Fluid Mechanics 2: Navier-Stokes Solutions

Represents the direction of a vector, often expressed with components like: !−, #!=,

Components of a vector, such as !−, #!=,

Pressure fields are used to calculate pressure from known velocity components.

The process of using known velocity components to calculate the pressure field.

A mathematical representation that describes the variation of pressure across a specific region.

The relationship between pressure and velocity fields is crucial for understanding fluid dynamics.

Velocity fields provide information about the flow of a fluid and how it changes over time.

Pressure is a scalar quantity that measures the force acting perpendicular to a surface.

The change in pressure with respect to position. It's a vector quantity, indicating both magnitude and direction.

A mathematical equation describing the relationship between pressure and velocity in a fluid. It states that the pressure gradient is proportional to the negative of the acceleration of the fluid.

A method of calculating the pressure field in a fluid by integrating the Euler's equation.

The process of finding the unknown function of a variable that arises during partial integration.

A variable that arises during partial integration, representing an unknown function of the other variable(s).

The process of understanding and defining the physical setup of a problem, including its shape, dimensions, and relevant parameters. This helps visualize and understand the problem before solving it.

Simplifying assumptions and conditions based on the problem's context. These assumptions help in reducing complexity and are applied to the boundaries surrounding the problem.

Describing the governing equations that represent the physical laws at play within the problem. These equations are used to relate different variables and express the behavior of the system.

Process of combining the equation of motions with calculus to find a general solution. This involves applying integration techniques to derive a final equation describing behavior.

Utilizing the specific boundary conditions and assumptions to solve for unknown constants in the integrated equation. This leads to a unique solution that describes the problem's specific behavior.

A step-by-step process of calculating the pressure at any point in the system based on its location. This involves utilizing the pressure field equation and substituting coordinates to find the pressure.

A mathematical expression that defines the pressure at different points in the system. It is usually obtained after solving for the pressure field and integrating the equation of motion.

The Navier-Stokes equations are a set of partial differential equations that describe the motion of viscous, incompressible fluids. They are named after Claude-Louis Navier and George Gabriel Stokes.

The continuity equation expresses the conservation of mass for fluid flow. It states that the rate of change of mass within a control volume is equal to the net mass flow rate across the control volume's boundaries.

Couette flow is a type of fluid flow that occurs between two parallel plates when one or both are moving. The flow is characterized by having a constant shear rate and a linear velocity profile. It is an example of laminar flow where the fluid moves in layers.

No-slip boundary conditions state that the fluid velocity at a solid surface is equal to the velocity of the surface. This means that the fluid sticks to the surface and does not slip past it.

Steady flow is a type of fluid flow where the fluid velocity at a given point in space does not change over time. Incompressible flow is a type of fluid flow where the density of the fluid remains constant.

Laminar flow is a type of fluid flow where the fluid moves in smooth layers, with no mixing between layers. This is typically observed at low velocities and with fluids of high viscosity.