A fluid flows along the x axis with a velocity given by V = (xt) i ˆ, where x is in feet and t in seconds. (a) Plot the speed for 0 ≤ x ≤ 10 ft and t = 3 s. (b) Plot the speed for x = 7 ft and 2 ≤ t ≤ 4 s. (c) Determine the local and convective acceleration. (d) Show that the acceleration of any fluid particle in the flow is zero. (e) Explain physically how the velocity of a particle in this unsteady flow remains constant throughout its motion

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A fluid flows along the x axis with a velocity given by V = (xt) i ˆ, where x is in feet and t in seconds. (a) Plot the speed for 0 ≤ x ≤ 10 ft and t = 3 s. (b) Plot the speed for x = 7 ft and 2 ≤ t ≤ 4 s. (c) Determine the local and convective acceleration. (d) Show that the acceleration of any fluid particle in the flow is zero. (e) Explain physically how the velocity of a particle in this unsteady flow remains constant throughout its motion.

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(e) The particles flow into areas of higher velocity as seen in plot "a", but at any given location the velocity is decreasing in time as seen in plot "b". For the given velocity field the local and convective accelerations are equal and opposite, thereby resulting in zero acceleration.

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