B.A. Gonzales Jan 2015

Review: Units and Dimensions

DIMENSION

-Qualitatively defines a measurable/observable

physical entity

Examples: time, length, mass, area, volume,

force, and energy

B.A. Gonzales Jan 2015

Review: Units and Dimensions

7 Primary Dimensions

Expresses a physical entity:

Length, Time, Mass, Temperature

Electric Current, Amount of Substance

Luminous Intensity

B.A. Gonzales Jan 2015

Review: Units and Dimensions

UNIT

-Quantitative magnitude of a dimension

Ex.

Mass: grams, kilograms, ounces, pounds

Viscosity: Pascal-second, centipoise

Energy: Joule, calories

B.A. Gonzales Jan 2015

REMINDERS

- Dimensions should always be consistent on

both sides of an equation

- Write units for each dimensional quantity

within the equation to avoid mistakes in

calculations

B.A. Gonzales Jan 2015

yummymummyclub.ca

SI vs English Units

English system with so many symbols to

designate units

SI has 7 base units, 2 supplementary

units, and many derived units

BASE UNITS:

- Can be easily observed and directly

measured but cannot be expressed in

simpler forms

B.A. Gonzales Jan 2015

SI Base Units

Measurable attribute or

Phenomena of Matter Name Symbol

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

B.A. Gonzales Jan 2015

Units of Measurement

Sample definition:

Unit of time (second) - The second (s)

is the duration of 9,192,631,770

periods of radiation corresponding to the

transition between the two hyperne

levels of the ground state of the cesium-

133 atom.

B.A. Gonzales Jan 2015

Comparison of the two systems

for primary or basic units

Primary

Quantities Symbol

Units

SI English

Mass M, m 1 kg 2.204 lb

Length L 1 m 3.281 ft

Time t 1 s 1 s

Temperature T 1oC 1.8oF

B.A. Gonzales Jan 2015

Units of Measurement

DERIVED UNITS

Algebraic combination of base units by either

multiplication or division.

Quantity Name Symbol

Area square meter m2

Volume cubic meter m3

Speed,

Velocity meter per second m/s

Acceleration meter per second squared m/s2

Units of Measurement

Quantity Name Symbol

Density, mass

density Kilogram per cubic meter Kg/m3

Current

Density Ampere per square meter A/m2

Magnetic Field

Strength Ampere per meter A/m

Concentration Mole per cubic meter mol/m3

B.A. Gonzales Jan2015

Units of Measurement

Quantity Name Symbol

Specific

Volume Cubic meter per kilogram m3/kg

Luminance Candela per square meter cd/m2

B.A. Gonzales Jan2015

Sample Definition of a Derived Unit

Newton (N): The Newton is the force that

gives to a mass of 1 kg an acceleration of 1

m/s2

(Singh and Heldman, 2009)B.A. Gonzales Jan2015

(Singh and Heldman, 2009)B.A. Gonzales Jan 2015

Units of Measurement

Dimensionless Units

-simply numeric without dimensions

(i.e. Specific gravity)

-useful in analysis of complex phenomenon

(modeling)

Ex. Nusselt No. (Nu), Reynolds No. (Re)

Body Mass Index (BMI)

B.A. Gonzales Jan 2015

Conversion Factors

1 ft = 12 in = 0.3048m 1 kWh = 3600kJ

1 in = 2.54 cm oF = 32 +1.8*oC

1 US gallon = 3.7854 l oR = 460 + oF

1 lbm =0.4536 kg K = 273.15 + oC

1 lbf = 4.4482 N

1 atm = 101,325 Pa = 14.696 psi

1 HP = 745.7 W

1 Btu = 1055.06 J = 0.25216kcal

B.A. Gonzales Jan 2015

Sample Conversions

1. Convert 25.7 PSI to kPa

2. Convert 100 Btu/h ft2oF to kW/m2oC

3. Convert 0.5lbf s/ft2 to Pas

B.A. Gonzales Jan 2015

Systems

B.A. Gonzales Nov 2012

System: Definition of Terms

System: region prescribed in space or a finite quantity of matter

enclosed by a boundary

Boundary: can be real or imaginary; may be stationary or moveable (see below)

Surroundings: everything outside the boundary

(Singh and Heldman, 2009)

System can be:

Closed system

the boundary of the

system is impervious to

flow of mass

System: Definition of Terms

(Singh and Heldman, 2009)

System can be:

Open system

both heat and mass

can flow into or out of

the system boundary

System: Definition of Terms

(Singh and Heldman, 2009)

System can be:

Adiabatic

closed or open system without heat

transfer (unrealistic)

Isothermal

system processes at constant

temperature

System: Definition of Terms

(Singh and Heldman, 2009)

PROPERTIES

Extensive / Extrinsic

depends on the extent of the size of the

system (ex. Mass, volume, length,

energy)

System: Definition of Terms

(Singh and Heldman, 2009)

PROPERTIES

Intensive / Intrinsic

does not depends on the size of the

system (ex. Density, temperature,

pressure)

System: Definition of Terms

(Singh and Heldman, 2009)

Equilibrium

all properties of a system do not change

State

equilibrium condition of the system

Steady State Condition

flow rate does not change

with time

System: Definition of Terms

glogster.com

(Singh and Heldman, 2009)

Thermal equilibrium

uniform temperature

Mechanical equilibrium

uniform pressure

System: Definition of Terms

(Singh and Heldman, 2009)

phase equilibrium

two or more phases with constant mass

Chemical equilibrium

chemical composition of materials

remain constant with time

System: Definition of Terms

(Singh and Heldman, 2009)

process

happens when system undeoes a change

of state

System: Definition of Terms

(Singh and Heldman, 2009)