Derivation_of_continuity_equation

# Derivation_of_continuity_equation - Derivation of the...

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Derivation of the Continuity Equation (Section 9-2, Ç engel and Cimbala) We summarize the second derivation in the text – the one that uses a differential control volume . First, we approximate the mass flow rate into or out of each of the six surfaces of the control volume, using Taylor series expansions around the center point, where the velocity components and density are u , v , w , and ρ . For example, at the right face, The mass flow rate through each face is equal to ρ times the normal component of velocity through the face times the area of the face. We show the mass flow rate through all six faces in the diagram below (Figure 9-5 in the text): Ignore terms higher than order dx . Infinitesimal control volume of dimensions dx , dy , dz . Area of right face = dydz . Mass flow rate through the right face of the control volume. Next, we add up all the mass flow rates through all six faces of the control volume in

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