Air flows into the atmosphere from a nozzle and strikes a vertical plate as shown in the figure below. A horizontal force of 12 N is required to hold the plate in place. Determine the reading on the pressure gage. Assume the flow to be incompressible and frictionless. p=? 12N Area = 0.003 m? Area = 0.01 m?
Air flows into the atmosphere from a nozzle and strikes a vertical plate as shown in the figure below. A horizontal force of 12 N is required to hold the plate in place. Determine the reading on the pressure gage. Assume the flow to be incompressible and frictionless. p=? 12N Area = 0.003 m? Area = 0.01 m?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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#### Control Volume Analysis Concepts:
1. **Momentum Flux**:
- Result of fluid motion across the control surface.
2. **External Forces**:
- Surface forces and body forces act on a control volume.
3. **Resultant Force on Control Volume**:
- Interaction of momentum fluxes, surfaces, and body forces.
4. **Multiple Control Volumes**:
- May be used within a problem for comprehensive analysis.
5. **Conservation Equations**:
- Fluids follow a system of equations. These can include the conservation of mass, momentum, and energy.
#### Steps for Analysis:
1. **Identify Known Variables**:
- Force (12 N), Inlet Area, Outlet Area, Incompressible Flow, and Frictionless Flow.
2. **Determine Control Volume**:
- Choose a control volume that allows determination of the velocity of the air exiting the nozzle.
By analyzing the forces and applying the conservation equations for fluid mechanics—specifically the momentum equation—you can determine the pressure reading needed on the pressure gage for the given setup. This process involves understanding how fluid dynamics principles apply to the control volumes under examination.
### Further Reading and Exercises:
- Explore examples of momentum flux and control volume problems.
- Practice solving similar problems using conservation equations.
- Understand the derivation and application of the momentum equation in fluid dynamics.
**Note**: This guide is intended as an introduction. For detailed problem-solving steps and mathematical derivations, please refer to supplementary course materials or textbooks on fluid mechanics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98008a06-d82c-4142-b41a-5dfba7495134%2Fcbe57368-7e88-4638-b64e-d2381ab74140%2Fnjpjz1ck_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analysis of Air Flow Impact on a Vertical Plate
Air flows into the atmosphere from a nozzle and strikes a vertical plate as shown in the figure below. A horizontal force of 12 N is required to hold the plate in place. Determine the reading on the pressure gage. Assume the flow to be incompressible and frictionless.
#### Diagram Description
- **Inlet**: A nozzle with an area of \(0.01 \, m^2\)
- **Outlet**: A point where the air strikes the plate with an area of \(0.003 \, m^2\)
- **Force**: A horizontal force of 12 N is applied to hold the plate in position
*Note: Replace this placeholder with the actual image URL when publishing.*
#### Control Volume Analysis Concepts:
1. **Momentum Flux**:
- Result of fluid motion across the control surface.
2. **External Forces**:
- Surface forces and body forces act on a control volume.
3. **Resultant Force on Control Volume**:
- Interaction of momentum fluxes, surfaces, and body forces.
4. **Multiple Control Volumes**:
- May be used within a problem for comprehensive analysis.
5. **Conservation Equations**:
- Fluids follow a system of equations. These can include the conservation of mass, momentum, and energy.
#### Steps for Analysis:
1. **Identify Known Variables**:
- Force (12 N), Inlet Area, Outlet Area, Incompressible Flow, and Frictionless Flow.
2. **Determine Control Volume**:
- Choose a control volume that allows determination of the velocity of the air exiting the nozzle.
By analyzing the forces and applying the conservation equations for fluid mechanics—specifically the momentum equation—you can determine the pressure reading needed on the pressure gage for the given setup. This process involves understanding how fluid dynamics principles apply to the control volumes under examination.
### Further Reading and Exercises:
- Explore examples of momentum flux and control volume problems.
- Practice solving similar problems using conservation equations.
- Understand the derivation and application of the momentum equation in fluid dynamics.
**Note**: This guide is intended as an introduction. For detailed problem-solving steps and mathematical derivations, please refer to supplementary course materials or textbooks on fluid mechanics.
Transcribed Image Text:### Fluid Mechanics Homework Solutions: Pressure Calculation
#### Problem Statement:
**(f)** What is the gage pressure of the jet traveling radially outward beyond the edges of the plate?
- **Given:** \( p = \boxed{1.819} \) kPa
**(g)** What is the gage pressure acting on the right-hand face of the plate?
- **Given:** \( p = \boxed{4} \) kPa
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