About

The following simulation try to illustrate how pressure change in the liquid

\(P(h)=P_0+\rho g h\) where \(p_o\) is the atmosphere pressure, \(h\) is the depth measured from the surface of the liquid.

You can drag the control point to change the shape of the container, and watch how pressure change with depth.

 

Translations

Code	Language		Translator	Run

Credits

Fu-Kwun Hwang - Dept. of Physics, National Taiwan Normal Univ.; Fremont Teng; Loo Kang Wee

Briefing Document: Pressure in a Fluid Simulator JavaScript Simulation Applet

1. Overview:

This document summarizes the "Pressure in a Fluid Simulator JavaScript Simulation Applet HTML5" resource from Open Educational Resources / Open Source Physics @ Singapore. The simulation is designed to illustrate the relationship between pressure and depth in a liquid. It is an interactive tool that allows users to manipulate the shape of a container and observe the resulting changes in pressure at different depths.

2. Main Themes and Important Ideas/Facts:

• Pressure-Depth Relationship: The core concept demonstrated by the simulation is the principle that pressure in a liquid increases with depth. The simulation aims to illustrate the formula: (P(h)=P_0+\rho g h), where:
• (P(h)) is the pressure at depth (h).
• (P_0) is the atmospheric pressure.
• (\rho) is the density of the liquid.
• (g) is the acceleration due to gravity.
• (h) is the depth measured from the surface.
• Interactive Manipulation: A key feature is the ability for users to "drag the control point to change the shape of the container, and watch how pressure change with depth." This interactivity allows students to explore the concept visually and understand how pressure distribution is independent of container shape for a given depth.
• HTML5 Applet: The resource is an HTML5 applet, making it accessible through web browsers without requiring specific plugins, "Pressure in a Fluid Simulator JavaScript Simulation Applet HTML5".
• Customization: The resource provides options to adjust parameters using "Combo Box and Options. Display will give you check boxes While Liquid Height and Density give sliders."
• Reset Functionality: A Reset button is included to restore the simulation to its initial state, allowing for repeated experimentation.
• Embedding: The simulation can be embedded in other webpages using an <iframe> tag, facilitating its integration into online learning platforms.
• Creators: The simulation was developed by Fu-Kwun Hwang, Fremont Teng, and Loo Kang Wee.

3. Target Audience and Learning Goals:

• The resource is suitable for physics education, particularly for introductory courses on fluid mechanics and pressure.
• Sample Learning Goals: The document mentions "Sample Learning Goals" but does not explicitly state them. However, inferred learning goals include:
• Understanding the relationship between pressure and depth in a fluid.
• Visualizing how pressure changes with depth in different container shapes.
• Applying the formula (P(h)=P_0+\rho g h) to predict pressure at a given depth.
• Understanding the influence of density on pressure.

4. Intended Use and Instructions:

• Teachers: The resource is intended for use by teachers to demonstrate the principles of fluid pressure.
• Students: The resource is intended for students to explore and understand pressure with depth in liquids.
• **Instructions:**The instructions include how to use the combo box to view options, toggling full screen, and resetting the simulation.

5. Related Resources:

The page lists a wide range of other interactive simulations and resources available from Open Source Physics @ Singapore, covering various physics and mathematics topics. These include simulations on:

• Mechanics (e.g., Floating Block Stability, Buoyancy Force, Projectile Motion).
• Electromagnetism (e.g., Magnetic Fields, Faraday's Law).
• Optics (e.g., Refraction, Lenses, Mirrors).
• Waves (e.g., Electromagnetic Waves, Sound Waves).
• Mathematics (e.g., Fractions, Graphing, Geometry).

6. Technical Details and Licensing:

• The simulation is built using JavaScript and HTML5.
• The content is licensed under the Creative Commons Attribution-Share Alike 4.0 Singapore License. Commercial use of the EasyJavaScriptSimulations Library requires a separate license from the University of Murcia (um.es).

