4. Air flows into a pipe from the region between a circular disk and a cone as shown in Fig. P4.55. The fluid velocity in the gap between the disk and the cone is closely approximated by V = V₁R²/r², where R is the radius of the disk, r is the radial coordinate, and is the fluid velocity at the edge of the disk. Determine the acceleration for r = 0.5 and 2 m if V0 = 5 m/s and R = 2 m. -Pipe sh Disk Cone
4. Air flows into a pipe from the region between a circular disk and a cone as shown in Fig. P4.55. The fluid velocity in the gap between the disk and the cone is closely approximated by V = V₁R²/r², where R is the radius of the disk, r is the radial coordinate, and is the fluid velocity at the edge of the disk. Determine the acceleration for r = 0.5 and 2 m if V0 = 5 m/s and R = 2 m. -Pipe sh Disk Cone
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![**Problem Description:**
Air flows into a pipe from the region between a circular disk and a cone as shown in Figure P4.55. The fluid velocity in the gap between the disk and the cone is closely approximated by the formula:
\[ V = V_0 R^2 / r^2 \]
Where:
- \( R \) is the radius of the disk.
- \( r \) is the radial coordinate.
- \( V \) is the fluid velocity at the edge of the disk.
**Objective:**
Determine the acceleration for \( r = 0.5 \, \text{m} \) and \( 2 \, \text{m} \) if \( V_0 = 5 \, \text{m/s} \) and \( R = 2 \, \text{m} \).
**Diagram Explanation:**
The illustration depicts a pipe where air enters from the space between a disk and a cone. The disk is oriented horizontally, while the cone is positioned such that its tip faces the disk, creating a gap through which the air flows. The air is then directed vertically into the pipe. The velocity \( V \) of the fluid varies with the radial coordinate \( r \), illustrating how the velocity distribution is influenced by the given parameters.
**Task:**
Given the relationship for velocity, calculate the acceleration of the fluid at the specified radial positions using the provided velocities and dimensions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce0a58ad-57fb-4927-ac11-40e4d0cfe182%2Fa5801408-1dd5-4488-9d3b-79a4cf68facc%2Fbevmhyi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
Air flows into a pipe from the region between a circular disk and a cone as shown in Figure P4.55. The fluid velocity in the gap between the disk and the cone is closely approximated by the formula:
\[ V = V_0 R^2 / r^2 \]
Where:
- \( R \) is the radius of the disk.
- \( r \) is the radial coordinate.
- \( V \) is the fluid velocity at the edge of the disk.
**Objective:**
Determine the acceleration for \( r = 0.5 \, \text{m} \) and \( 2 \, \text{m} \) if \( V_0 = 5 \, \text{m/s} \) and \( R = 2 \, \text{m} \).
**Diagram Explanation:**
The illustration depicts a pipe where air enters from the space between a disk and a cone. The disk is oriented horizontally, while the cone is positioned such that its tip faces the disk, creating a gap through which the air flows. The air is then directed vertically into the pipe. The velocity \( V \) of the fluid varies with the radial coordinate \( r \), illustrating how the velocity distribution is influenced by the given parameters.
**Task:**
Given the relationship for velocity, calculate the acceleration of the fluid at the specified radial positions using the provided velocities and dimensions.
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