4.16 A fluid flows along the x axis with a velocity given by V = = = (x/t), 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 accel- eration. (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.
4.16 A fluid flows along the x axis with a velocity given by V = = = (x/t), 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 accel- eration. (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.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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explain part d
![### Fluid Dynamics Problem: Velocity Analysis
**Problem 4.16**
A fluid flows along the \( x \) axis with a velocity given by:
\[ \mathbf{V} = \left(\frac{x}{t}\right) \hat{i} \]
where \( x \) is in feet and \( t \) in seconds.
#### Tasks:
(a) **Plot the speed** for \( 0 \leq x \leq 10 \) ft and \( t = 3 \) s.
(b) **Plot the speed** for \( x = 7 \) ft and \( 2 \leq t \leq 4 \) 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.**
### Diagram/Graph Explanation
- **Plot (a):** The graph should illustrate the behavior of speed as x varies between 0 and 10 feet for a constant time of 3 seconds.
- **Plot (b):** The graph should depict how speed changes over the time interval from 2 to 4 seconds at a constant position of 7 feet.
### Solution Steps:
- **Acceleration Analysis:** Calculate both local and convective components of acceleration to demonstrate that the total acceleration is zero, affirming constant velocity for fluid particles under the given conditions.
- **Physical Explanation:** Discuss the dynamics and properties of fluid motion in the context of unsteady flow and why the calculated accelerations result in constant particle velocity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe1f50f17-8873-45d4-b929-2ec6fdbb3e82%2F97de7196-aa3f-47e0-9644-f84839ea12f4%2Fs7cu9kv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Fluid Dynamics Problem: Velocity Analysis
**Problem 4.16**
A fluid flows along the \( x \) axis with a velocity given by:
\[ \mathbf{V} = \left(\frac{x}{t}\right) \hat{i} \]
where \( x \) is in feet and \( t \) in seconds.
#### Tasks:
(a) **Plot the speed** for \( 0 \leq x \leq 10 \) ft and \( t = 3 \) s.
(b) **Plot the speed** for \( x = 7 \) ft and \( 2 \leq t \leq 4 \) 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.**
### Diagram/Graph Explanation
- **Plot (a):** The graph should illustrate the behavior of speed as x varies between 0 and 10 feet for a constant time of 3 seconds.
- **Plot (b):** The graph should depict how speed changes over the time interval from 2 to 4 seconds at a constant position of 7 feet.
### Solution Steps:
- **Acceleration Analysis:** Calculate both local and convective components of acceleration to demonstrate that the total acceleration is zero, affirming constant velocity for fluid particles under the given conditions.
- **Physical Explanation:** Discuss the dynamics and properties of fluid motion in the context of unsteady flow and why the calculated accelerations result in constant particle velocity.
Expert Solution
Step 1
Given data:-
The given velocity function,
V=(X/t)i+0j+0k
we know,
i is a function of u so, u=(X/t)
j is a function of v so, v=0
k is a function of w, then w=0
Step by step
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