Dimensions & Units

Common

Property	Dimension	Units
Force	$MLT^{-2}$	$N,\;kgms^{-2}$
Energy/Work	$ML^{2}T^{-2}$	$J,\; Nm$
Power	$ML^{2}T^{-3}$	$Js^{-1}$
Frequency	$T^{-1}$	$s^{-1}$
Momentum	$MLT^{-1}$	$kgms^{-1}$

Electrical Fundamenta-a

Property	Dimension	Units
Charge	$IT$	$C$
Current	$I$	$A$
Voltage	$ML^{2}T^{-3}I^{-1}$	$V$
Resistivity	$ML^{3}T^{-3}I^{-2}$	$\Omega m$
Resistance	$ML^{2}T^{-3}I^{-2}$	$\Omega$
Conductivity	$M^{-1}L^{-3}T^3I^2$	$Sm^{-1}, \Omega^{-1}m^{-1}$
Capacitance	$M^{-1}L^{-2}T^{4}I^{2}$	$\text{F}$
Inductance	$ML^{2}T^{-2}I^{-2}$	$\text{H}$
Current Density	$IL^{-1}$	$Cm^{-1}s^{-1}$
Electric Field	$MLT^{-3}I^{-1}$	$NC^{-1}$
Impedance	$ML^{2}T^{-3}I^{-2}$	$\Omega$
Admittance	$M^{-1}L^{-2}T^3I^2$	$S, \Omega^{-1}$
Reactance	$ML^{2}T^{-3}I^{-2}$	$\Omega$
Active Power	$ML^{2}T^{-3}$	$\text{W},Js^{-1}$
Reactive Power	$ML^{2}T^{-3}$	$\text{var}$ (Volt-ampere reactive)
Apparent Power	$ML^{2}T^{-3}$	$\text{VA}$ (Volt-ampere)

Conversions

Unit	Equal to
Farad (F)	$1\,kg^{-1}m^{-2}s^4A^2$
Henry (H)	$1\,kgm^2s^{-2}A^{-2}$

Fluid Mechanics

Property	Dimension	Units
Mass Density	$ML^{-3}$	$kgm^{-3}$
Specific Weight or Unit Weight	$ML^{-2}T^{-2}$	$Nm^{-3}$
Relative Densiry or Specific Density	-	-
Bulk Modulus	$ML^{-1}T^{-2}$	$Nm^{-2}$
Vapour Pressure	$ML^{-1}T^{-2}$	$Nm^{-2}$
Surface Tension	$MT^{-2}$	$kgm^{-2}, Nm^{-1}$
Coefficient of dynamic viscosity	$ML^{-1}T^{-1}$	$kgm^{-1}s^{-1}, Nm^{-2}s, P$
Coefficient of kinematic viscosity	$L^{2}T^{-1}$	$m^{2}s^{-1},st$
Pressure	$ML^{-1}T^{-2}$	$Nm^{-2}, Pa,\text{Bar}$
Flow rate	$L^3 T^{-1}$	$m^3s^{-1}$
Head	$L$	$m$
Datum head	$L$	$m$
Pressure head	$L$	$m$
Velocity head	$L$	$m$
Loss coefficient	$L^{-5}T^2$	$m^{-5}s$

Conversions

Unit	Equal to
Poise (P)	$0.1\,kgm^{-1}s^{-1}$
Stokes (st)	$10^{-4}\,m^{2}s^{-1}$
Pascal (Pa)	$1\,Nm^{-2}$
Bar (bar)	$10^{-5}\,Pa$

Mechanics

Statics

Property	Dimension	Unit
First moment of area	$M^3$	$m^3$
Second moment of area	$M^4$	$m^4$
Product of moment of area	$M^4$	$m^4$
Polar moment of area	$M^4$	$m^4$
Radius of gyration	$M$	$m$

Properties of Materials

Property	Dimension	Units
Planar density	$L^{-2}$	$m^{-2}$
Stress	$ML^{-1}T^{-2}$	$Pa$
Strain	-	-
Yield strength	$ML^{-1}T^{-2}$	$Pa$
Young’s modulus	$ML^{-1}T^{-2}$	$Pa$
Secant modulus	$ML^{-1}T^{-2}$	$Pa$
Tangent modulus	$ML^{-1}T^{-2}$	$Pa$
Poisson’s ratio	-	-
Toughness	$ML^{2}T^{-2}$	$J$
Carrier Concentration	$L^{-2}TI$	$Cm^{-2}$
Carrier Mobility	$M^{-1}T^{2}I^1$	$m^{2}V^{-1}s^{-1}$
Charge Sensitivity	$M^{-1}L^{-1}T^3I$	$N^{-1}C$
Temperature Coefficient of Resistivity	$\theta^{-1}$	$K^{-1}$