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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genesisb6272 genesisb6272

19-03-2020
Engineering

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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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mkasblog mkasblog · Answer 1 · 2020-03-20T01:56:23+01:00

Answer

See explanation for step by step procedures towards getting answers

Explanation:

Given that;

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.

See attachments for further explanations

trenchard4ray trenchard4ray · Answer 2 · 2020-03-20T02:24:35+01:00

trenchard4ray trenchard4ray

20-03-2020

Answer:

Explanation:

The Solved solution is in the attached document.

(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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