosity of the fluid

Re is dimensionless and:

if < 2100 then Laminar Flowif > 2100 then Turbulent Flow

DVRe x


NEWTONIAN FLUIDS

Momentum Transport

(Newtons Law of Viscosity)

The ( ) sign indicates that:

The Momentum moves towards thedirection of decreasing velocity.

Similar to the Heat, which movestowards the direction of decreasingtemperature.

Y t = 0both plates are

motionless

y

x

Vx(y,t)

Vo

t > 0lower plate starts

to move with Vo

Vx(y)

Vo

t >> 0steady-state

vel.profile is linear

Y

V=

A

F

dy

dV= Velocity

gradient

Shear

stress

8/3/2019 Class-01-i

6/15


VISCOSITY CONCEPT (AND ITS UNITS)

Newtons

Law of Viscosity

All gases, many liquid metals, and metallurgically important slags obey

this law, and thus they are called NEWTONIAN FLUIDS.

On the other hand, polymer solutions, mudds, dyes, etc. disobey this

rule and they are named as NON-NEWTONIAN FLUIDS.

dy

dV=

Isaac Newton1643 - 1727


British System :

dydV

2f1

2f

fthlbft/hft

ftlb11

m11

22m

fthlbft)hft(

ft)hftlb(

Metric System :

centipoise (cP) = 0.01 P(viscosity of water at 20.2 C)

11

2

cmsg

cmsdyn)P(Poise

Units of Viscosity

Jean Louis Marie Poiseuille1799 - 1869

8/3/2019 Class-01-i

7/15


Kinematic Viscosity :

= ft2 h 1 British system

= cm2 s 1 (Stoke) SI system

viscosity

density

1 lbm = 453.9 g

1 lbf = 32.174 lbm ft s 2

1 cP = 2.42 lbm h 1 ft 1

1 cP = 2.09 10 5 lbf s ft 2

Some conversion factors

George Gabriel Stokes1819 - 1903


PROBLEMThere are 1/8 inch distance between two parallel plates. Upper plate

moves with a velocity of 5 ft s 1 while the lower plate rests. Calculate the

viscosity of the fluid between these plates, both in [lbm ft1 h 1] and [cP]

if the power required to move upper plate is 0.05 lbf ft2.

YV

AF

/

/21

2

261.1

1

2.32

1

05.0sftlb

lb

sftlb

ft

lb

A

Fm

f

mf

11

480

961

5s

ft

sft

Y

V

11

1

21

08.121

3600

480

61.1hftlb

h

s

s

sftlbm

m

cP99.442.2

08.12

8/3/2019 Class-01-i

8/15


PROBLEM

Calculate the kinematic viscosity (ft2 h 1) of liquid iron at 1700 C.

( = 5.6 cP, = 7.06 g cm 3).

122

3

112

10793.006.7

106.5scm

cmg

cmsg

12

2

22

122

0305.01

3600

48.30

1

10793.0 hfth

s

cm

ft

scm


FACTORS AFFECTING VISCOSITY

Temperature Composition Pressure

As the temperature increases: viscosity of gases increases,

viscosity of liquids decreases.

Pressure has a very little effect on liquids viscosity. (can be ignored)

Keeping the viscosity of slags and metals low is important in terms ofmetallurgical mass transport operations.

(suitable contact and mass separation)

8/3/2019 Class-01-i

9/15


Fluid Viscosity (cP)

Hydrogen

0.00840.0088

0.01260.01670.0214

Air

0.01710.01830.02640.03410.04420.0521

Water

1.7901.0100.4690.284

Iron

Temp. ( C)

020.7

229490825

018

229409810

1134

02060

100

15501600170018001850

6.76.15.65.35.2


Effect of temperature on the

viscosity of liquid silica.

8/3/2019 Class-01-i

10/15


Effect of temperature

on the viscosity ofZinc-Aluminumalloys.


VISCOSITY OF GASES

Molecular Field of Force model uses the potential energy(Lennard-Jones Potential) of intra-molecular interaction :

Chapman & Enskog equation:

: viscosity (P)M : mol wt of gasT : temperature (K)

: diameter of gas molecule (): collision integral of C&E theory

is a function of dimensionless temperature parameter ( BT / ).

