Gc (engineering) explained

In engineering and physics, g_c is a unit conversion factor used to convert mass to force or vice versa.^[1] It is defined as

g _{c} = (ma)/(F)

In unit systems where force is a derived unit, like in SI units, g_c is equal to 1. In unit systems where force is a primary unit, like in imperial and US customary measurement systems, g_c may or may not equal 1 depending on the units used, and value other than 1 may be required to obtain correct results.^[2] For example, in the kinetic energy (KE) formula, if g_c = 1 is used, then KE is expressed in foot-poundals; but if g_c = 32.174 is used, then KE is expressed in foot-pounds.

Motivations

According to Newton's second law, the force F is proportional to the product of mass m and acceleration a:

F \propto ma orF = K ma

If F = 1 lbf, m = 1 lb, and a =, then

1 ~ lbf = K ⋅ 1 ~ lb ⋅ 32 . 174 ~ (ft)/(s ^{2}) Leading toK = (1 ~ lbf)/(1 ~ lb ⋅ 32 . 174 ~ (ft)/(s ^{2})) =0 . 03108 ~ (lbf ⋅ s ^{2})/(lb ⋅ ft)

g_c is defined as the reciprocal of the constant K

g _{c} = (1)/(K) =32 . 174 ~ (lb ⋅ ft)/(lbf ⋅ s ^{2}) or equivalently, asg _{c} = (ma)/(F)

Notes and References

1. Book: Janna . William . 2015 . Introduction to Fluid Mechanics . . 9781482211610 . 5 . 5th.
2. Book: Cengel . Yunus . Boles . Michael . 2014 . Thermodynamics: An Engineering Approach . . 9781259822674 . 6 . 9th.