Ch2 Engineering Calculations

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CHEE 2331

em ca rocessesem ca rocesses

Spring 2012Spring 2012

Cha ter Cha ter 2:2:

Engineering CalculationsEngineering Calculations

Department of Chemical andDepartment of Chemical and Biomolecular Biomolecular EngineeringEngineering



Flow DiagramInput Stream(s) Heat (energy)

Output Stream(s)

Work (energy)

General Material/Energy balance:

Accumulation = Input + Generation – Output – Consumption



Quantities (how much)…

Two types:

e.g., apples, children, cows

Measured: quantities that are measured with an

instrument of given precision and accuracy

. ., .value

95% sure it is

unit dimension of length

between 12.335

and 12.345)



Units…

1. Base units System of units

SI cgs American

Length L

me r c ng neer ng

m cm ft

Mass M kg g lbm

Temperature T K oC oF

(Electrical current i)

(Light intensity I)



Units…2. Multiple units

American

Length L

me r c ng neer ng

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

Mass M mg, g, kg, ton oz, lbm, ton

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

System of units

SI cgs American

Volume, L3

m3 cm3, liter ft3, gal

Velocity, L/t m/s cm/s, km/h ft/s, miles/hr

Acceleration, L/t

Force ML/t2

m/s2 cm/s2 ft/s2

K m/s2 cm/s2 lb

Energy, ML2 /t2

(Newton) (dyne) (lb force)

N m dyne cm lbf ft

Power, ML2

/t3

J/s erg/s lbf ft/s(Watt) (hp)



…

• n y a an su rac quan es w

the same units.

• Multiply and divide derived units.

• Convert between units using the

conversion factors (see table in the front

cover of the textbook).



.

27.7 kg 2.20462 lbm 5x10

-4

tonkg lbm= 0.0305 ton

OR:

27.7 kg 5x10-4 ton0.4536 kg

= 0.0305 ton



Mass (M) and weight (W)…

Newton’s Second Law of Motion…force = mass * acceleration

= *

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 g

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

. .

W = Mg (compare to F = Ma)

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

= 980.66 cm/s (cgs)

= 32.174 ft/s2 AE

Acceleration of gravity g is changing with

, .

m



Number of Significant Figures (NSF)…Rules:

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

-

to the last non-zero or zero number.

. .

(2) For numbers without a decimal point, the NSF iscounted from the first non-zero number of the left to

the last non-zero number.

35260 4 SF

, ,

factor, NSF is infinite.



(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 whoselast 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.

• Leadin zeros to the left of the first nonzero di it are

not significant: 0.012 grams 2 significant figures• Trailing zeros to the right of a decimal are significant:

.

• 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

.

5.06 x 104 has 3 significant figures



Validate answers

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

(2) Order-of-magnitude estimation.



Sample Mean, Variance, Standard Deviation

, .

•Reaction: A products, always start with the same amount of

pure A.

• ,

conversion of A; let’s call it X.

•Repeat the same experiment multiple times.

Will you get the same X for every experiment? What is the true

value of X?



1 1 N

1 2 3

1

... N j

j N N

2 2 2 2

1 2[( ) ( ) ...( ) ]

1 X N s X X X X X X

N

Variance

Data set (b) shows greater variance



2

X X s sStandard Deviation

Roughly 2/3 of the data points are within 1 standard deviation

,

about 99% are within 3 standard deviations.



Data representation and analysisImagine 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, wecan 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

rom wo a a po n s x1, y1 , x2, y2 :

1 x x 12

12

1

x x



Non-linear relations can often be rearranged and plotted as

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

Z = a e 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.

Ch2 Engineering Calculations

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