# 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).