A piston compresses gas in a cylinder by moving at constant speed V, as in Fig. P4.18. Let the gas density and length at t = 0 be ρo and Lo, respectively. Let the gas velocity vary linearly from u = V at the piston face to u = 0 at x = L. If the gas density varies only with time, find an expression for ρ(t).

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V = constant p(r) x=L(t)