: energy parameter of intra-molecular interaction

B : Boltzmann constant (1.38044 10 16 erg mol 1 K 1)

2

51067.2

TM (valid for low pressure andnon-polar gases)

Ludwig Boltzmann1844-1906
http://enlarge%28%27boltzmann.jpeg%27%29/

8/3/2019 Class-01-i

11/15


Intra-molecular force parameters of some gases

Mol Weight (Angstrm) / B (K)

Hydrogen 2.016 2.915 38.0Helium 4.003 2.576 10.2

Neon 20.183 2.789 35.7

Argon 39.944 3.418 124

Krypton 83.80 3.498 225

Xenon 131.3 4.055 229

Air 28.97 3.617 97

Nitrogen 28.02 3.681 91.5

Oxygen 32.00 3.433 113

Carbon monoxide 28.01 3.590 110

Carbon dioxide 44.01 3.996 190

Sulfur dioxide 64.07 4.290 252Fluorine 38.00 3.653 112

Chlorine 70.91 4.115 357

Lennard - Jones Parameters

Methane 16.04 3.822 137


Temperature parameter & collision integral for gas viscosities

0.3 2.785

0.4 2.492

0.5 2.257

0.6 2.065

0.7 1.908

0.8 1.780

0.9 1.675

1.0 1.587

2.0 1.175

4.0 0.9700

6.0 0.8963

8.0 0.8538

10 0.8242

20 0.7432

40 0.6718

60 0.6335

80 0.6076

100 0.5882

200 0.5320

400 0.4811

B T /

8/3/2019 Class-01-i

12/15


Viscosityofsomegasesat1atm


Problem :Determine the viscosity (P) of hydrogen at 1 atm and 2000 F.

From the tables : / B = 38 K and = 2.915

BT / = 1364 / 38 = 35.89 which corresponds to 0.69

Substituting in the formula:

Poise42

51048.2

69.0915.2

136421067.2

2.44 10 4 P (measured value)

8/3/2019 Class-01-i

13/15


Formula developed for multi-component gas mixtures:

where;

xi : mol fraction of i

Mi : mol weight of i

2/1

2/1

ii

iii

Mx

Mx

mix

Viscosity of H2

and CO2

gas mixture at 15 C.


Problem :Calculate the viscosity of gas mixture containing: 20% Zn, 50% N2 and30% CO, at 1000oC.

For zinc

Similarly, for N2 and CO (from ChemicalEngineers Handbook):

N2 = 500 106 P and CO = 480 10

6 P

Poise6

2

510745

638.151.2

127337.651067.2

xi i Mi xi Mi1/2 xi i Mi

1/2

Zn 0.2 745 106

65.37 1.62 1210 106

N2 0.5 500 106 28.02 2.65 1325 10 6

CO 0.3 480 10 6 28.00 1.59 762 10 6

5.86 3297 10 6

PoiseMx

Mx

ii

iii

mix6

6

2/1

2/1

1056186.5

103297

8/3/2019 Class-01-i

14/15


The International Solvay Institutes for Physics and Chemistry, locatedin Brussels, were founded by the Belgian industrialist Ernest Solvay in 1912,following the historic invitation-only 1911 Conseil Solvay, the first worldphysics conference. The Institutes coordinate conferences, workshops,seminars, and colloquia.

The Solvay Congressof 1927

Max Planck H.A. Lorentz Einstein Max Born

Niels Bohr

Werner Heisenberg

Louis de Broglie

Erwin Schrdinger


They occur every three years. The 23rd Solvay Conference took place inBrussels during December 1-3, 2005, on the subject: "The QuantumStructure of Space and Time".Perhaps the most famous conference was the October 1927 Fifth SolvayInternational Conference on Electrons and Photons, where the world's mostnotable physicists met to discuss the newly formulated quantum theory.


8/3/2019 Class-01-i

15/15


The leading figures were Albert Einstein and Niels Bohr. Einstein,disenchanted with Heisenberg's "Uncertainty Principle," remarked "Goddoes not play dice." Bohr replied, "Einstein, stop telling God what to do."Seventeen of the twenty-nine attendees were or became Nobel Prizewinners, including Marie Curie, who alone among them, had won NobelPrizes in two separate scientific disciplines.


class-01-i

Documents