7. Overall Assessment:

The "Pressure in a Fluid Simulator" appears to be a valuable educational tool for teaching the fundamental concepts of fluid pressure. Its interactive nature and clear visualization of the pressure-depth relationship make it a potentially effective resource for both classroom instruction and independent learning. The availability of embedding options and related resources further enhances its utility.

 

Fluid Pressure Simulation Study Guide

I. Key Concepts

• Pressure (P): Force exerted per unit area. In fluids, pressure acts equally in all directions at a given depth.
• Fluid: A substance that can flow easily, such as a liquid or a gas.
• Density (ρ): Mass per unit volume of a substance.
• Depth (h): The vertical distance below the surface of a liquid.
• Atmospheric Pressure (P₀): The pressure exerted by the weight of the atmosphere.
• Hydrostatic Pressure: The pressure exerted by a fluid at rest.
• Pascal's Law: Pressure applied to a confined fluid is transmitted equally in all directions throughout the fluid.

II. Key Formula

• Pressure at a Depth in a Fluid: P(h) = P₀ + ρgh
• P(h) = Pressure at depth h
• P₀ = Atmospheric pressure
• ρ = Density of the fluid
• g = Acceleration due to gravity (approximately 9.8 m/s²)
• h = Depth below the surface of the fluid

III. Simulation Controls and Features

• Adjustable Container Shape: The simulation allows you to change the shape of the container holding the fluid.
• Adjustable Liquid Height: A slider controls the height of the liquid in the container.
• Adjustable Liquid Density: A slider controls the density of the liquid.
• Pressure Display: The simulation visually displays how pressure changes with depth.
• Combo Box Options: Allows you to toggle different display options.
• Full Screen Toggling: Double-clicking toggles full-screen mode.
• Reset Button: Returns the simulation to its initial state.

IV. Quiz

1. Explain the relationship between depth and pressure in a fluid. How does the simulation demonstrate this relationship?
2. What does the variable 'ρ' represent in the formula P(h) = P₀ + ρgh, and how does changing its value affect the pressure at a given depth?
3. Define atmospheric pressure and explain its role in determining the total pressure at a depth in a liquid.
4. How can the shape of the container affect the pressure at a specific point within the fluid?
5. What does 'g' represent in the pressure formula and what is its approximate value on Earth?
6. Describe how you can change the density of the liquid within the simulator and what that demonstrates.
7. Explain what happens to the pressure at a certain depth if you double the density of the liquid.
8. What are the units for Pressure (P), Density (ρ), and Depth (h)?
9. Explain what is meant by Hydrostatic Pressure.
10. Describe one practical, real-world application of the principles demonstrated in this simulation.

V. Quiz Answer Key

1. Pressure increases linearly with depth in a fluid. The simulation demonstrates this by visually showing how pressure changes as the depth is altered.
2. 'ρ' represents the density of the fluid. Increasing the density increases the pressure at a given depth because a denser fluid exerts more weight per unit volume.
3. Atmospheric pressure is the pressure exerted by the Earth's atmosphere. It acts as an additional constant pressure (P₀) on top of the hydrostatic pressure due to the fluid's weight.
4. The shape of the container does not directly affect the pressure at a specific point, so long as the depth remains the same. Pressure only depends on depth, density, and atmospheric pressure, not the container's geometry.
5. 'g' represents the acceleration due to gravity. Its approximate value on Earth is 9.8 m/s².
6. By using the liquid density slider. This will demonstrate that at any depth, an increase in liquid density also increases the pressure.
7. If you double the density of the liquid, the pressure increase due to the fluid's weight (ρgh) also doubles, assuming the depth remains constant.
8. Pressure (P) is measured in Pascals (Pa), Density (ρ) is measured in kilograms per cubic meter (kg/m³), and Depth (h) is measured in meters (m).
9. Hydrostatic Pressure is the pressure exerted by a fluid at rest due to the weight of the fluid above a certain point.
10. Submarines must be engineered to withstand immense pressures at great depths, directly related to the principles shown in this simulation.

