Engineering Question #5134

Gerry Nazareno, a 18 year old male from Philippines asks on December 7, 2010,

Who is the scientist to be attributed for equation or formula used in calculating engine exhaust back pressure? The formula for Exhaust Pressure Drop or Back Pressure is as follows: B = L x G x Q*2 x 3.7 x 10*8 ÷ D*5 Where: B = Back pressure (mm H2O) L = Length of pipe (metres) Q = Exhaust gas flow (m3/min) D = Inside diameter of pipe (mm) G = Specific weight of gas (kg/m3) G = 352 ÷ Exhaust temperature + 273˚C

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The answer

John Jones answered on December 8, 2010

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.

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