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A short class with Sarah and her students. The other ways are under More.
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Welcome class! Today we'll explore the properties of fluids. Can anyone tell me the difference between fluids and solids?
Fluids can flow and deform, while solids maintain their shape.
Exactly! Fluids deform continuously under shear. Now, what are some key properties of fluids?
Kinematic properties include velocity and acceleration.
Good! Kinematic properties involve motion, while transport properties include viscosity. Remember: Kinematic Kicks and Transport Transports! Let’s move on to the substantial derivative.
We define the total derivative of a fluid property Q. Can someone explain what the substantial derivative is?
It combines local changes and convective changes in the fluid property.
Exactly right! It's often written as dQ/dt and includes both spatial and temporal changes. Remember the acronym MCD: Material, Convective, and Derivative.
What do you mean by convective changes?
Good question! It refers to changes due to the motion of the fluid carrying properties with it.
Now let’s focus on the motion of fluid elements. What types of motion can a fluid element undergo?
Translation, rotation, dilation, and shear strain.
Exactly! Each of these motions affects how we analyze fluid behavior. Let's visualize this using the fluid element ABCD on the board.
So the fluid can stretch or shear as it moves?
Exactly! And as it rotates, we need to derive the angle changes. Tan d alpha and d beta are crucial for this understanding.
Let’s move to the derivation of strain rates. What did we learn about how to derive them?
We observed the changes in angle and created relationships between movement and velocity.
Yes! We established the relationships using limits as time approaches zero, leading to the expressions for d alpha and d beta.
And how do we calculate rotation in the z-direction?
Great question! It's done through the arithmetic mean of angular velocities. Key equations unite to describe motion thoroughly.
It captures both the local time change and the spatial movement of a fluid property.
Mathematical expressions that quantify how fast a fluid element deforms.
Essential characteristics that describe the movement of fluids, such as velocity and acceleration.
Under shear, fluids change, strain rates define their range.
Imagine a water drop sliding down a hill, twisting and turning, changing shape as it flows. This visual helps recall fluid motion and strain.
MCD helps you remember: Material, Convective, and Derivative show how fluids change.
KTS for Kinematic, Transport, and Shear helps classify fluid properties easily.
Term
What is the substantial derivative?
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Term
Define strain rate.
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Kinematic properties of fluids include?
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A mathematical representation of the total change of a fluid property concerning both space and time.
The measure of the rate at which deformation occurs in a fluid element.
Properties related to the motion of fluids without considering forces.
Changes to a fluid property due to the movement of the fluid itself.
A vector quantity that represents the rate of rotation of a fluid element.
This section introduces the derivation of strain rates in viscous fluid flow, focusing on the substantial derivative and the types of motion a fluid element can undergo.
The section elaborates on kinematic and transport properties of fluids, defines the substantial derivative, and discusses the transformations of a fluid element during motion. Key equations related to strain rates and fluid rotation are derived based on the elemental analysis of the fluid flow.
In this section of the hydraulics course, we focus on the derivation of strain rates in viscous fluid flow, emphasizing the importance of understanding fluid behavior under shear. We begin with an overview of fluid properties, distinguishing between kinematic, transport, and thermodynamic characteristics. The core concept introduced is the substantial (or material) derivative, which describes how fluid properties change with time and position. We analyze a fluid element undergoing translation, rotation, extensional strain, and shear strain, illustrated by a fluid element in the xy-plane. Key equations such as the angular velocities and the relationships between the rates of strain are discussed, leading to vital conclusions about fluid motion and behavior. Ultimately, formulas for rotation in the z-direction are derived, setting the stage for the subsequent deeper dive into the Navier-Stokes equations.