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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 going to explore how fluid behaves between two parallel plates, one stationary and one moving. Can anyone describe what happens to the fluid's velocity as we move away from the stationary plate?
The fluid closest to the stationary plate will have zero velocity because of the no-slip condition!
Exactly! As we move up to the top plate, the velocity increases linearly up to V. This linear distribution is a fundamental concept we'll build upon when we discuss shear stress.
So, if we have points A and B, with A at the moving plate and B at the stationary plate, the velocity gradient is important?
Very important! The velocity gradient reflects how shear stress changes with the distance in the fluid. Remember, shear stress is like the force causing layers of fluid to slide over one another.
Can you explain the relationship between shear stress and shear strain once more?
Sure! In a linear flow, shear stress is directly proportional to the rate of strain or velocity gradient, which leads us to the concept of viscosity. Let's keep this proportion in mind.
Isn't this similar to how solid mechanics works, where stress is proportional to strain?
Precisely! However, in fluid mechanics, we deal with shear strain rate, not absolute shear strain. This distinction is key to understanding fluid behavior.
To summarize, we learned about how fluid velocity changes in parallel flow and how shear stresses relate to these changes. Both concepts are foundational for understanding the behavior of fluids.
Now, let's discuss viscosity. Can anyone explain how temperature affects viscosity in fluids?
I remember that increasing the temperature of liquids usually reduces their viscosity.
Correct! This is due to increased molecular motion, which weakens intermolecular forces. What about gases?
For gases, increasing temperature tends to increase viscosity.
Right again! As gas temperatures increase, molecular motion intensifies, leading to more effective collisions and a rise in viscosity. This difference between the behavior of liquids and gases is important!
How do we quantify the relationship between viscosity and temperature?
Great question! We use the Sutherland correlation. Does anyone remember the formula?
It's μ = aT^(3/2) / (T + b), right?
Close! The correct version accounts for the constants a, b, and c, which can vary by substance. Understanding this correlation is essential for fluid dynamics applications.
To recap, we looked at viscosity's dependence on temperature and introduced the Sutherland correlation. Keep these relationships in mind for your future studies!
Next, let's differentiate between Newtonian and non-Newtonian fluids. Who can describe a Newtonian fluid for me?
A Newtonian fluid exhibits a constant viscosity regardless of the shear stress applied!
Exactly! This means the shear stress is linearly proportional to the shear strain rate. And what about non-Newtonian fluids?
Non-Newtonian fluids have a variable viscosity that changes based on the shear rate!
Fantastic! They can become thicker or thinner depending on the stress and strain they experience. Can anyone give an example of a non-Newtonian fluid?
Toothpaste! It starts solid and flows when you squeeze it.
Correct! Toothpaste is a Bingham plastic, which requires a yield stress to begin flowing. Let's also not forget about shear-thinning fluids, like ketchup!
So, the behavior of the fluid really impacts how we use them in everyday applications?
Absolutely! Understanding these differences helps engineers design better systems for various industrial applications. Let's summarize: Newtonian fluids have a constant viscosity, while non-Newtonian fluids can behave unpredictably under stress.
The behavior of fluids moving between surfaces.
The rate of change in velocity across a fluid element.
Force per unit area acting parallel to the flow section.
The internal friction of fluids, influencing their flow behavior.
A relationship defining viscosity changes with temperature.
When temperatures rise and flow gets smooth, viscosity's low, it's the right groove.
Imagine trying to pour a thick syrup; it's hard at first, but as it warms, it flows freely.
Remember 'N' for Newtonian: No change in viscosity, consistent strain rate.
VIS = Viscosity Influences Shear; it reminds you of how viscosity relates to shear stress.
Term
What is viscosity?
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Define shear strain rate.
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What is the Sutherland correlation?
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What defines a Newtonian fluid?
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Give an example of a non-Newtonian fluid.
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A measure of a fluid's resistance to flow or deformation.
The stress component parallel to a given surface, often caused by forces acting on a fluid.
The rate at which adjacent layers of fluid move with respect to each other.
A mathematical relationship used to find the viscosity of gases as a function of temperature.
A fluid with a constant viscosity that remains unchanged regardless of the shear rate.
A fluid whose viscosity changes with the shear rate applied to it.
The section discusses the Sutherland correlation and its significance in understanding the relationship between dynamic viscosity and temperature in fluid mechanics.
This section elaborates on fluid flow between parallel plates, explaining how velocity gradients relate to shear stress and introducing the Sutherland correlation for estimating dynamic viscosity as a function of temperature. It highlights the differences between fluids and their respective behaviors under changing temperature and pressure conditions.
This section delves into fluid mechanics, specifically the behavior of fluids flowing between parallel plates. When observing such a flow, one plate remains stationary while the other moves with a velocity V. The resultant velocity profile across the fluid element from one plate to the other exhibits linear variation, allowing us to derive relationships critical in fluid dynamics.
The section explains how, under these parallel flow conditions, the shear stress is proportional to shear strain rate, irrespective of external factors. This conclusion is important because it sets foundational principles for understanding fluids as either Newtonian or non-Newtonian.
A thorough examination of viscosity is conducted, emphasizing its dependence on temperature. The Sutherland correlation—which offers a quantitative relationship between dynamic viscosity (μ) and temperature (T)—is discussed in depth. The correlation is defined as:
μ = aT^3 / (1 + bT)
where T denotes absolute temperature and a, b, and c are empirically determined constants. The behavior of liquids and gases under temperature and pressure changes highlights varying trends in viscosity, establishing a contrasting relationship for gases and liquids. This relationship speaks to how viscosity impacts the flow behavior of different fluids, setting the stage for practical applications and fluid dynamics models.