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.
Introduction to Fluid Pressure
Unlock Audio Lesson
Today we’re going to explore how we calculate pressure in fluids at rest. Can anyone tell me what happens to shear stress in a stationary fluid?
Shear stress is zero in a stagnant liquid.
Correct! Since only normal stress acts on surfaces, we can consider pressure as the main force at work here. Another term for pressure is the normal force per unit area. Let’s remember this as the 'Pressure Principle: P = F/A'.
So does that mean pressure can change with depth?
Exactly! Pressure does change with depth due to the weight of the fluid above. We will explore how that works mathematically.
Equating Pressure and Fluid Weight
Unlock Audio Lesson
Let’s consider a control volume. If we have a column of fluid, we can express the pressure at a point due to the weight of the fluid above. Can anyone remind me how we express pressure related to this weight?
It’s like the weight of fluid divided by the area!
That’s right! Pressure is the weight of the liquid column divided by the area it acts upon. This leads us to know that pressure increases with depth as more fluid weight contributes to the pressure at lower levels.
So, pressure generally increases linearly with depth?
Yes! In hydrostatics, we say pressure is a linear function of depth, allowing us to derive many important formulas. Remember, the greater the height of the fluid column, the greater the pressure!
Gauge Pressure vs. Absolute Pressure
Unlock Audio Lesson
Now that we understand how pressure is calculated, let’s talk about gauge pressure and absolute pressure. What do these terms mean?
Isn’t gauge pressure the pressure above atmosphere?
Exactly! Gauge pressure measures the pressure relative to atmospheric levels. And when we talk about absolute pressure, we’re measuring from a perfect vacuum. This distinction is vital in applications like barometers.
So, how do we convert gauge pressure to absolute pressure?
Great question! You would add the atmospheric pressure to the gauge pressure. It’s all about knowing your reference point for pressure measurements.
Applying the Control Volume Approach
Unlock Audio Lesson
Finally, let’s discuss the control volume approach. Why is it crucial when analyzing fluid pressure?
It helps us understand how forces balance within a fluid.
Exactly! By defining a control volume, we can analyze all forces acting on it, including surface forces due to pressure and body forces due to gravity. Can anyone give me an example of where this might be applicable?
Like in dams or in measuring instruments?
Right again! This concept plays a crucial role not just in theory but in real-world engineering applications.
Pressure Distribution and Examples
Unlock Audio Lesson
To wrap up, can anyone summarize how we calculate pressure at a certain depth in water?
Pressure equals the unit weight of the fluid times the height of the fluid column!
That's perfect! Now, consider this example: If we have a 10-meter column of water, what’s the pressure at the base?
We would multiply the unit weight of water by 10 meters!
Correct! Understanding these calculations is vital for fluid mechanics applications.
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
The section discusses the relationships between pressure, gravity, and fluid columns at rest, emphasizing that pressure varies with depth in a fluid. It introduces gauge and absolute pressure concepts and details how to derive pressure equations based on fluid weight and control volumes.
Detailed
Detailed Summary
This section explores the pressure distribution within a fluid at rest, defining pressure as a function of the coordinates (x, y, z). It emphasizes that when a fluid is stationary, it does not experience shear stress, leading to pressure being the sole force acting on critical surfaces. For simplicity, the discussion revolves around a parallelepiped control volume to illustrate how pressure can be evaluated using the concept of virtual fluid balls. As gravity acts as a body force, students learn to equate surface pressure forces with the body forces established by fluid weight.
Furthermore, the section outlines the gradient of pressure components in relation to the control volume and demonstrates the application of the Taylor series for pressure approximation. It emphasizes both gauge pressure, which measures relative to atmospheric pressure, and absolute pressure, which considers a complete vacuum. In doing so, it establishes a framework for calculating the various forces acting upon the fluid and how pressure distributions are essential to understanding hydrostatic conditions in fluids.
Youtube Videos
Audio Book
Dive deep into the subject with an immersive audiobook experience.
Understanding Pressure in Fluids at Rest
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 the rest. That means I am just looking at the what could be the functions of the P, P = P (x, y, z). ... Only this normal stress which is as equivalent to the pressure will act over this control surface.
Detailed Explanation
When a fluid is at rest, we analyze the pressure within the fluid. The pressure at any point can be described as a function of its coordinates (x, y, z). In a simplified case, we can visualize a cube-shaped control volume containing the fluid. In this scenario, because the fluid is at rest, there is no shear stress acting on the surfaces of the volume. Instead, the pressure acts normally, which means it is at right angles to the surface of the control volume. This makes it easy to understand how pressure behaves in fluids when they are static.
Examples & Analogies
Think of a balloon filled with water that is completely still. The pressure you feel when you push on the surface is caused only by the water underneath pressing outward. There is no movement (shear stress) in the water itself because it is at rest.
Gravity Forces in a Control Volume
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, which is the body force component. The gravity force what will be there? It will be, unit weight multiply the volume of the control volume.
Detailed Explanation
In our control volume, we identify the gravitational force acting on the fluid, which is categorized as a body force. This force is calculated by multiplying the unit weight of the fluid by the volume of the control volume. With this, we now have two forces acting on our fluid: the surface forces (due to pressure) and the body force (due to gravity). The unit weight is essentially the weight of a unit volume of fluid, and this helps in determining how the force of gravity affects the pressure distribution in the fluid volume.
