Bird R.B., Stewart W.E., Lightfoot E.N. Transport Phenomena
Подождите немного. Документ загружается.
Appendix
F
Constants
and
Conversion
Factors
5F.1
Mathematical constants
5F.2
Physical constants
5F.3
Conversion factors
1
MATHEMATICAL CONSTANTS
5F.2
PHYSICAL CONSTANTS'
Gas law constant
(R)
Standard acceleration
of gravity
(go)
Joule's constant
(I,)
(mechanical equivalent of heat)
Avogadro's number
(N)
Boltzmann's constant
(K
=
R/I;I)
Faraday's constant
(F)
Planck's constant
(h)
Stefan-Boltzmann
constant
(a)
Electron charge
(e)
Speed of light in a
vacuum
(c)
J/g-mole
K
kg.
m2/s2. kg-mol
.
K
g
.
cm2/s2. g-mo1 K
cal/ g-mol
.
K
cm3 atm/g-mol
.
K
lb, f$/s2
lb-mol
.
R
ft
.
lbf/lb-mol
.
R
molecules /g-mol
C
/
g-equivalent
J.s
erg
.
s
W/m2.
K~
cal/s
.
cm2K4
Btu/hr
ft2R4
E.
R.
Cohen and
B.
N.
Taylor,
Physics
Today
(August
1996),
pp.
BG9-BG13;
R.
A.
Nelson,
Physics
Today
(August
1996),
pp.
BG15-BG16.
867
868
Appendix F Constants and Conversion Factors
5F.3
CONVERSION FACTORS
In the tables that follow, to convert any physical quantity from one set of units to an-
other, multiply it by the appropriate table entry. For example, suppose that
p
is given as
10 1bf/in.*, and we wish to have
p
in poundals/ft2. From Table F.3-2 the result is
The entries in the shaded rows and columns are those that are needed for converting
from and to
SI
units.
In
addition to the tables, we give a few of the commonly used conversion factors
here:
Given a quantity
in these units: Multiply by: To get quantity in these units:
Pounds
Kilograms
Inches
Meters
Gallons
(U.S.)
Gallons
(U.S.)
Gallons
(U.S.)
Cubic feet
Kelvins
Degrees Rankine
Grams
Pounds
Centimeters
Inches
Liters
Cubic inches
Cubic feet
Liters
Degrees Rankine
Kelvins
Table
F.3-1
Conversion Factors for Quantities Having Dimensions of
F
or
ML/t2
Table
F.3-2
Conversion Factors for Quantities Having Dimensions of
F/L2
or
M/L~~
(pressure, momentum flux)
6.8947
X
lo4
4.6330
X
lo3
144
1
6.8046
X
lop2
5.1715
X
10'
2.0360
atm
1.0133
x
lo6
6.8087
X
lo4
2.1162
x
lo3
14.696
1
760 29.921
1.3332
X
lo3
8.9588
X
10'
2.7845 1.9337
X
lo-'
1.3158
X
lop3
1
3.9370
X
lo-'
3.3864
X
lo4
2.2756
X
lo3
7.0727
X
10' 4.9116
X
lo-'
3.3421
X
lop2
25.400
1
"
This unit is preferably abbreviated "psia" (pounds per square inch absolute) or "psig" (pounds per square inch gage). Gage pressure is absolute pressure minus the prevailing
barometric pressure. Sometimes the pressure is reported in '%arsrs"; to convert from bars to pascals, multiply by lo5, and
to
convert from bars to atmospheres, multiply by 0.98692.
Table
F.3-3
Conversion Factors for Quantities Having Dimensions of
FL
or
ML~/~~
(energy, work, torque)
Given a Multiply by
quantity in table value foot
foot poundals
=
lb, ft2/s
3.1081
X
1.0072
X
3.9942
X
1.5698
X
lo-'
1.1706
X
lo-"
1.3558
X
lo7
32.1740
1
3.2405
X
lo-'
1.2851
X
lop3
5.0505
X
3.7662
X
thermochemical caloriesa
4.1840
X
lo7
9.9287
X
10' 3.0860
1
3.9657
X
1.5586
X
lop6
1.1622
X
British thermal units
1.0550
X
10'' 2.5036
X
lo4
778.16 2.5216
X
lo2
1
3.9301
X
2.9307
X
Horsepower hours
2.6845
x
1013 6.3705
x
lo7
1.9800
x
lo6
6.4162
x
lo5
2.5445
X
lo3
1 7.4570
X
lo-'
kilowatt hours
3.6000
X
1013 8.5429
X
lo7
2.6552
X
lo6
8.6042
X
lo5
3.4122
X
lo3
1.3410
1
"
This unit, abbreviated "cal," is used in some chemical thermodynamic tables. To convert quantities expressed in International Steam Table calories (abbreviated
"I.