VI. Essay Questions

1. Discuss how the fluid pressure simulation demonstrates the relationship between pressure, depth, and density. Provide specific examples of how manipulating the simulation's controls can illustrate these relationships.
2. Explain Pascal's Law and discuss how the fluid pressure simulation, though seemingly simple, provides a foundation for understanding it. How can the concept of pressure at a depth be extrapolated to understand hydraulic systems?
3. Describe the limitations of the simulation in representing real-world fluid pressure scenarios. What factors are not accounted for that might affect pressure in more complex systems?
4. Compare and contrast the concept of pressure in liquids versus gases. How does the fluid pressure simulation apply to both, and what key differences exist?
5. Design a hypothetical experiment using the fluid pressure simulation to investigate the effects of different variables on pressure. Outline your procedure, expected results, and potential sources of error.

VII. Glossary of Key Terms

• Pressure (P): The force exerted per unit area, measured in Pascals (Pa).
• Density (ρ): The mass per unit volume of a substance, measured in kilograms per cubic meter (kg/m³).
• Depth (h): The vertical distance below the surface of a liquid, measured in meters (m).
• Atmospheric Pressure (P₀): The pressure exerted by the weight of the atmosphere, approximately 101,325 Pa at sea level.
• Hydrostatic Pressure: The pressure exerted by a fluid at rest due to the weight of the fluid above a certain point.
• Pascal's Law: The principle that pressure applied to a confined fluid is transmitted equally in all directions throughout the fluid.

Sample Learning Goals

[text]

For Teachers

Pressure in a Fluid Simulator JavaScript Simulation Applet HTML5

Instructions

Combo Box and Options

Toggling Full Screen

Reset Button

Research

[text]

Video

[text]

 Version:

Other Resources

[text]

Frequently Asked Questions

What is the purpose of the Pressure in a Fluid Simulator?

The simulation is designed to illustrate how pressure changes within a liquid based on depth. It helps visualize the relationship described by the formula (P(h) = P_0 + \rho g h), where (P(h)) is the pressure at depth (h), (P_0) is the atmospheric pressure, (\rho) is the density of the liquid, and (g) is the acceleration due to gravity.

How can I interact with the Pressure in a Fluid Simulator?

You can interact with the simulation by dragging the control points to change the shape of the container. This allows you to observe how alterations in the container's form affect the pressure at different depths within the fluid. The combo box also lets you adjust display options, liquid height, and density using sliders and checkboxes.

How do I toggle full-screen mode in the simulation?

Double-clicking anywhere on the screen will toggle between normal and full-screen mode, providing a more immersive experience.

What is the purpose of the "Reset" button?

The "Reset" button allows you to quickly revert the simulation to its initial state, clearing any changes you've made to the container's shape or other parameters.

Can the simulation be embedded in other webpages?

Yes, the simulation can be embedded in other webpages using the provided iframe code. This allows educators and developers to integrate the simulation into their own online resources.

Who developed this simulation?

The simulation was developed by Fu-Kwun Hwang from the Dept. of Physics, National Taiwan Normal Univ., Fremont Teng, and Loo Kang Wee.

What are some other interactive resources available from Open Source Physics @ Singapore?

The Open Source Physics @ Singapore website offers a wide variety of interactive simulations covering topics such as buoyancy, collisions, electromagnetism, optics, mechanics, waves, quantum physics, and mathematics. Examples include simulators for floating block stability, buoyancy force, projectile motion, wave phenomena, electric circuits, and more.

What license governs the use of these simulations?

The content is licensed under the Creative Commons Attribution-Share Alike 4.0 Singapore License. For commercial use of the EasyJavaScriptSimulations Library, it's necessary to read the EJS License and contact This email address is being protected from spambots. You need JavaScript enabled to view it. directly.