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)
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).