T.
cal") to this
unit, multiply by 1.000654.
Table
F.3-4
Conversion Factors for Quantities Having dimensionsa of M/Lt or Ft/L2 (viscosity, density times diffusivity)
"
When moles appear in the given and the desired units, the conversion factor is the same as for the corresponding mass units.
Table
F.3-5
Conversion Factors for Quantities Having Dimensions of ML/t3T or F/tT (thermal conductivity)
Given a Multiply by
8.0068
X
lo5
3.2174
X
10' 1 1.9137
X
lo-'
4.6263
cal/s
.
cm
.
K
4.1840
X
lo7
1.6813
X
lo3
5.2256
X
10'
1
2.4175
X
10'
Btu/hr ft
.
F
2.1616
X
lo-'
4.1365
X
lop3
1
Table
F.3-6
Conversion Factors for Quantities Having Dimensions of
L2/t
(momentum
diffusivity, thermal diffusivity, molecular diffusivity)
Table
F.3-7
Conversion Factors for Quantities Having Dimensions of
M/t3~
or
F/LtT
(heat transfer coefficients)
Table
F.3-8
Conversion Factors for Quantities Having Dimensionsa of
M/L~~
or
F~/L~
(mass transfer coefficients
k,
or
k,,,)
"
When moles appear in the given and the desired units, the conversion factor is the same as for the corresponding mass units.
Notation
Numbers in parentheses refer to equations, sections, or tables in which the symbols are
defined or first used. Dimensions are given in terms of mass (M), length
(L),
time (t),
temperature
(T),
and dimensionless
(-).
Boldface symbols are vectors or tensors (see
Appendix A). Symbols that appear infrequently are not listed.
A
=
area,
L2
a
=
absorptivity (16.2-I),-
a
=
interfacial area per unit volume of packed bed (6.4-4),
L-'
a,
=
activity of species
a
(24.1-8),-
C,
=
heat capacity at constant pressure (9.1-71,
ML'/~'T
Cv
=
heat capacity at constant volume (9.3-61,
ML~/~~T
c
=
speed of light (16.1-I), L/t
c
=
total molar concentration (§17.7), moles/L3
c,
=
molar concentration of species a, (§17.7), moles/L3
D
=
diameter of cylinder or sphere,
L
D,
=
particle diameter in packed bed, (6.4-6),
L
QAB
=
binary diffusivity for system
A-B
(17.1-2),
L2/t
Qap
=
binary diffusivity for the pair
a-P
in a multicomponent system
(17.9-I), L2/t
Dnp
=
Maxwell-Stefan multicomponent diffusivity (24.2-4),
L2/
t
EDmp
=
Fick multicomponent diffusivity (24.2-3),
L'/
t
D:
=
multicomponent thermal diffusion coefficient (24.2-3), M/Lt
d
=
molecular diameter (1.4-3),
L
d,
=
diffusional driving force for species a (24.149,
L-'
Etot
=
U,,
+
Ktot
+
a,,,
=
total energy in a macroscopic system (15.1-2),
ML~/~~
E,
=
compression term in mechanical energy balance (7.4-31, ML2/t3
E,
=
viscous dissipation term in mechanical energy balance (7.4-4),
ML2/t3
e
=
2.71828.
.
.
