CHEE 2331

Chemical Processes

Summer 2015

Chapter 2:

Engineering Calculations

Department of Chemical and Biomolecular Engineering

Process

Input Stream(s)

General Material/Energy balance:

Accumulation = Input + Generation – Output – Consumption

Heat (energy)

Work (energy)

Flow Diagram

Output Stream(s)

Quantities (how much)…

Two types:

Counted: individual items that can be counted

e.g., apples, children, cows

Measured: quantities that are measured with an

instrument of given precision and accuracy

e.g., 12.34 cm

value

(95% sure it is

between 12.335

and 12.345)

unit dimension of length

Units…

1. Base units

Length L

Mass M

Time t

Temperature T

(Electrical current i)

(Light intensity I)

System of units

SI cgs American

(metric) Engineering

m cm ft

kg g lbm

s s s

K oC oF

(also Rankine)

Units…

2. Multiple units

Length L

Mass M

Time t

American

(metric) Engineering

mm, cm, m, km in, ft, yd, mile

mg, g, kg, ton oz, lbm, ton

s, min, hr, day, week, month, year

Prefixes

tera(T) = 1012 centi(c) = 10-2

giga(G) = 109 milli(m) = 10-3

mega(M)= 106 micro(μ) = 10-6

kilo(k) = 103 nano(n) = 10-9

Units…

3. Derived units

(combinations of

base units)

Volume, L3

Velocity, L/t

Acceleration, L/t2

Force, ML/t2

Energy, ML2/t2

Power, ML2/t3

System of units

SI cgs American

(metric) Engineering

m3 cm3, liter ft3, gal

m/s cm/s, km/h ft/s, miles/hr

m/s2 cm/s2 ft/s2

Kg m/s2 g cm/s2 lbf

(Newton) (dyne) (lb force)

N m dyne cm lbf ft, BTU

(Joule) (erg)

J/s erg/s lbf ft/s, hp

(Watt)

Please note…

• Only add and subtract quantities with

the same units.

• Multiply and divide derived units.

• Convert between units using the

conversion factors (see table in the front

cover of the textbook).

Convert 27.7 kg to tons

27.7 kg 2.20462 lbm 5x10-4 ton

kg lbm

= 0.0305 ton

OR:

27.7 kg 5x10-4 ton

0.4536 kg

= 0.0305 ton

Mass (M) and weight (W)…

Newton’s Second Law of Motion…

force = mass * acceleration

F = (M)*(a)

SI units: 1 N (newton) = 1 kg*m/s2

cgs units: 1 dyne = 1 g*cm/s2

AE units: definition: 1 lbf = 32.174 lbm*ft/s2

This “conversion factor” is designated as gc

gc = 32.174 (lbm * ft/s2)/lbf

Conversion factors from “Natural” to “Derived” force units (N, dynes, lbf)

“Weight” is the force on a body due to

the acceleration of gravity. i.e

W = Mg (compare to F = Ma)

where g = 9.8066 m/s2 (SI) at 45o, sea level

= 980.66 cm/s2 (cgs)

= 32.174 ft/s2 (AE)

Acceleration of gravity g is changing with

latitude, altitude and global location.

What is the weight of 1 lbm?

Number of Significant Figures (NSF)… Rules:

(1) For numbers with a decimal point, the NSF is counted

from the first non-zero number on the left

to the last non-zero or zero number.

352.60 5 SF 0.003526 4 SF

(2) For numbers without a decimal point, the NSF is

counted from the first non-zero number of the left to

the last non-zero number.

35260 4 SF

(3) If a number is a pure integer, counted, or a conversion

factor, NSF is infinite.

35260. 5 SF

35260.0 6 SF

(4) For multiplication or division, the final NSF is equal to the

lowest NSF of the numbers involved.

3 4 3 3

(3.57)(4.386) = 15.30102 15.3

(5) For addition or subtraction, the NSF of the number whose

last significant figure is farthest to the left is the final NSF.

1530 – 2.56 1530

-2.56

1527.44 1530

(6) When the last number to be dropped is 5, round off to

give an even number.

1.35 1.4

1.25 1.2

(7) For a long series of calculations, carry extra SF and round off

at the end of the calculation.

More Rules on significant figures

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Leading zeros to the left of the first nonzero digit are

not significant: 0.012 grams 2 significant figures

• Trailing zeros to the right of a decimal are significant:

• 0.0230 mL 3 significant figures

• To avoid ambiguity use scientific notation:

50,600 may be 3, 4, or 5 significant figures

50,600 = 5.0600 x 104 has 5 significant figures

5.060 x 104 has 4 significant figures

5.06 x 104 has 3 significant figures

Validate answers

(1) Back-substitute to see if it works.

(2) Order-of-magnitude estimation.

(3) Is it reasonable?

Data representation and analysis Imagine an instrument or process, in which a directly-measured

quantity (“x”) (such as light absorbance or titration volume) is

related to a process variable “y” (such as concentration).

Based on collected data in which the process variable is known, we

can generate a calibration curve (essentially an equation).

Process variable (y) is now calculated from new measured “x” data

by interpolation or extrapolation.

In the simplest case, x and y are related linearly: y = ax + b

From two data points (x1, y1), (x2, y2):

12

12

11 yy

xx

xxyy

What is the internal energy of saturated water at 3oC?

At what Temp does steam have a specific volume of 150 m3/kg?

At what Temp does steam have a specific volume of 150 m3/kg?

Non-linear relations can often be rearranged and plotted as

straight lines

• Convert to a linear form by selecting appropriate variables (does not

work always).

• Log-log and semi-log plots are often used.

•a and b are constants.

Relationship X axis Y axis Slope Intercept

Z = a M2 + b M2 Z a b

Z = 1/[a (M+b)] M 1/Z a ab

Z = a Mb ln(M) ln(Z) b ln(a)

Z = a ebM M ln(Z) b ln(a)

Non-linear relations can often be rearranged and plotted as

straight lines

• Convert to a linear form by selecting appropriate variables (does not

work always).

• Log-log and semi-log plots are often used.

•a and b are constants.

Relationship X axis Y axis Slope Intercept

Z = a M2 + b M2 Z a b

Z = 1/[a (M+b)] M 1/Z a ab

Z = a Mb ln(M) ln(Z) b ln(a)

Z = a ebM M ln(Z) b ln(a)

When you plot values of variable y on a logarithmic scale you

are essentially plotting the logarithm of y on a linear scale.

Semilog plot: y axis is logarithmic, x axis is linear.

Log plot: both y and x axes are logarithmic.

Semi-log plot looks linear