CHAPTER 1Introduction to

Engineering Calculations

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Elementary Principles of Chemical Processes, by Richard M. Felder and Ronald W. Rousseau

By Siti Nur Fadhilah ZainudinEmail: fadhilah@ucsiuniversity.edu.my

What do you have to learn in this chapter?

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Introduction to Engineering Calculation

Units & Dimensions

Conversion of Units

Systems of Units

Force & WeightNumerical

Calc. & Analysis

Dimensional Analysis

Process Data Representation

Learning OutcomeConvert a quantity expressed in one set of units to another.Identify units for mass and weight in SI, CGS and AE systems.Identify the number of significant figures in a given value, state

the precision with which the value is known and determine the correct number of significant figures in the result of a series of arithmetic operations.

Apply the concepts of dimensional consistency to determine the units of any term in a function.

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Units and Dimensions

A measured or counted quantity has a numerical value and a unit.

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• Dimensions are:• Properties that can be measured such as length, time,

mass, temperature. • Properties that can calculated by multiplying or dividing

other dimensions, such as length/time, length3, mass/length3.

• Units are used for expressing the dimensions such as feet

(ft) or meter (m) for length, hours/seconds (hr/s) for time.• Perform similar to algebraic variables

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Engineers and scientists have to be able to communicate not only with words but also by carefully defined numerical descriptions.

The Reality….On November 10, 1999, the Mars Climate Orbiter crashed into the surface of Mars. One reason cited was a discrepancy over the units used. The navigation software expected data in Newton second; the company who built the orbiter provided data in pound-force seconds.

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Reality Check...

• Are units really important?

• Is checking your work and your team’s work really important?

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Another case….

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Conversion of Units• A measured quantity can be expressed in terms of any units

having the appropriate dimension.• 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

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36 mg 1 g = 0.036 g

1000 mg 0.001 is a conversion factor

Conversion of Units To convert a quantity with a unit to its

equivalent in term of other units, set up a dimensional equation:

a) Write the given quantity and units on leftb) Write the units of conversion factors that

cancel the old unit and replace them with the desired unit

c) Fill the value of the conversion factorsd) Carry out the arithmetic value

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• Convert 1 cm/s2 to km/yr2

1 cm s2 h2 day2 m kms2 h2 day2 yr2 cm m

1 cm 36002 s2 242 h2 3652 day2 1 m 1 kms2 12 h2 12 day2 12 yr2 100 cm 1000 m

36002 x 242 x 3652 km= 9.95 x 109 km/ yr 2

100 x 1000 yr2

Conversion of Units

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• Convert 4 kg/m3 to lbm/ft3

4 kg 0.028317 m3 1 lbm

m3 1 ft3 0.453593 kg

4 kg m3 lbm

m3 ft3 kg

4 x 0.028317 x 1 lbm = 0.2497 lbm/ft3

1x 0.453593 ft3

Conversion of Units

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Systems of Units• Components of a system of units:

• Base units - units for the dimensions of mass, length, time, temperature, electrical current, and light intensity.

• Multiple units – multiples or fractions of base units such as minutes, hours, milisecond.

• Derived units - units that are obtained in one or two ways;

• By multiplying and dividing base units also referred to as compound units

• Example: ft/min (velocity), cm2(area), kg.m/s2 (force)

• Two most commonly used system of units:• SI – Systeme Internationale d’ Unites

• AE – American Engineering System of Units

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SI Units - Base Units

14CGS: centimeter gram second system units

Prefixes are used to indicate powers of ten.

nano

micro

milli

centi

deci

deka

hecto

kilo

mega

giga

Prefix Decimal Multiplier Symbol10-9

10-6

10-3

10-2

10-1

10+1

10+2

10+3

10+6

10+9

n

μ

m

c

d

da

h

k

M

G

SI Units - Multiple Units

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SI Units - Derived Units

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American Engineering System Units

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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)

Force & Weight• Force is proportional to product of mass and

acceleration (i.e. F = m x a) • Usually defined using derived units ;

1 Newton (N) = 1 kg m s-2

1 dyne = 1 g cm s-2

1 Ibf = 32.174 Ibm ft s-2

• Weight of an object is force exerted on the object by gravitational attraction of the earth i.e. force of gravity, g.

• gc is used to denote the conversion factor from a natural force unit to a derived force unit.

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Value of g

9.8066 m s-2

980.66 cm s-2

32.174 ft s-2

gc1 kg m s-2 /

1 N32.174 lbm ft s-2 /

1 lbf

Force & WeightGiven the density of 2 ft3 water is 62.4 lbm/ft3. At the sea level, the gravitational acceleration is 32.174 ft/s2. What is the weight of the water in lbf?

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2 ft3 62.4 lbm 32.174 ft

1 lbf

ft3 s2 32.174 lbm ft s-2

= 124.8 lbf

Numerical Calculation & Estimation

Scientific Notation

To represent a very large and very small numbers in process calculations. Scientific Notation is based on powers of the base number 10.

Example: The number 123,000,000,000 in scientific notation is written as

The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10.

The second number is called the base . It must always be 10 in scientific notation. The base number 10 is always written in exponent form.

In the number 1.23 x 10^11 the number 11 is referred to as the exponent or power of ten.

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Numerical Calculation & EstimationSignificant Figures

Accuracy refers to how closely a measured value agrees with the correct value.

Precision refers to how closely individual measurements agree with each other.

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Rules for Working with Significant Figures: Leading zeros are never significant.

Imbedded zeros are always significant. Trailing zeros are significant only if the decimal point is specified.

Addition or Subtraction:Position of last significant figure relative to decimal should be compared. The one farthest to the left is the position of the last permissible significant number of the sum or difference.

Multiplication or Division:The result should contain the lowest number of significant figures of any of the quantities.

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Dimensional Homogeneity & Dimensionless Quantities

• Every valid equation must have dimensional homogeneity; that is, all additive terms on both sides of the equation must have the same dimensions.

• A dimensionless quantity can be a pure number or a multiplicative combination of variables with no net dimensions.

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CBAD All have identical dimensions

Dimensional Homogeneity & Dimensionless Quantities

Importance of Dimensionless Quantities• Used in arguments of special functions such as exponential,

logarithmic or trigonometric functions.

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Dimensional Homogeneity & Dimensionless QuantitiesDimensional Consistency• Each term in the equation must have the same net

dimensions and units as every other term to which it is added, subtracted or equated

As an example, A + B = C –DEIf A has a dimension of L3

Then, what about B, (A+B), (C-DE), C & DE?

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Process Data Representation and Analysis

Two Point Linear Interpolation

If you are given a set of tabulated data, and you are required to get the data of an unknown, y, linear interpolation equation can be used to get the desired data.

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1

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1

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1

)( yyyxxxxy

xxxx

yyyy

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Time to Practice

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Practice 1

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Practice 2

Thank You