e
=
emissivity (16.2-3),-
e
=
combined energy flux vector (9.8-5), M/t3
F,,,
F,,
=
direct, indirect view factor (16.4-91, (16.5-151,-
F,+
=
force exerted by the solid on the fluid (7.2-I), ML/t2
f
=
friction factor (or drag coefficient) (6.1-I),-
G
=
H
-
TS
=
Gibbs free energy (24.1-2), ML2/t2
G
=
(pv)
=
mass velocity (6.4-8),
M/L~~
g
=
gravitational acceleration (3.2-8), ~/t~
g,
=
body force per unit mass acting on species
a
(Table 19.2-I), L/t2
H
=
U
+
pV
=
enthalpy (9.8-6), ML'/~~
h
=
Planck's constant (14.1-2), ML2/t
h
=
elevation (2.3-lo),
L
h,
hl,
hl,,
hl,,,
h,,
h,
=
heat transfer coefficients (14.1-1 to
6),
M/~~T
i
=
(4.1-43),-
J,,
J:
=
molar fluxes (Table 17.8-1
),
moles/12f
j,,
jz
=
mass fluxes (Table 17.8-11, M/L2t
j,,
j,
=
Chilton-Colburn j-factors (14.3-19, Table 22.2-I),-
Notation
873
K
=
kinetic energy (7.4-I),
ML'/~'
K,,
K,
=
two-phase mass transfer coefficients (22.4-4), moles/ t12
K
=
R/N
=
Boltzmann's constant (1.4-1)' ML2/t2T
k
=
thermal conductivity (9.1-1 and 24.2-6)'
ML/PT
k,
=
single-phase mass transfer coefficients (22.1-7,22.3-4, Table 22.2-I),
moles
/
t
L2
k:,
k:
=
mass transfer coefficient for small mass-transfer rates and small
species concentration (22.1-9,22.4-21, moles/ t12
k;
=
mass transfer coefficient for high net mass-transfer rates (22.8-2a),
moles
/
t
L2
k,
=
thermal diffusion ratio (24.2-lo),-
k,
=
electrical conductivity (9.5-I), ohm-' cm-'
k:
=
heterogeneous chemical reaction rate coefficient (18.0-3),
moles1-"/ L2-3"t
kr
=
homogeneous chemical reaction rate coefficient (18.0-2),
moles1"
/
L3p3n
t
L
=
length of film, tube, or slit (2.2-22),
L
L,,,
=
total angular momentum within a macroscopic system (7.3-I),
ML~I~
1
=
mixing length (5.4-4),
L
I,
=
characteristic length in dimensional analysis (3.7-3),
L
M
=
molar mean molecular weight (Table 17.7-I), M/mole
M,
=
molecular weight of species
a
(Table 17.7-I), M/mole
Ma,,,,
=
total number of moles of species
a
in macroscopic system (23.1-3),
moles
rn
=
mass of a molecule (1.4-1)' M
m,
n
=
parameters in power law viscosity model (8.3-3), M/Lt2-",-
ma,,,,
=
total mass of species
a
in macroscopic system (23.1-I), M
N
=
rate of shaft rotation (3.7-28), tpl
N
=
number of species in a multicomponent mixture (17.7-I),-
I?
=
Avogadro's number, (g-mole)-'
N,
=
combined molar flux vector for species
a
(17.8-2), moles/L2t
n
=
unit normal vector (A.5-I),--
n,
=
combined mass flux vector for species
a
(17.8-1)'
M/L'~
n
=
molecular concentration or number density (1.4-2),
LV3
P,,,
=
total momentum in a macroscopic flow system (7.2-I), ML/t
9
=
p
+
pgh
=
modified pressure (for constant
p
and
g)
(2.3-10)'
M/L~*
9,
=
characteristic pressure used in dimensional analysis (3.7-4),
MIL^^
p
=
fluid pressure, M/ Lt2
Q
=
rate of heat flow across a surface (9.1-1,15.1-I),
ML'/
t3
QG
=
radiant energy flow from surface
1
to surface 2 (16.4-5),
ML'/
t3
Q12
=
net radiant energy interchange between surface
1
and surface 2
(16.4-8),
ML'/
t3
q
=
heat flux vector (9.1-4), M/t3
q0
=
interfacial heat flux (10.8-14), M/t3
R
=
gas constant (in
=
RT),
ML2/t2T mole
R
=
radius of a cylinder or a sphere,
L
R,
=
molar rate of production of species
a
by homogeneous chemical
reaction (18.0-2), moles/t13
Rh
=
mean hydraulic radius (6.2-16),
L
874
Notation
R
=
real part (of complex quantity) (4.1-43)
r
=
position vector (3.4-I),
L
r
=
=
radial coordinate in cylindrical coordinates,
