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 fo
r 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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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.
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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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Answer:
a) The slip coefficient is 0.9
b) Blade tip speed is 345.57 m/s
c) Stagnation temperature exiting the impellor is 416.84 k
d) Exit flow velocity is 84.88 m/s
e) Exit flow angle is 76.2°
f) Exit static temperature is 353.84 k
g) Impellor exit Mach number is 0.943
Explanation:
Flow at entry is axial α₁ = 0
Tagential velocity at entry = 0
Blade at exit is radial β₂ = 0
μ₂ =
