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A short class with Sarah and her students. The other ways are under More.
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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.
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.
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.
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.
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.
Pressure increases linearly with depth due to the weight of fluid above.
A defined volume in which pressure and force interactions are analyzed.
Absolute pressure, gauge pressure, and vacuum pressure each serve different contexts in fluid measurement.
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.
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.
To remember the pressure types: A G V - Absolute, Gauge, and Vacuum pressure.
P V W - Pressure Varies With depth to recall how hydrostatic pressure functions.
Term
What happens to shear stress in a fluid at rest?
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What is the equation for hydrostatic pressure?
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What type of pressure is measured relative to atmospheric pressure?
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What defines absolute pressure?
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The force exerted per unit area within a fluid.
A force that acts over the volume of a fluid, such as gravitational force.
A force acting on the surface of a fluid, typically caused by pressure.
The total pressure measured from vacuum conditions (zero pressure).
Pressure measured relative to atmospheric pressure.
Pressure below atmospheric pressure.
This section discusses the components of forces acting on a fluid at rest, focusing on pressure distribution defined by the gradient of pressure in three-dimensional coordinates.
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.
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.