# System of Units

Itasca software 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 FLAC.

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)

(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)

(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

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).