This is the D'Arcy-Weisbach pressure drop equation, named for the French engineer Henry D'Arcy (1803-1858) and the German mathematician and engineer Julius Weisbach (1806-1871). It applies to the steady flow of any incompressible fluid through any pipe of circular cross-section.
The version of the formula quoted here uses a peculiar mixture of units and has a correction factor to calculate the density of the exhaust gas at exhaust temperature from its specific weight at room temperature. The numerical factor in this version of the formula, 3.7 x 10*8, includes an assumed value for the D'Arcy-Weisbach friction coefficient. In general this coefficient varies with flow conditions according to the Moody diagram; the numerical value used here is appropriate for typical conditions of flow in an engine exhaust.