L
r
=
Vx2
+
y2
+
z2
=
radial coordinate in spherical coordinates,
L
r,
=
mass rate of production of species
a
by
homogeneous chemical
reaction (19.1-5), M/tL"
S,,
S,
=
cross-sectional area at planes 1 and 2 (7.1-11,
L2
S
=
entropy (11D.1-l,24.1-I), ML2/t2T
T
=
absolute temperature,
T
T,,f
=
torque exerted by a solid boundary on the fluid (7.3-I),
ML~/~'
T,,,
=
external torque acting on system (7.3-11, ML'/~~
TI
-
To
=
characteristic temperature difference used in dimensional analysis
(1 1.5-51,
T
t
=
time, t
U
=
internal energy (9.7-I),
ML'/~'
U
=
overall heat-transfer coefficient (10.6-151, M/t3T
-
u
=
arithmetic mean molecular speed (1 &I),
L/
t
u
=
unit vector in direction of flow (7.2-I),-
V
=
volume,
L3
v
=
mass average velocity (17.7-I), L/t
V*
=
molar average velocity (17.7-2),
L/
t
v,
=
velocity of species
a
(17.1-3, Table 17.7-I), L/t
v,
=
characteristic velocity in dimensional analysis (3.7-4), L/t
v,
=
speed of sound (9.4-2,llC.l-4), L/t
v,
=
a
=
friction velocity (5.3-2),
L/
t
W
=
molar rate of flow across a surface, (23.1-4), moles/t
W,
=
molar rate of flow of species
a
across a surface (23.1-3), moleslt
W,,
=
rate of doing work on a system by the surroundings via moving
parts (7.4-I), ML~/~~
w
=
mass rate of flow across a surface (2.2-21), M/t
w,
=
mass flow rate of species
a
across a surface (23.1-I), M/t
x,
=
mole fraction of species
a
(Table 17.7-I),-
x,
y,
z
=
Cartesian coordinates
y
=
distance from wall (in boundary layer theory and turbulence)
(54.41, L
y,
=
mole fraction of species
a
(22.4-2),-
Z
=
wall collision frequency (1.4-2), ~-~t-'
z,
=
ionic charge, (24.4-5), equiv/mole
alpha
a
=
k/&
=
thermal diffusivity (9.1-7). L2/t
beta
p
=
thermal coefficient of volume expansion (10.9-61, T-'
p
=
velocity gradient at a surface (12.4-6),
s-'
gamma
y
=
Cp/CV
=
heat capacity ratio (11.4-56),-
9
=
Vv
+
(Vv)+
=
rate-of-deformation tensor (8.3-I), tp'
delta
AX
=
X2
-
XI
=
difference between exit and entry values
6
=
falling-film thickness (2.2-22), boundary layer thickness
(4.4-14),
L
B
=
unit tensor (1.2-2, A.3-lo),-
6,
=
unit vector in the i direction (A.2-9),-
6,;
=
Kronecker delta (A.2-I),-
epsilon
s
=
fractional void space (6.4-3),-
F,
sAB
=
maximum attractive energy between two molecules (1.4-10,
17.3-13),
ML~/~~
silk
=
permutation symbol (A.2-3),-
Notation
875
zeta
efa
6
=
composition coefficient of volume expansion (19.2-2 and Table
22.2-I),-
7
=
non-Newtonian viscosity (8.2-I), M/Lf
q', qrr
=
components of the complex viscosity (8.2-4), M/Lt
-
7
=
elongational viscosity (8.2-5), M/Lt
q0
=
zero shear rate viscosity (8.3-4), M/Lt
theta
8
=
arctan(y/x)
=
angle in cylindrical coordinates (A.6-5),-
8
=
arctan(m/z)
=
angle in spherical coordinates (A.6-23),-
kappa
K
=
dilatational viscosity (1.2-6), M/Lt
K,
KO,
KI,
KZ
=
dimensionless constants used in turbulence
(5.3-1,5.4-3,5.4-5,5.4-6)
lambda
A,
A,, A,
A,
=
diffusivity ratios (20.2-29),-
A
=
wavelength of electromagnetic radiation (16.1-I),
L
A
=
mean free path (1.4-31,
L
A,
A,, A,,
A,,
A,
=
time constants in rheological models (58.4 to §8.6),
t
mu
J.L
=
viscosity (1.1-11, M/Lt
nu
Y
=
,u/p
=
kinematic viscosity (1 .I-3), ~~/t
Y
=
frequency of electromagnetic radiation (16.1-I), t-'
xi
6
=
composition coefficient of volume expansion (Table 22.2-I),-
pi
II,
II,,
II,,
II,
=
dimensionless profiles
(4.4-25,12.4-21,20.2-28),-
IT
=
3.14159.
. .
