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
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