System of Units
The program accepts any consistent set of engineering units. Examples of consistent sets of units for basic parameters are shown in the tables below. The user should use great care when converting from one system of units to another. An excellent reference on the subject of units and conversion between the imperial and SI systems can be found in [JPT1977]. The program does not perform conversions.
Mechanical Analysis
Table 1: System of Units - Mechanical Parameters
| Property |
SI |
Imperial |
|---|
| Length |
m |
m |
m |
cm |
ft |
in |
| Density |
kg/m3 |
103 kg/m3 |
106 kg/m3 |
106 g/cm3 |
slugs/ft3 |
snails/in3 |
| Force |
N |
kN |
MN |
Mdynes |
lbf |
lbf |
| Stress |
Pa |
kPa |
MPa |
bar |
lbf /ft2 |
psi |
| Gravity |
m/sec2 |
m/sec2 |
m/sec2 |
cm/sec2 |
ft/sec2 |
in/sec2 |
| Ball stiffness |
N/m |
kN/m |
MN/m |
Mdynes/cm |
lbf/ft |
lbf/in |
| where: |
1 bar |
= 106 dynes/cm2 = 105 N/m2 = 105 Pa ; |
| |
1 atm |
= 1.013 bars = 14.7 psi = 2116 lbf/ft2 = 1.01325 \(\times\) 105 Pa ; |
| |
1 slug |
= 1 lbf-sec2 /ft = 14.59 kg ; |
| |
1 snail |
= 1 lbf-sec2 /in ; and |
| |
1 gravity |
= 9.81 m/sec2 = 981 cm/sec2 = 32.17 ft/sec2 |
this bit from flac3d not in pfc.
One exception to the conversion rule above: for quantities representing angles, conversions are performed in FLAC3D.
Angles are always entered on the command line (and in the user interface) in degrees, though they may be stored and used in radians. The exception is FISH, which (like most programming languages) assumes all angle values are in radians.
Thermal Analysis
All thermal quantities must be given in a consistent system of units.
No conversions are performed by the program. The tables below present examples of consistent sets of units for thermal parameters.
Table 3: System of SI units for thermal problems
| Property |
Units |
|
|
|
|---|
| Length |
m |
m |
m |
cm |
| Density |
kg/m3 |
103 kg/m3 |
106 kg/m3 |
106 g/cm3 |
| Stress |
Pa |
kPa |
MPa |
bar |
| Temperature |
K |
K |
K |
K |
| Time |
s |
s |
s |
s |
| Specific Heat |
J/(kg K) |
10-3 J/(kg K) |
10-6 J/(kg K) |
10-6 cal/(g K) |
| Thermal Conductivity |
(W/mK) |
(W/mK) |
(W/mK) |
(cal/s)/cm2 K4 |
| Convective Heat-Trans. Coefficient |
(W/m2 K) |
(W/m2 K) |
(W/m2 K) |
(cal/s)/(cm2 K) |
| Radiative Heat-Trans. Coefficient |
(W/m2 K4) |
(W/m2 K4) |
(W/m2 K4) |
(cal/s)/cm2 K4 |
| Flux Strength |
W/m2 |
W/m2 |
W/m2 |
(cal/s)/cm2 |
| Source Strength |
W/m3 |
W/m3 |
W/m3 |
(cal/s)/cm3 |
| Decay Constant |
s-1 |
s-1 |
s-1 |
s-1 |
Table 4: System of imperial units for thermal problems
| Property |
Units |
|
|---|
| Length |
ft |
in |
| Density |
slugs/ft3 |
snails/in3 |
| Stress |
lbf |
psi |
| Temperature |
R |
R |
| Time |
hr |
hr |
| Specific Heat |
(32.17)-1 Btu/(lb R) |
(32.17)-1 Btu/(lb R) |
| Thermal Conductivity |
(Btu/hr)/(ft R) |
(Btu/hr)/(in R) |
| Convective Heat-Trans. Coefficient |
(Btu/hr)/(ft2 R) |
(Btu/hr)/(in2 R) |
| Radiative Heat-Trans. Coefficient |
(Btu/hr)/(ft2 R4) |
(Btu/hr)/(in2 R4) |
| Flux Strength |
(Btu/hr)/ft2 |
(Btu/hr)/in2 |
| Source Strength |
(Btu/hr)/ft3 |
(Btu/hr)/in3 |
| Decay Constant |
hr-1 |
hr-1 |
| where: |
1K |
= 1.8 R; |
| |
1J |
= 0.239 cal = 9.48 × 10-4 Btu; |
| |
1J/kg K |
= 2.39 × 10-4 btu/lb R; |
| |
1W |
= 1 J/s = 0.239 cal/s = 3.412 Btu/hr; |
| |
1W/m K |
= 0.578 Btu/(ft/hr R); and |
| |
1W/m2 K |
= 0.176 Btu/ft2 hr R. |
Note that temperatures may be quoted in the more common units of °C (instead of K) or °F (instead of R),
| where: |
Temp(°C) |
= [Temp(°F) - 32]×(5/9); |
| |
Temp(°F) |
= [1.8 Temp(°C) + 32]; |
| |
Temp(°C) |
= Temp(K) - 273; and |
| |
Temp(°F) |
= Temp(R) - 460. |
Fluid Analysis
Any set of units can be used as long as they are consistent with the units used in the mechanical calculation.
Table 7: System of SI units for fluid flow
| Property |
Unit |
Symbol |
|---|
| Length |
m |
l |
| Fluid Density |
kg/m3 |
\(\rho_f\) |
| Time |
s |
t |
| Fluid Velocity |
m/s |
\(\vec{v}\) |
| Particle Velocity |
m/s |
\(\vec{u}\) |
| Porosity |
|
\(\epsilon\) |
| Dynamic Viscosity |
Pa·s |
\(\mu\) |
| Drag Coefficient |
|
\(C_d\) |
| Reynolds Number |
|
\(Re\) |
| Fluid Pressure |
Pa |
p |
| Fluid Pressure Gradient |
Pa/m |
\(\vec{\nabla}p\) |
| Fluid Kinematic Pressure |
m2/s 2 |
P |
| Kinematic Viscosity |
m2/s |
\(\nu\) |
Structural Elements
| Property |
Unit |
SI |
Imperial |
|---|
| area |
length2 |
m2 |
m2 |
m2 |
cm2 |
ft2 |
in2 |
| axial or shear stiffness |
force/disp |
N/m |
kN/m |
MN/m |
Mdynes/cm |
lbf /ft |
lbf/in |
| exposed perimeter |
length |
m |
m |
m |
cm |
ft |
in |
| moment of inertia |
length4 |
m4 |
m4 |
m4 |
cm4 |
ft4 |
in4 |
| plastic moment |
force-length |
N-m |
kN-m |
MN-m |
Mdynes-cm |
ft-lbf |
in-lbf |
| yield strength |
force |
N |
kN |
MN |
Mdynes |
lbf |
lbf |
| Young’s modulus |
stress |
Pa |
kPa |
MPa |
bar |
lbf /ft2 |
psi |
where, 1 bar = 106 dynes/cm2 = 105 N/m2 = 105 Pa.
Reference
| [JPT1977] | Journal of Petroleum Technology. “The SI Metric System of Units and SPE’s Tentative Metric Standard”, 1575-1616 (December 1977). |
