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  3. 3 the velocity field in an unsteady moving fluid is...

Question: 3 the velocity field in an unsteady moving fluid is...

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3 The velocity field in an unsteady moving fluid is given by Vuvwk, where u Ξ u(x, y, z, t), ν Ξ ν(x, y, z, t) and w Ξ (x, y, z, t). () By considering the density. p(x. y, z, t), and an infinitesimal control volume, δν, in the fluid moving from a point (xiMA) at time t1 to a point (X2. /2. /2) at time t2. then derive the substantial (or total) derivative of p and interpret the meanings of the first two terms on the right-hand side of this latter expression. () G that the divergence of V is defined by 1 D(5V) then, by considering the mass of the moving control volume,6m ρδν derive the equation of continuity (that is, of mass conservation) for a compressible fluid and show that this can be rearranged in conservative form as

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