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A short class with Sarah and her students. The other ways are under More.
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Today, we’re diving into how pressure is defined and measured in fluids. Can anyone tell me what happens to shear stress when a fluid is at rest?
I think shear stress becomes zero.
Exactly! When a fluid is stationary, the only force acting on the control surface is the normal stress, which is equivalent to pressure. Now, can anyone provide an example of where we encounter pressure like this in daily life?
Like when we dive underwater, the deeper we go, the more pressure we feel?
Great example! The pressure increases with depth due to the weight of the fluid above. Remember this concept: 'Pressure increases with depth.' Let us move on and explore how we can measure this pressure.
Now, let's talk about how pressure is measured. We have gauge pressure and vacuum pressure. Can anyone explain what these terms mean?
Gauge pressure is the pressure relative to atmospheric pressure.
Correct! Gauge pressure is measured above atmospheric pressure. And what about vacuum pressure?
Isn't it measured below atmospheric pressure?
Exactly! Vacuum pressure helps us understand the pressure levels when they drop below atmospheric levels. It's crucial to know your reference point in pressure measurement. Can anyone recall how we can visualize atmospheric pressure?
We can use a mercury barometer, right?
Yes! A mercury barometer uses the height of mercury to indicate atmospheric pressure based on hydrostatic equilibrium. Alright, let’s summarize what we learned.
Can someone tell me how pressure changes as we move deeper in a fluid?
It increases linearly with depth.
Right! This is because the pressure at a certain depth is the weight of the liquid above it. Can anyone summarize why we say pressure does not vary in the x and y directions for a resting fluid?
Because, in hydrostatic equilibrium, the only change happens in the vertical direction.
Exactly! Since there are no horizontal forces acting, pressure remains constant on any horizontal plane. This concept is fundamental when we're solving fluid dynamics problems.
Now, let’s touch on the impact of surface tension on fluid behavior like in capillary action! Can someone explain what happens when water is in a thin tube?
The water rises in the tube due to surface tension.
Yes! The height to which the water rises (capillary height) depends on gravity and the surface tension of the liquid. Do you recall what kind of tube makes water rise higher?
A narrower tube rises water higher than a wider tube.
Correct! The smaller the diameter, the higher the rise is due to stronger surface tension relative to gravitational force. Remember this relationship: 'Smaller tube, higher rise'.
To wrap up, let’s integrate what we’ve learned about pressure and its measurement. Why is it important to differentiate between absolute, gauge, and vacuum pressure?
It impacts how we apply the pressure measurements in real-world applications.
Absolutely! Knowing the right type of pressure helps in everything from engineering designs to environmental monitoring. Can anyone summarize the pressure gradient concept?
The pressure gradient describes how pressure changes in space, typically pointing out that it's higher at lower depths.
Exactly! And it can be represented mathematically. Well done, everyone! Let’s remember these concepts as we move further into fluid mechanics.
Pressure is higher at greater depths due to the weight of the fluid above.
Gauge pressure is referenced to atmospheric pressure while vacuum pressure is measured below it.
Pressure changes are indicated through gradients in the fluid, generally increasing with depth.
Pressure is nice, it builds with the height, dive in the lake, and it feels just right.
Imagine a tall drink, where ice melts fast, pressure rises as you sip, oh how long will it last?
To remember types of pressure: 'GAV' - Gauge Above Vacuum.
CAP - Capillary Attracts Pressure.
Term
What is gauge pressure?
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Term
What is hydrostatic pressure?
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The force applied perpendicular to the surface of an object per unit area.
The pressure measured relative to the atmospheric pressure.
The pressure that is measured below the atmospheric pressure.
The pressure exerted by a fluid at equilibrium due to the force of gravity.
The ability of a liquid to flow in narrow spaces without external forces, driven by surface tension.
This section explores the definitions and measurement methods related to fluid pressure, including the concepts of hydrostatic pressure and gauge pressure.
The section discusses hydrostatic pressure in fluids at rest, detailing the forces acting on a control volume, the role of gravity, and how pressure is measured in terms of gauge and vacuum pressure. It highlights the significance of understanding pressure gradients and distributions in fluid mechanics.
In fluid mechanics, the measurement of pressure is essential for understanding fluid behavior. This section elaborates on how to derive the pressure field when the fluid is at rest. It begins by describing the concept of a control volume and outlining that when a fluid is stationary, shear stress is zero, and only normal stress (pressure) acts on the control surfaces. Gravity and body forces are discussed as they contribute to pressure measurements. The section clarifies the distinction between gauge pressure and vacuum pressure, where gauge pressure is measured relative to ambient atmospheric pressure while vacuum pressure refers to a measurement below atmospheric pressure. Furthermore, it emphasizes that pressure varies linearly with depth in a gravitational field and can be expressed mathematically through a gradient vector. This includes acknowledging various measurement techniques such as the use of barometers and the implications of capillary action, which highlights the complexities of pressure measurement in real-world scenarios.