Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Interactive Audio Lesson
Listen to a student-teacher conversation explaining the topic in a relatable way.
Understanding Pressure Fields
Unlock Audio Lesson
Today, we are going to explore how pressure acts in a fluid that is at rest. Can anyone tell me what happens to shear stress in this scenario?
Shear stress becomes zero, right?
Exactly! When the fluid is at rest, only normal stress, which we refer to as pressure, is acting on the control surfaces. This pressure can be expressed as a function of position, P(x, y, z). Let’s think of a control volume as a rectangular box. What are the three axes we're measuring pressure along?
X, y, and z.
Correct! And we can look at the midpoint of this box to define the pressure acting at the centroid. Now, why is it important to consider pressure as a function of these coordinates?
Because pressure may change based on where you are in the fluid?
Great point! Pressure in a fluid at rest can be influenced by depth, which relates to the concept of hydrostatic pressure. Let's keep this in mind.
Body Forces and Surface Forces
Unlock Audio Lesson
Now that we've established our pressure function, let's discuss the forces involved. What type of forces act on our control volume?
There are surface forces and body forces, right?
Exactly! The surface force is the pressure acting on the surfaces of the control volume, while the body force is typically due to gravity. Can anyone tell me how we express the weight of this control volume?
It would be the unit weight of the fluid multiplied by the volume of the control volume.
Spot on! For our control volume, it’s calculated as ρg multiplied by the volume - this is essential for understanding how forces interact within our fluid system.
Types of Pressure
Unlock Audio Lesson
We've talked a bit about pressure in the fluid. Now let's explore the different types of pressure. Can anyone define what absolute pressure is?
It’s the pressure measured from absolute zero pressure, like in a vacuum.
Great! And how does gauge pressure differ from absolute pressure?
Gauge pressure is measured above atmospheric pressure, so it can be either positive or negative.
That's right! Gauge pressure can sometimes confuse us, especially when dealing with atmospheric or vacuum conditions. Can anyone give an example of when we would use gauge pressure?
When measuring tire pressure, it's usually given in gauge pressure since it’s above atmospheric pressure.
Exactly! It's crucial to understand the context of measurement to apply the right type of pressure for calculations.
Hydrostatic Pressure Distribution
Unlock Audio Lesson
Now, let’s discuss how pressure varies with depth in a fluid at rest. Can anyone tell me why we typically measure pressure changes as we go deeper?
Because the weight of the fluid above increases, applying more pressure?
Exactly! The pressure increases linearly with depth, which can be defined as P = ρgh. This means pressure is a function of height above a reference point. Who can explain why pressure remains constant on a horizontal plane within the fluid?
Because the fluid is at rest! If it weren’t, it would create gradients.
Perfect! A good understanding of this principle is essential when applying hydrostatic conditions in real-world problems.
Practical Applications and Measurement
Unlock Audio Lesson
Finally, let’s think about practical applications of our discussion, particularly in using devices like a barometer. What is a mercury barometer used for?
It measures atmospheric pressure, right?
Yes! And it does so by balancing the weight of a column of mercury against atmospheric pressure. What would happen to the measurement if you moved to a higher altitude?
The atmospheric pressure decreases, so the mercury would drop lower in the barometer.
Exactly! Pressure decreases with altitude, and this can have effects on physical conditions, such as altitude sickness in humans. Understanding these concepts can help us address challenges in various fields like meteorology and engineering.
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
The section explores how pressure acts normal to surfaces within a control volume when fluid is at rest, distinguishing between surface and body forces. It also introduces concepts of absolute, gauge, and vacuum pressure, providing equations that describe how these pressures interact with gravitational forces.
Detailed
Detailed Summary of Section 1.5: Force Components due to Pressure
In this section, we examine how pressure influences force components on a fluid at rest within a defined control volume. We consider a simple model where the shear stress is zero, resulting in normal stress (pressure) acting on the control surfaces. We define pressure as a function, P(x, y, z), and describe how gravitational forces contribute to the total force acting on the fluid.
