3582456518

Mass Transfer

1 m²/s = 3.875 x 10⁴ ft²/h = 10⁴ cm²/s 1 m²/h = 10.764 ft²/h = 10⁴ cm²/h 1 m/s = 1.1811 ft/h = 0.01 cra/s

1 kg-mol/s-m² = 737.35 lb-mol/h-ft² = 0.1 g-mol/s-cm² 1 kg-mol/s • m² • atm = 737.35 lb-mol/h • ft² • atm = 0.1 g-mol/s • cm² • atm

1 kg-mol/s • m² • kPa = 7.4712 x 10⁴ lb-mol/h ■ ft² - atm = 10.1325 g-mol/s • cm² • atm

Useful Finite Difference Approximations

Table A-1 First-Order Finite Difference Approximations

Difference

First Order Formula

Porwani Difference for

First Derivative

(A-1)

Backward Difference for

First Derivative

d    f(x_i)-f(x_i_,)

dx ^X‘    Ax

(A-2)

Forward Difference for

Second Derivative

f(Xj)-2f(x_i+{) + f(x_{i + 2}) -

Ax~

(A-3)

Backward Difference for

Second Derivative

i

f(Xj) - 2f(Xj _i) + f(x_i_₂) -

(A-4)

Table A-2 Second-Order Finite Difference Approximations

Difference	Second Order Formula
For-ward Difference for First Derivative	d , -3A*i) + 4A*i+l)-/(*i + 2) dx^nXl) 2Ax	(A-5)
Central DifTerence for First Derivative	d _ f(^xi+l)-f(^xi-l) dx ' ‘ 2Ax	(A-6)
Backward Difference for First Derivative	d ,, x ^3A*f) ~ ^Ąf(^xi - 1) + f(*t - 2) dx^nXl’ 2Ax	(A-7)

Table A-2 Second-Order Finite Difference Approximations

Difference

Second Order Formula

Forward Difference	2
for Second Derivative	u .■-•. H C (<N
Central Difference	2
for Second Derivative	-V (lx
Backward Difference	,2
for Second Derivative	^= dx

l_{f{x) =} ²    ) - ⁵ H ) ⁺ Ąf(^xi + ₂) - A*j ₊ 3)

Ax~

f(X, ₊ | ) - ²f(Xj) + f(Xi _ ,)

Ajc"

~ 5A*j_ 1) + 4A*j _ ₂) -    _ 3)

A*'

(A-

(A-

(A-l

Error Function

Table A-3 Error and Complimentary Error Functions

Z	erf(2)	erfc(z)
0	0	1
0.1	0.11246278	0.88753722
0.2	0.22270233	0.77729767
0.3	0.32862638	0.67137362
0.4	0.42839185	0.57160815
0.5	0.52049927	0.47950073
0.6	0.60385538	0.39614462
0.7	0.6778004	0.3221996
0.8	0.7421001	0.2578999
0.9	0.79690728	0.20309272
1	0.84269981	0.15730019
1.1	0.88020404	0.11979596
1.2	0.91031291	0.089687086
1.3	0.93400685	0.065993147
1.4	0.95228401	0.047715994
1.5	0.96610402	0.033895983
1.6	0.97634724	0.023652758