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# hemical Engineering Process Principl

CHAPTER 1
Basic Concepts

## In designing a new process or analyzing an

existing one, calculation of amounts and
properties of raw materials and products is
crucial.
This chapter presents the calculation
techniques of expressing the values of
process variables.

Topic Outcomes
At the end of Chapter 1, you should:
Convert one set of units in a function or
equation into another equivalent set for
mass, length, area, volume, time, energy and
force using conversion factor tables.
Identify the units commonly used to express
both mass and weight.
Identify the number of significant figures in a
given value and state the precision with
which the value is known.

## What are in this chapter?

Introduction to
Engineering
Calculations

Units and
Dimensions

Conversion of
Units

Systems of
Units

Units
Example: 2.05kg

Units

+3.56kg (yes)
Subtracted
Example: 5m 3m
(yes)
7hr 2min (no)
Multiplied
Divided
Example : 4m

12 m2

x 3m =

Conversion of Units
To convert a quantity expressed in terms of one unit to
equivalent in terms of another unit, multiply the given
quantity by the conversion factor.

Conversion factor

## a ratio of equivalent values

of a quantity expressed in different units.

## Let say to convert 36 mg to gram.

36 mg

1g
1000 mg

0.036 g
Conversion
factor

Dimensional Equation
Convert 1 cm/s2 to km/yr2
1. Write the given quantity and units on left.
2. Write the units of conversion factors that cancel the old unit and
replace them with the desired unit.
1 cm

s2

h2

day2

km

s2

h2

day2

yr2

cm

1 cm

36002 s2

s2

12 h2

12 day2

km

100 x 1000

yr2

12 yr2
=

1m

1 km

100 cm

1000 m

Systems of Units
8

Base Units

Base Units
Quantity
Length

SI

Symbol

American

Symbol

CGS

Symbol

meter

foot

ft

centimeter

cm

lbm

gram

Mass

kilogram

kg

pound
mass

Moles

grammole

mole

pound mole

lbmole

gram-mole

mole

Time

second

second

second

Temperature

Kelvin

Rankine

Kelvin

Multiple Units
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-Example :
Years
Days
Hours
Minutes

Seconds

-Example :

## Multiple Unit Preferences

tera (T) = 10

12

centi (c) = 10

-2

giga (G) = 10

milli (m) = 10

-3

mega (M) = 10

micro () = 10

-6

nano (n) = 10

-9

kilo (k) = 10

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Derivatives SI Units
Derived SI Units
Quantity

Unit

Volume

Liter

## 0.001m3 = 1000 cm3

Force

Newton
(SI)
Dyne
(CGS)

1 kg.m/s2
1 g.cm/s2

Pressure

Pascal

Pa

1 N/m2

Energy/
Work

Joule
Calorie

J
cal

1 N.m = 1 kg.m2/s2
4.184 J =4.184 kg.m2/s2

Power

Watt

1 J/s = 1 kg.m2/s3

Systems of Units
3 systems of unit:

a) SI system
b) American engineering system
c) CGS system

Derived unit for velocity in the SI System? The CGS
System? The American Engineering System?

EXERCISE

## Convert 1 miles per hour to meter per

second
Length
1 m = 100 cm = 1000 mm
=106 microns = 1010
angstrom
= 39.37 in = 3.2808 ft
= 1.0936 yd =
0.0006214 mile
1 ft = 12 in = 1/3 yd =
0.3048 m
= 30.48 cm

mi
mile
1
m
1 hr
m
1 1

0.447
hr
hr 0.0006214 mile 3600 s
s
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EXERCISE
Convert 23 Ibm.ft/min

kg.cm/s2

Mass
1 kg = 1000 g = 0.001
metric tonne
= 2.20462 Ibm =
35.2739 oz
1 Ibm = 16 oz = 5 x 10-4 ton
= 453.593 g =
0.453593 kg

to its equivalent

Length
1 m = 100 cm = 1000 mm
=106 microns = 1010
angstrom
= 39.37 in = 3.2808 ft
= 1.0936 yd =
0.0006214 mile
1 ft = 12 in = 1/3 yd =
0.3048 m
= 30.48
cm2
100 cm
12 min
kg.cm

Ibm. ft
Ibm. ft 0.453593 kg
23
23

2 2
2
2
min
min
1 Ibm
3.2808 ft 60 s
15

0.088

s2

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## Force & Weight

Force is proportional to product of mass and acceleration.
Usually defined using derived units ;

