Ch6 Dimension Units Conversion

8/18/2019 Ch6 Dimension Units Conversion

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MEC 400 –

INTRODUCTION TO ENGINEERINGAND PROBLEM SOLVING

CHAPTER 6Dimensions, Units n!Unit Con"e#sions


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The magnitude of physical quantities can be understood only when they are

compared with predetermined reference amounts, called units.

Examples of physical quantities:

$en%t&, mss, time, 'o#(e, "e$o(it), ((e$e#tion, moment*m,+#ess*#e, ene#%) o# o#-, +oe#, to#.*e, e$e(t#i( (*##ent n!"o$t%e, &et, m%neti( /*, $*minn(e, (on(ent#tion, n! et(1


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Dimensions: used to describe physical quantities and are independent of

units

Types of dimension: fundamental and derived

Fundamental dimension

◦ Dimension that can be conveniently and usefully manipulated when

expressing physical quantities of particular field.

PhysicalQuantity

Dimension Possible unit

LengthMass

TimeForceDensityPower

Volume

L M

T F M / L3

F ⋅ L/ T

L3

meter, feet, milekilogram, slugs, oun!"mass

secon!, hour, !ay, oun!"forcekg/m3, g/cm3

watt, ft⋅lbf /s

m3, in3


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Tee '*n!ment$ !imensions #e ne(ess#) to 'o#m (om+$eteme(&ni($ !imension$ s)stem, nme$), $en%t& 2L3, mss 2M3, n!time 2T 31 I' tem+e#t*#e is im+o#tnt, t&en 'o*#t& !imension,

tem+e#t*#e 2θ 3 is !!e!1

De#i"e! !imensions

◦ ombinations of fundamental dimensions.

Example:

!elocity is derived from length and time as

# $ % L&%T &"'

Force "using absolute system# is derived from length, mass, and time as F $ % M &% L&%T &"(

A !imension$ s)stem (n e !e5ne! s t&e sm$$est n*me# o''*n!ment$ !imensions t&t i$$ 'o#m (onsistent n! (om+$eteset 'o# 5e$! o' s(ien(e1

T&e absolute system &s s its '*n!ment$ !imensions L, T n! M1

A!"(om+#ison o' msses t "#io*s $o(tion (n e m!e7no %#"ittion$ e8e(t

T&e gravitational system &s s its '*n!ment$ !imensions L, T n!91

A!" sim+$i') (om+*ttion &en ei%&t is '*n!ment$ .t) in (om+*ttions


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Two basic !imensional system

Dimensional Analysis - a manipulation of fundamental dimensions to express the

new derived dimensions or to get consistent dimensions for all terms in the

equations. $n other words, the equation must be dimensionally homogeneous at

every stage in the manipulation.

Example:

%ressure: p & "force#'"area#

&( p & ML)*T )+

or-: W & "force#"distance#

&( W & "M #"L#"T #)+"L# or ML+T )+

Quantity )bsolute *ra#itationalLength L L

Time T T"

Mass M FL"'T(

Force MLT"( F

Velocity LT"' LT"'

Pressure ML"'T"( FL"(

Momentum MLT"' FT

+nergy ML(T"( FL

Power ML(T"3 FLT"'

Torue ML(T"( FL


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Throughout the world, there are several systems of units in use. The most

common systems of units are $nternational ystem "$# and / ustomaryystem"/# .

$nternational ystem of /nit "$#

0asis for worldwide standardi1ation of measurements.

Divided 2 classes of units:

*. 0ase units)3

+. upplementary units)+

2. Derived units)combine base 4supplementary 4other derived units


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Table of base units

Table of supplementary units

Quantity -nit .ame -nitymbol

LengthMassTime

+lectric currentThermo!ynamic

temerature

)mount of substanceLuminous intensity

meter kilogramsecon!amerekel#inmole

can!ela

mkgs)0

mol

c!

Quantity -nit .ame

-nit ymbol

Plane angleoli! angle

ra!ianstera!ian

ra!sr


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Table of some derived units

Quantity -nit .ame -nit ymbol 1ase unit

FreuencyForce2

Pressure or tress2+nergy or ork 2

Power 2+lectric charge2

+lectric otential2+lectric con!uctance2Magnetic flu42

5n!uctance2

hert6newton2 ascal2 7oule2watt2

coulomb2

#olt2siemens2weber 2henry2

86 .2Pa292

2:2

V22b282

s"'kg2m2s"(

kg2m"'2s"(

kg2m(2s"(

kg2m(2s"3

)2s

/);

2)/V;2V2s;

b/);2


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/nit ymbols and 5ames

*. %eriods should never be used after symbols unless symbol is at end ofsentence.$ units symbols are not abbreviations.

+. /nit symbols are written in lower case"unless symbol from propername#.

2. ymbols rather than self)styled abbreviations should be used torepresent units.

6. 5ever add s to symbol to indicate plural

Lowercase Uppercase

7,-g,s,mol 8,9,1,%a

Correct Not correct

9 amps sec


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;. 9dd a space between numerical value and unit symbol.

8 m, ? F

Correct Not correct

;


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@. ymbol should be used in preference to unit name because symbols arestandardi1ed."except when number is written in words preceding unit#.

e.g: ten meters, not ten m

7ultiplication and Division.

*. /se space'hypen when write unit names. Eg: 5ewton meter or 5ewton)meter

+. hen a quotient is expressed using unit names, always use the word

AperB and a space between them) not a slash "'#.

2. hen unit names require a power, a modifier such as squared or cubed

are employed.

Correct Not correct

7eter per second 7eter'second

Correct Not correct

7illimeter squared quare millimeter


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6. riting products and quotients using symbols, the center dot " ⋅ # and the

slash " ' # are used respectively.

;. hen denoting a quotient by unit symbols, any of following methods areaccepted form:

or m/s or ms"'

5umbers

*. To denote decimal poiunt, use period on line. hen expressing numbersless than *, a 1ero should be written before decimal mar-er.E.g: *6.3,C.C2

+. 9dd space to group or separate digits of 2.

Correct5.7 for 5ewton meter

Correct and recommended procedure


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ince many unit systems have been used around the world, we need to

-now how to convert the units from one system to another system.

Some o' t&e im+o#tnt n! '#e.*ent$) *se! (on"e#sion '(to#s #e%i"en in t&e t$es e$o1

Numerical relationship between SI and English units Relationships between certain quantities in English system

+nglish 5

' ft .

' slug '=2?A kg

'oB 8

A

?

' ft $ '( inch

' mi $ ?(>< ft

' slug $ 3(2( lbm' y! $ 3 ft

' ki $ '


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Ch6 Dimension Units Conversion

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