The section discusses the gradient of pressure in a three-dimensional Cartesian system and introduces the Taylor series to approximate pressure at points within the control volume. We derive formulas for force components caused by pressure along different axes (x, y, z) and illustrate the equilibrium conditions for fluids at rest, referencing Newton’s laws of motion.
Furthermore, we differentiate between absolute pressure, gauge pressure, and vacuum pressure, establishing their definitions based on atmospheric pressure, and discuss the implications of using each type in practical applications. Lastly, we conclude with insights into pressure distributions, demonstrating how they vary with depth and the effect of hydrostatic forces on pressure in fluids.
Youtube Videos
Audio Book
Dive deep into the subject with an immersive audiobook experience.
Understanding Pressure Fields
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
Now if I go for the next ones that how to get the pressure field when fluid is at rest. That means I am just looking the what could be the functions of the P, P = P (x, y, z).
Detailed Explanation
In this part, we explore how to define the pressure field in a fluid that is at rest. The notation P = P(x, y, z) indicates that pressure can vary at different points in a three-dimensional space, depending on the coordinates x, y, and z. This means that pressure is not uniform; instead, it can change based on where you are looking within the fluid.
Examples & Analogies
Imagine a calm lake. The pressure at the surface of the lake (where you would dip your finger) is different from the pressure felt deeper underwater. The deeper you go, the higher the pressure due to the weight of the water above you. This concept is similar to understanding how pressure changes in various locations within any fluid.
Control Volume Concept
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
If it that it is now again I am considering a very simple case, let us consider a control volume like this okay. This is what my control volume. As I said it when the fluid is at rest the shear stress becomes zero.
Detailed Explanation
A control volume is a specific region in space that we analyze for pressure effects. In a fluid at rest, shear stresses (which arise from parallel layers of fluid sliding past each other) do not exist, meaning only normal stresses (force per unit area acting perpendicular to the surface) are present. This simplifies our calculations since we only need to consider the force acting due to pressure at the control surface.
Examples & Analogies
Think of sitting in a swimming pool. When you're still, the water exerts pressure evenly on you from all sides, but if you start moving your arms, the water exerts different forces on your arms versus on the rest of your body. At rest, the pressure is constant, making calculations straightforward.
Components of Force in the Control Volume
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
So we can have two force components. One is the surface force component and other is body force. The body force components if you look it that it will be unit weight multiply the volume of the control volume.
Detailed Explanation
In our control volume analysis, we focus on two types of forces: surface forces and body forces. The surface force acts due to pressure on the walls of the control volume, while body forces arise due to gravity acting on the fluid within the control volume. The body force can be calculated by multiplying the unit weight of the fluid by the volume of the control volume.
Examples & Analogies
Picture a box submerged in water. The water exerts an upward force on the box (body force), while the walls of the box feel the pressure from the water against them (surface force). The total effect of these forces will determine how the box behaves in the water.
Pressure Distribution and Forces
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
The pressure at the centre of the fluid control volume is assumed to be P (x, y, z). At that point, the gravity force is acting it which is the body force component.
Detailed Explanation
We define pressure at a specific point in the control volume as P (x, y, z). This point is usually at the center of the volume. The pressure at this point contributes to the gravity force, which acts as a body force since it influences the fluid's behavior due to its weight. The gravity force and pressure together will determine how the fluid will flow or behave under various conditions.
Examples & Analogies
Consider the weight of the ocean. The pressure at the deepest parts contributes to the overall force acting on water layers above, influencing how currents behave or the types of organisms that can live at certain depths.
Understanding Pressure Variation with Depth
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
Now if you look it over this control volume, all these pressure is going to act it as the Pascal law says that pressure acts normal to the surface.
Detailed Explanation
According to Pascal's Law, any change in pressure applied to a confined fluid is transmitted undiminished throughout the fluid. This means that the pressure in our control volume acts perpendicular to the surfaces of the volume. Importantly, this characteristic leads to pressure increasing with depth due to the weight of the fluid above, creating higher pressures at lower depths.
Examples & Analogies
When you dive into the ocean, you can feel a pressure increase on your ears the deeper you go. This is because of the water's weight above you, illustrating how pressure increases with depth according to Pascal's Law.
