Introduction to Engineering ENGR 1100 - System of Units
System of Units The SI system of units (Le Systeme International d unites) is the system used worldwide except for the United States, Liberia and Burma. It is the system used by scientists and engineers.
Dimensions & Units Dimension - abstract quantity (e.g. length) Unit - a specific definition of a dimension based upon a physical reference (e.g. meter)
What does a unit mean? How long is the rod? The unknown rod is 3 m long. unit number Rod of unknown length Reference: Three rods of 1-m length The number is meaningless without the unit!
Base Dimensions and Units Dimension Symbol Unit Abbreviation length [L] meter m mass [M] kilogram kg time [T] second s electric current [A] ampere A temperature [] kelvin K luminous intensity [I] candela cd amount of [N] mole mol substance
Types of SI units 1. Supplementary SI units 2. Base SI units 3. Derived SI units
Base SI units Dimension Symbol Unit Abbreviation length [L] meter m mass [M] kilogram kg time [T] second s electric current [A] ampere A temperature [] kelvin K luminous intensity [I] candela cd amount of [N] mole mol substance
Derived SI units Derived SI units are derived from various combinations of the base units Examples of derived SI units area: square meter volume: cubic meter velocity: meter per second density: kilogram per cubic meter
Derived SI units Derived SI units are also sometimes given special names Examples Frequency: hertz (per second) Force: newton (meter kilogram per square second) Pressure: pascal (newton per square meter)
How do dimensions behave in mathematical formulae? Rule 1 - All terms that are added or subtracted must have same dimensions D A B C All have identical dimensions
How do dimensions behave in mathematical formulae? Rule 2 - Dimensions obey rules of multiplication and division D C AB 2 [M] [T ] 2 [T ] [L] [M] 2 [L ] [L]
How do dimensions behave in mathematical formulae? Rule 3 - In scientific equations, the arguments of transcendental functions must be dimensionless. A B ln( x) exp( x) C D sin( x) 3 x x must be dimensionless Exception - In engineering correlations, the argument may have dimensions
Dimensionally Homogeneous Equations An equation is said to be dimensionally homogeneous if the dimensions on both sides of the equal sign are the same.
Dimensional homogeneity Example: Newton s second law F ma where F is force, m is mass and a is Using dimensional analysis: ML 2 T L T M 2 acceleration.
Dimensional homogeneity Dimensional homogeneity - used to verify the validity of an equation p T where p is pressure, is Using dimensional analysis: M LT 2 M 3 L - Is this equation correct? density and T is temperature.
Units - Conversion Factors Conversion factors developed from identities that are determined experimentally Example: feet to meter 1 ft 0.3048m 0.3048m 5 ft 5 ft 1.524m 1 ft 1 ft 1.524m 1.524m 5 3048m ft - what is 5 ft 2 equal to?
The Datum A datum is a reference point used when making a measurement. The datum should be chosen such that it does not change during the calculation. Example: What is the difference in height between the 3 rd floor and 5 th floor of a building if the 3 rd floor is 30 ft above the ground and the fifth floor is 50 ft above the ground? Assume that the ground is 100 ft above the sea-level.
Temperature Temperature is the measure of a body s thermal energy. A temperature scale uses two reference points on the mercury-in-glass thermometer.
The four temperature scales Celsius Kelvin Fahrenheit Rankine Boiling point 100 C 373.15 K 212 F 671.67 R Freezing point 0 C 273.15 K 32 F 491.67 R Absolute zero 273.15 C 0 K 459.67 F 0 R
Relationships between the temperature scales Formulas showing the relationship between the temperaturescales K C F C 32 1.8 32 F 1.8 C R K 1.8 273.15 :
Examples Convert the following to the Kelvin temperature 0 0 scale: 100 C and 100 R Using the relationships between the temperature scales K C 273.15 100 0 C 273.15 373.15 0 K : R K 1.8 R 1.8 100 R 1.8 K 55.56 K
Example The velocity of sound in air (c) can be expressed as a function of temperature (T) as given below. Find the units of the constant 49.02. c 49.02 c is in T is in ft s 0 R T
Example Solution: ft s units 49.02 s units R ft R 1/ 2 1/ 2
Example The force of wind acting on a body can be computed by the formula: where: F = 0.6375 C d V 2 A F = wind force ([ML/T 2 ]) C d = drag coefficient (dimensionless) V = wind velocity A = projected area To keep the equation dimensionally homogeneous, what are the dimensions of the constant 0.6375?
Example The force of wind acting on a body can be computed by the formula: where: F = 0.6375 C d V 2 A F = wind force is in N (N=kg m/s 2 ) C d = drag coefficient (no units) V = wind velocity is in m/s A = projected area is in m 2 What are the units of the constant 0.6375?