.rr
=
T
+
pi5
=
molecular momentum flux tensor, molecular stress
tensor (1.2-2,1.7-I), M/L~'
rho
p
=
density, M/L3
p,
=
mass of species
a
per unit volume of mixture (Table 17.7-I),
M/L~
sigma
a
=
Stefan-Boltzmann constant,
M/
t3T4
a
=
surface tension (3.7-12), M/t2
a,
=
collision diameter (1.4-10,17.3-11),
L
tau
.r
=
(viscous) momentum
flu
tensor, (viscous) stress tensor (1.2-2), M/Lt2
=
magnitude of shear stress at fluid-solid interface (5.3-I), M/Lt2
phi
0
=
potential energy (3.3-2),
ML~/~~
0,
=
viscous dissipation function (3.3-3), tp2
+
=
n
+
pw
=
combined momentum flux tensor (1.7-I), M/Lt2
6
=
arctan y/x
=
angle in spherical coordinates (A.6-24),-
6
=
electrostatic potential (24.4-5), volts
=
intermolecular potential energy
(1
&lo),
ML~/~~
psi
TI,
T2
=
first, second normal stress coefficient (8.2-2,3), MIL
T,
=
viscous dissipation function (3.3-3), t-*
+
=
stream function (Table 4.2-I), dimensions depend on the
coordinate system
omega R,, R,, R,
=
collision integrals (1.4-14,9.3-13, 17.3-11),-
o,
=
mass fraction of species
a
(17.1-2, Table 17.7-I),-
o,,
-
w,,
=
characteristic mass fraction difference used in dimensional
analysis (1 9.5-7),-
Overlines
-
X
=
per mole
X
=
per unit mass
2
=
partial molar (19.3-3,24.1-2)
-
X
=
time smoothed (5.1-4)
2
=
dimensionless (3.7-3)
Brackets
(X)
=
average value over a flow cross section
(X),
[XI,
(X)
=
used in vector-tensor operations when the brackets enclose dot or
cross operations (Appendix A)
876
Notation
[[
=
dimensionless groupings
[=I
=
has the dimensions of
Superscripts
Xt
=
transpose of a tensor
X"'
=
turbulent (5.2-8)
X'"'
=
viscous (5.2-9)
X'
=
fluctuating quantity (5.2-1)
Subscripts
A,
B
=
species
A
and
B
in binary systems
a,
/3,
.
. .
=
species in multicomponent systems
a
=
arithmetic-mean driving force or associated transfer coefficient
(14.1-3)
b
=
bulk or "cup-mixing" value for an enclosed stream (10.8-33,14.1-2)
c
=
evaluated at the critical point (1.3-1)
In
=
logarithmic-mean driving force or associated transfer coefficient
(14.1-4)
loc
=
local driving force or associated transfer coefficient (14.1-5)
rn
=
mean transfer coefficient for a submerged object (14.1-6)
r
=
reduced, relative to critical value (§I .3)
tot
=
total amount of entity in a macroscopic system
0
=
evaluated at a surface
1,2
=
evaluated at cross-sections 1 and 2 (7.1-1)
Named dimensionless groups designated with two letters
Br
=
Brinkman number (10.4-9, Table 11.5-2)
Ec
=
Eckert number (Table 11.5-2)
Fr
=
Froude number (3.7-1 1)
Gr
=
Grashof number (10.9-18, Table 11.5-2)
Gr,,
Gr,
=
Diffusional Grashof number (19.5-13, Table 22.2-1)
Ha
=
Hatta number (20.1-41)
Le
=
Lewis number (17.1-9)
Ma
=
Mach number (11.4-71)
Nu
=
Nusselt number (14.3-10 to
15)
Pk
=
Pkclet number (Table 11.5-2)
Pr
=
Prandtl number (9.1-8, Table 11.5-2)
Ra
=
Rayleigh number (Table 11.5-2)
Re
=
Reynolds number (3.7-10)
Sc
=
Schmidt number (17.1-8)
Sh
=
Sherwood number (22.1-5)
We
=
Weber number (3.7-12)
Mathematical operations
D/Dt
=
substantial derivative (3.5-2),
tF'
9
/9t
=
corotational derivative (8.5-2),
tF1
V
=
del operator (A.4-I),
L-'
In
x
=
the logarithm of
x
to the base e
log,,
x
=
the logarithm of
x
to the base 10
exp
x
=
ex
=
the exponential function of
x
erf
x
=
error function of x (4.1-14,
SC.6)
T(x)
=
the (complete) gamma function (12.2-24, sC.4)
T(x,
U)
=
the incomplete gamma function (12.2-24)
0(.
.
.)
=
"of the order of"