Consider the flow with velocity vector v = xi. Show that the individual particles have the position
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Consider the flow with velocity vector v = xi. Show that the individual particles have the position vectors r(t) = c1eti + c2j + c3k with constant c1, c2, c3. Show that the particles that at t = 0 are in the cube of Prob. 11 at t = 1 occupy the volume e.
Data from Prob. 11
Show that the flow with velocity vector v = yi is incompressible. Show that the particles that at time t = 0 are in the cube whose faces are portions of the planes x = 0, x = 1, y = 0, y = 1, z = 0, z = 1 occupy at t = 1 the volume 1.
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