# Foundations of Mechanics: 2nd Edition by Ralph Abraham By Ralph Abraham

E-book through Ralph Abraham, Jerrold E. Marsden, Tudor Ratiu, Richard Cushman

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Extra info for Foundations of Mechanics: 2nd Edition

Example text

25)) for Ea /R = 15000 K. 1). 2, such conditions will occur if the mixture is too rich or too lean. 3 illustrates the strong temperature dependence of the exponential factor in k for a value Ea /R = 15000 K, which is typical for hydrocarbon gas fuels burning in air (Quintiere, 2006). 2, it was mentioned that the adiabatic flame temperature for combustion of hydrocarbon gas with air at atmospheric pressures is about 2200 K at stoichiometric conditions. Fig. 3 reveals that if the mixture hydrocarbon gas/air is so lean or so rich that the adiabatic flame temperature becomes as low as 1500 K, the reaction rate is at least 2 orders of magnitude less than in stoichiometric conditions.

This implies treating fluids as continuous media, not as an ensemble of individual molecules (Batchelor, 1967). This is justified in ‘normal’ fire related applications. The continuum hypothesis effectively allows defining local fluid properties, which can be interpreted as average values over a very small volume around the position considered (but assuming that this volume is still very large compared to distances between molecules). The continuum hypothesis is adopted throughout this book. 1 Mass density The mass density (or ‘density’), ρ, is the amount of fluid mass, m, inside a volume, V: ρ= m .

This boils down to the expression of Newton’s second law, applied to flows: the net change in momentum of a system per unit time in a certain sense and direction equals the net force exerted on that system in that sense and direction. Expressed for a stationary volume, this reads: The total force exerted onto a stationary volume equals the sum of the net outflow of momentum per unit time out of that same volume plus the accumulation of momentum per unit time in that same volume. n)dA = Ftot . 35) ∂V Eq.