what is coherent system of units
A coherent derived unit is defined as a derived unit that, for a given system of quantities and for a chosen set of base units, is a product of powers of base units with no other proportionality factor than one.[1] The concept of coherence was developed in the mid-nineteenth century by, amongst others, Kelvin and James Clerk Maxwell and promoted by the British Association for the Advancement of Science. The concept was initially applied to the Centimetre–gram–second system and the Foot–pound–second systems of units in 1873 and 1875 respectively. The International System of Units (1960) was designed around the system of coherence.
In SI, which is a coherent system, the unit of power is the "watt" which is defined as "one joule per second".[2] In the US customary system of measurement, which is non-coherent, the unit of power is the "horsepower" which is defined as "550 foot-pounds per second" (the pound in this context being the pound-force), similarly the gallon is not equal to a cubic yard (nor is it the cube of any length unit).
SI [edit]
The following is a list of coherent SI units:
Frequency (Hertz) = reciprocal of time (s-1)
force (newtons) = mass (kilograms) × acceleration (m/s2)
pressure (pascals) = force (newtons) ÷ area (m2)
energy (joules) = force (newtons) × distance (metres)
power (watts) = energy (joules) ÷ time (seconds)
potential difference (volts) = power (watts) ÷ electric current (amps)
electric charge (coulombs) = electric current (amps) × time (seconds)
equivalent radiation dose (sieverts) = energy (joules) ÷ mass (kilograms)
absorbed radiation dose (grays) = energy (joules) ÷ mass (kilograms)
Radioactive activity (becquerels) = reciprocal of time (s-1)
Capacitance (farads) = electric charge (coulombs) ÷ potential difference (volts)
Electrical resistance (ohms) = potential difference (volts) ÷ electric current (amperes)
Electrical conductance (ohms) = electric current (amperes) ÷ potential difference (volts)
Magnetic flux (weber) = the magnetic flux which, linking a circuit of one turn, would produce in it an electromotive force of one volt if it were reduced to zero at a uniform rate in one second
Magnetic flux density (tesla) = magnetic flux (webers) ÷ area (square metres).
... more ...
CGS [edit]
The following is a list of coherent centimetre–gram–second (CGS) system of units:
acceleration (gals) = distance (centimetres) ÷ time2 (s2)
force (dynes) = mass (grams) × acceleration (m/s2)
energy (ergs) = force (dynes) × distance (centimetres)
pressure (barye) = force (dynes) ÷ area (cm2)
dynamic viscosity (poise) = mass (grams) ÷ (distance (centimetres) × time (seconds))
kinematic viscosity (stokes) = area (cm2)÷ time (seconds)
... more ...
FPS [edit]
The following is a list of coherent foot-pound-second (FPS) system of units:
force (poundal) = mass (pounds) × acceleration (ft/s2)
... more ...