1 Newton (N)
=
1 kg.m/s2
1 dyne
=
1 g.cm/s2
1 Ibf
= 32.174 Ibm.ft/s2
Weight of an object is force exerted on the object by
gravitational attraction of the earth i.e. force of gravity, g.
Value of gravitational acceleration:
g
= 9.8066 m/s2 = 980.66 cm/s2
= 32.174 ft/s2

## Force & Weight

gc is used to denote the conversion factor from a natural

## force unit to a derived force unit.

gc

1 kg.m/s2
1N

= 32.174 lbm.ft/s2
1 lbf

## Weight & Mass

See this example:
Given the density of 2 ft3 water is 62.4 lbm/ft3. At the sea level,
the gravitational acceleration is 32.174 ft/s2.(Refer to page 13)
The mass of water is

lbm
M 62.4 3 2 ft 3 124.8lbm
ft

## The weight of water is

lbm
W 62.4 3 2 ft 3 32.174 ft / s 2
ft

Conversion factor

1lb f
2

32.174lbm ft / s

124.8lb f

Dimensions

## BASE UNITS DIMENSIONS

Quantity

SI
Unit

Dimension

Kilogra
m

Meter

Temperature

Time

Mass
Length

21

22

EXAMPLE
Spaghetti Recipe
Ingredients:
20 ml of cooking oil
100 gram of minced meat
15 cm spaghetti sticks

Value

Unit

Dimension

20

milliliter

LENGTH
[L]

100

gram

MASS
[M]

15

centimete
r

LENGTH
[L]

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Dimensional Homogeneity
Quantities can be added/subtracted if ONLY their units
are same.
Unit same, the DIMENSION of each term must be the
same.
Eg. : VELOCITY = LENGTH / TIME
(L) / (T)
(L) / (T)
(m/s)
(m/s)

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## Every valid equation must be

dimensionally homogeneous:
all additive terms on both sides of
the equation must have same
dimensions

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Examples:
F = ma

## where F = Force (N = kg.m/s2)

m = mass (kg) = ( M )
a = acceleration (m/s2)= ( L) / ( T )2

Unit:

## kg.m/s2 = (kg )(m/s2)

Dimension:
(M)(L) =(M) x (L)
( T )2
( T )2
(M)(L) =(M)(L)
( T )2
( T )2
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LEFT
= RIGHT

DIMENSIONALLY
HOMOGENEOUS
(CONSISTENT )

Dimensional Analysis
This is a very important tool to check your work
Eg. : Doing a problem you get the answer distance
d = v t2 (velocity x time2)
Units on left side = ( L )
Units on right side = ( L )/( T ) x ( T )2 = ( L ) .( T )

## Left units and right units dont match, so

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The period P of a swinging pendulum depends only
on the length of the pendulum d and the
acceleration of gravity g.
Which of the following formulas for P could be
correct ?
Given :

d = units of length ( L )
g = units of ( L / T 2).

(a)

P 2 dg

(b)

P 2

(c

d
g
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P 2

d
g

## Identify unit of P. P has units of time (T )

Make sure Left & Right unit dimensionally
homogeneous (consistent).
(a) P
(a)
(a)

2 dg
2

L L
L 2 4 T
T T
Not
Right !!

(b) P 2

d
g

L
T2 T
L
T2

Not
Right !!
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(c) P 2

d
g

L
T2 T
L
T2

Correct units!!

If an equation is dimensionally
homogeneous but its additive terms have
inconsistent unit, the terms may be made
consistent by applying conversion factors

Example:
V (m/s) = Vo (m/s) + g (m/s2) t
(min)
Apply the conversion factor

## V (m/s) = Vo (m/s) + g (m/s2) t

(min)
V = Vo + 60 g t
(60s/min)
Free Template from www.brainybetty.com

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## An equation is only VALID when it is dimensionally

Homogeneous
= consistent in UNITS!!!

## Free Template from www.brainybetty.com

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Dimensionless Quantities
Can be a pure number
Eg. : 2, 1.3 ,5/2
a multiplicative combination of variables with no net
dimensions
Eg. :

ud
Re

= (g/cm3) , u = (cm/s),
d = (cm), = (g/cm.s)
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DIMENSIONLESS
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