Derive the continuity equation from first principles using an infini- tesimal control volume of rectangular shape and having dimensions (Sx, dy, 8z). Identify the net mass flow rate through each surface of this element as well as the rate at which the mass of the element is increasing. The resulting equation should be expressed in terms of the Cartesian coordinates (x,y,z,t), the Cartesian velocity compo- nents (u,v,w), and the fluid density p.

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Chapter1: Units, Trigonometry. And Vectors
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Derive the continuity equation from first principles using an infini-
tesimal control volume of rectangular shape and having dimensions
(8x, dy, &z). Identify the net mass flow rate through each surface of
this element as well as the rate at which the mass of the element is
increasing. The resulting equation should be expressed in terms
of the Cartesian coordinates (x,y,z,t), the Cartesian velocity compo-
nents (u,v,w), and the fluid density p.
Transcribed Image Text:Derive the continuity equation from first principles using an infini- tesimal control volume of rectangular shape and having dimensions (8x, dy, &z). Identify the net mass flow rate through each surface of this element as well as the rate at which the mass of the element is increasing. The resulting equation should be expressed in terms of the Cartesian coordinates (x,y,z,t), the Cartesian velocity compo- nents (u,v,w), and the fluid density p.
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