engineering question #5134

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

Q:

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, A:

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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