### Example Problem: Submarine Testing**Problem Statement:**1. A model submarine is tested in a sea water tank at a speed of \(30 \, \text{m/s}\). The prototype speed should be \(21.6 \, \text{km/hr}\). (a) Determine the geometric scale between the model and the prototype. (b) Determine the model speed if it is tested in a pressurized air wind tunnel with kinematic viscosity \( v = 8 \times 10^{-7} \, \text{m}^2/\text{s} \). For sea water use \( v = 1.124 \times 10^{-6} \, \text{m}^2/\text{s} \). **Additional Diagram/Graph Explanation:**If a diagram or graph were provided, it would typically show relationships between the model and the prototype speeds, viscosity values, or potentially a scale diagram comparing both versions of the submarine. However, without a specific visual, calculations focus on utilizing the given vector quantities and viscosity factors to find solutions. **Understanding Kinematic Viscosity:**- **Kinematic Viscosity (\(v\))**: A measure of a fluid's internal resistance to flow under gravitational forces. It is calculated as the dynamic viscosity divided by the fluid density. In this problem, the values for both sea water and air are given to allow accurate simulation of the submarine in different testing environments.

Reynolds number similarity in both the cases are used to arrive the solution.

A model submarine is tested in a sea water tank at a speed of 30 m/s. The prototype speed should be 21.6 km/hr. (a) Determine the geometric scale between the model and the prototype (b) Determine the model speed if it is tested in a pressurized air wind tunnel with kinematic viscosity v = 8 × 10-7 m² / s. For sea water use v = 1.124 × 10-6 m² /s.

A model submarine is tested in a sea water tank at a speed of 30 m/s. The prototype speed should be 21.6 km/hr. (a) Determine the geometric scale between the model and the prototype (b) Determine the model speed if it is tested in a pressurized air wind tunnel with kinematic viscosity v = 8 × 10-7 m² / s. For sea water use v = 1.124 × 10-6 m² /s.

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

### Example Problem: Submarine Testing

**Problem Statement:**

1. A model submarine is tested in a sea water tank at a speed of \(30 \, \text{m/s}\). The prototype speed should be \(21.6 \, \text{km/hr}\).

(a) Determine the geometric scale between the model and the prototype.

(b) Determine the model speed if it is tested in a pressurized air wind tunnel with kinematic viscosity \( v = 8 \times 10^{-7} \, \text{m}^2/\text{s} \). For sea water use \( v = 1.124 \times 10^{-6} \, \text{m}^2/\text{s} \).

**Additional Diagram/Graph Explanation:**

If a diagram or graph were provided, it would typically show relationships between the model and the prototype speeds, viscosity values, or potentially a scale diagram comparing both versions of the submarine. However, without a specific visual, calculations focus on utilizing the given vector quantities and viscosity factors to find solutions.

**Understanding Kinematic Viscosity:**

- **Kinematic Viscosity (\(v\))**: A measure of a fluid's internal resistance to flow under gravitational forces. It is calculated as the dynamic viscosity divided by the fluid density. In this problem, the values for both sea water and air are given to allow accurate simulation of the submarine in different testing environments.

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