Measuring Pressure: Gauge vs. Absolute
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
Now the point is what we are going to discuss is that gauge pressure and vacuum pressure.
Detailed Explanation
In measuring pressure, we differentiate between gauge pressure and absolute pressure. Gauge pressure measures the pressure relative to atmospheric pressure, while absolute pressure is the total pressure measured from a perfect vacuum (where no particles exist). Understanding this distinction is crucial for accurately calculating and reporting pressure in different situations.
Examples & Analogies
An example can be found in car tires. When you check your tire pressure, the gauge shows you gauge pressure, which indicates how much air pressure is higher than the outside atmospheric pressure. However, absolute pressure would consider the atmosphere as a baseline, showing a lower number for the same tire.
Gravity and Pressure Gradients
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
As you consider the gravity in one of the coordinate axes most times, we align the gravity with the z-direction.
Detailed Explanation
Typically, when analyzing pressure gradients, we align gravity along the vertical z-axis. This simplification allows us to analyze the pressure changes vertically more straightforwardly. Under normal conditions, it reveals that pressures do not vary in horizontal directions (x and y) while they vary in the direction of gravity (z). This creates a pressure gradient that increases with depth.
Examples & Analogies
If you think of a tall tower of water—like in a water tank—pressure at the bottom is significantly greater than at the top due to the weight of the water above, illustrating this concept of pressure gradient with depth.
Linear Variation of Pressure
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
So if you consider a horizontal plane, at that horizontal plane you will be pressure will be the constant.
Detailed Explanation
When observing a horizontal plane within a fluid at rest, we find that pressure remains constant across that plane. This is because, at any given depth, the weight of the fluid above is balanced and does not change, reflecting the idea that pressure varies with depth, but remains the same horizontally at any given level.
Examples & Analogies
Picture the surface of a swimming pool: if you were to check the pressure at multiple points just below the same depth, it would be equal everywhere, illustrating how pressure remains constant across a level surface.
Real-World Application of Pressure Concepts
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
As we have derived pressure distribution equations which in vector forms and let we simplify that equations.
Detailed Explanation
In real-world applications, understanding the derivations of pressure distribution equations is essential. These equations, often represented in vector forms, help simplify analysis across different dimensions. Recognizing how to adapt these principles allows engineers and scientists to accurately model fluid behavior for various systems.
Examples & Analogies
Consider designing a dam: engineers rely on pressure distribution equations to predict how water will exert force on different parts of the structure, ensuring safety and effectiveness in real-world applications where human lives may be at stake.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
-
Hydrostatic Pressure: Pressure increases linearly with depth due to the weight of fluid above.
-
Control Volume: A defined volume in which pressure and force interactions are analyzed.
-
Types of Pressure: Absolute pressure, gauge pressure, and vacuum pressure each serve different contexts in fluid measurement.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
-
Example of gauge pressure: Tire pressure is often measured in gauge pressure since it’s above atmospheric pressure.
-
When calculating the weight of fluid in a control volume, use the formula: Weight = ρg * Volume.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
-
In fluids at rest, shear stress is zero, pressure's the hero, acting like a phantom, a force we can see, with weight and density.
📖 Fascinating Stories
-
Imagine a deep well filled with water. As you go down, you feel the pressure increase. This story illustrates hydrostatic pressure; the deeper you go, the more pressure you encounter due to the weight of the water above you.
🧠 Other Memory Gems
-
To remember the pressure types: A G V - Absolute, Gauge, and Vacuum pressure.
🎯 Super Acronyms
P V W - Pressure Varies With depth to recall how hydrostatic pressure functions.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
-
Term: Pressure
Definition:
The force exerted per unit area within a fluid.
-
Term: Body Force
Definition:
A force that acts over the volume of a fluid, such as gravitational force.
-
Term: Surface Force
Definition:
A force acting on the surface of a fluid, typically caused by pressure.
-
Term: Absolute Pressure
Definition:
The total pressure measured from vacuum conditions (zero pressure).
-
Term: Gauge Pressure
Definition:
Pressure measured relative to atmospheric pressure.
-
Term: Vacuum Pressure
Definition:
Pressure below atmospheric pressure.