Examples & Analogies
Consider a tall glass filled with water. The weight of the water above any point in the glass contributes to the pressure at that depth. For instance, if you look at a point halfway down, the weight of all the water above that point pressing down contributes to the pressure experienced at that point.
Pressure Distribution and Gradient
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. ... The gradient and the volume of the control panel.
Detailed Explanation
According to Pascal’s Law, the pressure in a fluid at rest is transmitted uniformly in all directions. The gradient of pressure within our control volume can be expressed in terms of the volume and the pressure acting on the surfaces of that volume. By simplifying the equations using Taylor series for approximation, we can conclude that pressure varies with respect to the height (z-direction) in a linear manner, while remaining constant in the horizontal (x and y) directions.
Examples & Analogies
Imagine the pressure felt at the bottom of a tall swimming pool. The deeper you go, the more water there is above you, pressing down. The pressure increases as you descend but remains constant horizontally at any given depth because there is no water rushing around in horizontal currents.
Gauge Pressure vs. Absolute Pressure
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. Components now is coming it what is your datum to measure the pressure.
Detailed Explanation
In fluid mechanics, it is essential to understand the difference between gauge pressure and absolute pressure. Gauge pressure is measured relative to atmospheric pressure, which means if it's above atmospheric pressure, it is positive, and if it’s below, it is regarded as vacuum pressure. The reference level (datum) for this measurement could be either absolute zero (vacuum) or a local atmospheric condition, which is commonly used in everyday applications.
Examples & Analogies
Consider a car tire. A pressure gauge on the tire measures the pressure inside relative to the atmospheric pressure outside. If the gauge shows 30 psi, that means the pressure inside is 30 psi higher than atmospheric pressure; if there's a leak, that value could drop below atmospheric pressure, indicating that the tire is 'sucking' in air.
Hydrostatic Pressure Distribution
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
Now as we derive pressure distribution equations which in vector forms and let we simplify that equations which earlier we consider the acceleration due to gravity is a vector which will have...
Detailed Explanation
To find out the hydrostatic pressure at varying depths, we take the gradient of pressure with respect to height along the z-axis. If we align our coordinate system so that gravity acts in the negative z direction, we find that at any given depth z, the pressure can be expressed linearly as a function of depth. This means as you move deeper into a fluid (like water in a lake), the pressure increases with depth in a predictable way based on the weight of the fluid column above that level.
Examples & Analogies
A scuba diver feels a noticeable increase in pressure as they descend deeper in the ocean. This pressure increase is a direct result of the weight of the water above them, and they can use the same concept of hydrostatic pressure we've discussed.
Applications of Pressure Concept in Everyday Life
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
Similar way, we can derive the pressure component, the force component due to the pressures in x directions and the z directions respectively.
Detailed Explanation
Understanding pressure calculations is crucial in various fields such as engineering, medicine, and environmental science. For example, knowing how pressure varies in a fluid helps in designing water systems such as dams, water supply lines, and even in the field of medicine, such as in developing devices that measure blood pressure. The general principles of hydrostatics are applied in these cases to ensure safety and effectiveness.
Examples & Analogies
Think about a water supply system in a city. Engineers must calculate the pressure at different points in the system to ensure that water flows properly and reaches every home. If the pressure is too low, some homes won’t receive water; if it’s too high, it may cause pipes to burst. Understanding fluid pressure is critical for designing a safe and functional water delivery system.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
-
Pressure Calculation: Pressure varies with depth and is calculated using the weight of fluid above.
-
Hydrostatic Equations: These equations govern how pressure is distributed in a fluid at rest.
-
Control Volume Analysis: A systematic method to analyze forces and pressure in fluid mechanics.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
-
If a 5 m tall column of water where the unit weight is 9.81 kN/m³, the pressure at the base is calculated as P = γ × h = 9.81 × 5 = 49.05 kPa.
-
In a mercury barometer, the height of mercury in the tube gives an absolute atmospheric pressure reading based on the column weight.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
-
In the depths where waters flow, pressure builds from weight, you know!
📖 Fascinating Stories
-
Imagine a tall column of water standing still; its pressure at the bottom grows strong according to its height.
🧠 Other Memory Gems
-
To remember pressure increases with depth, think 'WPD' - Weight, Pressure, Depth.
🎯 Super Acronyms
P = Fur*A for Pressure, Force under the Area.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
-
Term: Pressure
Definition:
The force exerted per unit area, defined as normal stress acting on a surface.
-
Term: Gauge Pressure
Definition:
The pressure measurement relative to atmospheric pressure.
-
Term: Absolute Pressure
Definition:
The total pressure measured from a perfect vacuum.
-
Term: Control Volume
Definition:
A defined volume in fluid mechanics for analyzing flow and pressure distribution.
-
Term: Hydrostatic Pressure
Definition:
The pressure exerted by a fluid at equilibrium due to the force of gravity.
-
Term: Body Force
Definition:
A force acting on a body due to gravitational or other fields.