1. INTRODUCTION TO BASIC CONCEPTS AND CALCULATIONS

2. TOPICS Units and dimensions Conversion units
Systems of units Dimensional
Dimensional homogeneity and dimensionless quantities
Process data presentation

3. Units
A measured or counted quantity that has a numerical value and unit
Example: 10 m

4. DIMENSIONS Is a property that can be:
measured, such as length, time, mass or temperature
Calculated by multiplying or dividing other dimensions, such as length/time (velocity), lenght3 (volume), or mass/length3 (density)

5. UNITS AND DIMENSIONS Units can be treated like algebraic variables
Numerical values and their corresponding units may always be combined by multiplication or division

6. CONVERSION OF UNITS
To convert a quantity expressed in terms of one unit to its equivalent in terms of another unit, multiply the given quantity by the conversion factor.

7. Conversion Factor Example:
To convert 100 mg to its equivalent in grams, write
(100 mg)*1g/1000 mg=0.1 g
The equivalence between two expressions of a given quantity defined in terms of ration (new unit/old unit)

8. Other example
Convert an acceleration of 1 cm/s2 to its equivalent in km/y2
km/y2

9. COMPONENTS OF THE SYSTEMS OF UNITS
Base units:
Mass
Length
Time
Temperature
Electrical current and
Light intensity

10. COMPONENTS OF THE SYSTEMS OF UNITS
Multiple variables
Defined as multiples or fractions of base units such as minutes, hours and milliseconds.
Example: Is more convenient to refer
3 years than 94,608,000 s

11. COMPONENTS OF THE SYSTEMS OF UNITS
Derived units
a) By multiplying or dividing
Example, m/s, kg.m/s
b) defined equivalents of compounds units
Example, 1 lbf = lbm.ft/s2

12. SYSTEMS OF UNITS Systeme Internationale d’Unities (or the SI system)
CGS (Centimetre-Gram-Second)
American Engineering System

13. Quantity
Unit
Symbol
Length
meter (SI)
Centimeter m cm
Mass
Kilogram (SI)
Gram kg g
Moles
Gram-mole
mol or g-mole
Time
Second s
Temperature
Kelvin K

14. Quantity
Unit
Symbol
Electric current
Ampere A
Light
Candela cd

15. Derived units Quantity Unit Symbol Equivalent terms of Base Units
Volume
Liter
l or L
0.001 m3
Force
Newton(SI)
Dyne(CGS) N
1 kg.m/s2
1 g.cm/s2
Pressure, Energy, Work
Pascal(SI)
Joule (SI)
Erg (CGS)
Gram-calorie Pa J
cal
1 N/m2
1N.m=1 kg.m2/s2
1dyne.cm=4.184kg.m2/s2
4.184J=4.184 kg.m2/s2

16. Derived units Quantity Unit Symbol Equivalent in terms of Base Units
Power
Watt W
1 J/s=1 kg.m2/s2

17. Dimensional homogeneity
Every valid equation must be dimensionally homogeneous.
1. All additive terms on both sides of the equation must have the same dimensions
2. An exponent must itself be dimensionless – a pure number.
3. All the factors in the equation must be collectible into a set of dimensionless groups
Example

18. Dimensional Method Purpose: To solve engineering problems
Method of attacking experimentation
Method to intermediate between formal mathematical development and a completely empirical study.

19. Dimensional Analysis
Algebraic treatment of the symbols for units considered independently of magnitude.
Advantages: simplify the task of fitting experimental data to design equations.

20. THE END