# Units Conversions - PowerPoint PPT Presentation

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Units Conversions. Chapter 14. It is absolutely essential to report units with the number answers. Unit History. inch width of your thumb foot originally the length of your foot, now greater yard three feet, from nose to middle finger. Unit History. fathom 6 feet, arm span mile

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Units Conversions

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## Units Conversions

Chapter 14

It is absolutely essential to report units with the number answers.

### Unit History

• inch

• foot

• originally the length of your foot, now greater

• yard

• three feet, from nose to middle finger

### Unit History

• fathom

• 6 feet, arm span

• mile

• 1000 paces, 5280 feet

• furlong

• 220 yards

Example:

T = 77 K

### Mass

• the quantity of matter in an object

• the measurement of the inertia

• measured in kilograms (kg)

### Weight

• the force upon an object due to gravity

• Weight = Mass  Acceleration of gravity

Fg = mg

• measured in Newtons (N) in the metric system or pounds (lb) in the British system

### Engineering Mass and Weight

• Pound-Mass

• lbm

• One pound-mass weighs 1 pound.

• 1 slug = 32.2 lbm

• Pound-Force

• lbf

• It is the same as a pound (lb).

• 1 lbf = 1 lb

### Chapter 15

Dimension

Symbol

Length

Mass

time

force

electric current

absolute temperature

luminous intensity

[L]

[M]

[T]

[F]

[A]

[q]

[/]

### Dimensions

Base Unit

Fundamental Dimension

time

electric current

absolute temperature

luminous intensity

amount of substance

second (s)

ampere (A)

kelvin (K)

candela (cd)

mole (mol)

### Base Units

Fundamental Dimension

Base Unit

length [L]

mass [M]

time [T]

electric current [A]

absolute temperature [q]

luminous intensity [l]

amount of substance [n]

meter (m)

kilogram (kg)

second (s)

ampere (A)

kelvin (K)

candela (cd)

mole (mol)

### What are these things?

• See fundamentalSI.ppt for information about these 'things'

Decimal Multiplier

Prefix

Symbol

nano

micro

milli

centi

deci

deka

hecto

kilo

mega

giga

10-9

10-6

10-3

10-2

10-1

10+1

10+2

10+3

10+6

10+9

n

m

m

c

d

da

h

k

M

G

### Supplementary SI Dimensions

Supplementary Dimension

Base Unit

plane angle

solid angle

### Force = (mass) (acceleration)

Fundamental Dimension

Base Unit

length [L]

force [F]

time [T]

foot (ft)

pound (lb)

second (sec)

### U.S. Customary System of Units (USCS)

Derived Dimension

Unit

Definition

lbf sec2/ft

mass [FT2/L]

slug

### Force = (mass) (acceleration)

F = ma

W = mg

Fundamental Dimension

Base Unit

length

mass

force

time

electric charge [Q]

absolute temperature

luminous intensity

amount of substance

foot (ft)

pound (lbm)

pound (lbf)

second (sec)

coulomb (C)

degree Rankine (oR)

candela (cd)

mole (mol)

### Converting Between Foot and Meter

• To convert from foot to meter, multiply by

3.048* E-01

• To convert from meter to foot, multiply by

(3.048* E-01)-1

### Thought Item

• Concerning the previous slide, which of the following is true?

a. There are exactly 0.3048 m/ft.

b. There are exactly 0.3048 ft/m.

c. Neither a not b.

### American Engineering System

• Note, there is a problem when we use the same unit(“pound”, meaning lbf and lbm) to describe two different dimensions.

• Newton's Second Law: F = ma

 1 lbf = 1 lbm ft/s2 ??? NO!!!

• Must have conservation of units.

### Conservation of Units

• Principle of conservation of units:

• units on the left side of an equation must be the same as those on the right side of an equation

• dimensional homogeneity

### AES and Newton’s Law

• Must maintain dimensional homogeneity:

• Now we have lbf = lbf

• See gcderived.ppt for the derivation of gc

### Pairs Exercise (5 min.)

• Use a different pairing...

• The force of wind acting on a body can be computed by the formula:

F = 0.00256 Cd V2 A

where: F = wind force in lbf , Cd= drag coefficient (no units), V = wind velocity in miles per hour and A = projected area in ft2

• Is this dimensionally homogeneous?

• What are the dimensions of 0.00256?

Are units really important?

Mars Lander (ABC news)

Mars Lander (NASA)

### Temperature Exercise

• You take water from the faucet (80 oF) and bring it to a boil on the stove.

• What is the temperature change in oC?

• What is the initial temperature in oC?

### A Solution

• For the temperature change, the best solution process is to use degree equivalents

### A Solution

• For the temperature value we use temperature conversion:

oC = (5/9)*(80 - 32) = 26.7 oC