Dimensions and Units

8/9/2019 Dimensions and Units

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DIMENSIONS AND UNITSCHAPTER 1


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CONVERSIONS AND

APPLICATIONS DIMENSION

Quantity that can be measured

UNITS

Its how you express dimension


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SYSTEMS OF MEASUREMENT

A set of units which can be used tospecify anything which can be

measured and were historically

important, regulated and definedbecause of trade and internal

commerce.


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SYSTEM OF UNITS

CGS Centimeter-Gram-Secondsystem

American Engineering System

MKS Meter-Kilogram-Second

system

International System of Units (SI)


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Quantity SI CGS AES

Length m cm ft

Mass kg g lb

Moles gmole gmole lbmole

Time s s s

Temperature K K F

Force N dyne lbf


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UNITS

FUNDAMENTAL

Set of units of physical quantities from

which every other unit can be generated.

DERIVED

Combination of fundamental units by

multiplying or dividing dimensions


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FUNDAMENTAL UNITS

Quantity Name of Unit

length meter (m)

mass kilogram (kg)

time second (s)electric current ampere (A)

thermodynamic temperature kelvin (K)

amount of substance mole (mol)

luminous intensity candela (cd)


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DERIVED UNITSQuantity Name of Unit Definition

capacitance farad (F)Coulomb/volt, (amp *

second/volt)

charge, quantity of Coulomb (C) (amp * second)

energy (work) Joule (J) Newton-meter, (kg * m2 / sec2)

force Newton (N) Joules/meter, kg * m / sec2

inductance Henry (H) volt * second/Ampere

magnetic flux Weber (Wb) volt * second, (Mead page11)

magnetic flux density Tesla (T)

(Webers / meter2); (joules *

second) / (Coulomb *

meter2);

(Note: 1 tesla = 1.0e4 Gauss

= 1Newton/(amp * meter))

potential difference

(electromotive force)volt (V)

joules/Coulomb, (kg * m2 /

(sec2 * Coulomb)),

watts/Ampere

power Watt (W)joules/second, (volts *

Ampere)

resistance Ohm volts/Ampere


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Convert the following


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Dimensional Analysis

Dimensions & units can be treated algebraically.

Variable from Eq. x m t v=(xf-xi)/t a=(vf-vi)/t

dimension L M t L/t L/t2


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Dimensional Analysis

Checking equations with dimensionalanalysis:

Each term must have same dimension

Two variables can not be added if

dimensions are different Multiplying variables is always fine

Numbers (e.g. 1/2 or p) are dimensionless

xf xi vit1

2

at2


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Example 1.1

Check the equation for dimensional consistency

2

2

2

)/(1mc

cv

mcmgh

Here, m is a mass, g is an acceleration,

c is a velocity, h is a length


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Example 1.3

Given x has dimensions of distance, u has

dimensions of velocity, m has dimensions of

mass and g has dimensions of acceleration.

Is this equation dimensionally valid?

Is this equation dimensionally valid?

x (4 / 3)ut

1 (2gt2 /x)

x vt

1mgt2


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Dimensions and Units