**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.

The velocity is given by relation The value are

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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Question

**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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