As shown in the figure below, a "noisemaker" B is towed behind a minesweeper A to set off enemy acoustic mines such as at C. The drag force of the noisemaker is to be studied in a water tunnel at a 1/6 scale model (model 1/6 the size of the prototype). The drag force is assumed to be a function of the speed of the ship, the density and viscosity of the fluid, and the diameter of the noisemaker. (a) If the prototype towing speed is 3 m/s, determine the water velocity in the tunnel for the model tests. (b) If the model tests of part (a) produced a model drag of 900 N, determine the drag expected on the prototype.
As shown in the figure below, a "noisemaker" B is towed behind a minesweeper A to set off enemy acoustic mines such as at C. The drag force of the noisemaker is to be studied in a water tunnel at a 1/6 scale model (model 1/6 the size of the prototype). The drag force is assumed to be a function of the speed of the ship, the density and viscosity of the fluid, and the diameter of the noisemaker. (a) If the prototype towing speed is 3 m/s, determine the water velocity in the tunnel for the model tests. (b) If the model tests of part (a) produced a model drag of 900 N, determine the drag expected on the prototype.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![### Understanding Drag Force Using Scale Models in Water Tunnels
#### Concept Overview
When researching the effects of drag on certain marine equipment, such as the "noisemaker" B towed by a minesweeper A, scale models in water tunnels are commonly used. The noisemaker’s drag force, which can activate underwater acoustic mines like at point C, needs to be accurately studied. This force is determined by factors such as the ship's speed, the water's density and viscosity, and the device's diameter.
#### Problem Breakdown
Let's examine how to analyze the prototype and model:
1. **Model Description**:
- **Prototype**: Actual noisemaker
- **Model**: 1/6 scale of the prototype (i.e., model is 1/6th the size of the prototype).
2. **Drag Force Analysis**:
- Drag force (D) depends on speed (V), fluid density, fluid viscosity, and the object's diameter.
- Testing the model in a water tunnel helps determine these forces in a controlled environment.
#### Questions
(a) **Determine the Water Velocity in the Tunnel for the Model Tests**:
- Given the prototype towing speed is 3 m/s.
- Calculate the corresponding water velocity (V<sub>m</sub>) needed in the tunnel for accurate model testing.
(b) **Determine the Drag Expected on the Prototype**:
- Given the model tests produced a drag force of 900 N.
- Using the results, estimate the drag force (D<sub>p</sub>) on the actual prototype.
#### Diagram Explanation
The diagram illustrates:
- **A Minesweeper (A)** towing a **Noisemaker (B)**.
- The Noisemaker, intended to set off the **Acoustic Mine (C)**.
- The depiction under water shows the linkage and relative placements of the different components as described in the problem.
#### Calculation Input Fields
- **Field for Velocity Calculation**:
> (a) V<sub>m</sub> = [Textbox for input] m/s
- **Field for Drag Force Calculation**:
> (b) D<sub>p</sub> = [Textbox for input] N](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4312e33f-77b0-4b80-923c-eb8ae7571481%2Ff3fa02e3-1b4b-42cb-8a9e-66b4b6bc7aa3%2F2wknd07_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Drag Force Using Scale Models in Water Tunnels
#### Concept Overview
When researching the effects of drag on certain marine equipment, such as the "noisemaker" B towed by a minesweeper A, scale models in water tunnels are commonly used. The noisemaker’s drag force, which can activate underwater acoustic mines like at point C, needs to be accurately studied. This force is determined by factors such as the ship's speed, the water's density and viscosity, and the device's diameter.
#### Problem Breakdown
Let's examine how to analyze the prototype and model:
1. **Model Description**:
- **Prototype**: Actual noisemaker
- **Model**: 1/6 scale of the prototype (i.e., model is 1/6th the size of the prototype).
2. **Drag Force Analysis**:
- Drag force (D) depends on speed (V), fluid density, fluid viscosity, and the object's diameter.
- Testing the model in a water tunnel helps determine these forces in a controlled environment.
#### Questions
(a) **Determine the Water Velocity in the Tunnel for the Model Tests**:
- Given the prototype towing speed is 3 m/s.
- Calculate the corresponding water velocity (V<sub>m</sub>) needed in the tunnel for accurate model testing.
(b) **Determine the Drag Expected on the Prototype**:
- Given the model tests produced a drag force of 900 N.
- Using the results, estimate the drag force (D<sub>p</sub>) on the actual prototype.
#### Diagram Explanation
The diagram illustrates:
- **A Minesweeper (A)** towing a **Noisemaker (B)**.
- The Noisemaker, intended to set off the **Acoustic Mine (C)**.
- The depiction under water shows the linkage and relative placements of the different components as described in the problem.
#### Calculation Input Fields
- **Field for Velocity Calculation**:
> (a) V<sub>m</sub> = [Textbox for input] m/s
- **Field for Drag Force Calculation**:
> (b) D<sub>p</sub> = [Textbox for input] N
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