Navier Stokes Equation to create a Velocity Profile

In summary, the conversation discusses using the Navier-Stokes equations to derive a velocity distribution between two horizontal, infinite, parallel plates with an incompressible, viscous fluid. The plates are moving in opposite directions with constant velocities and the only body force is due to the fluid weight. The pressure gradient in the x-direction is zero and laminar flow is assumed. A helpful link is also provided for further understanding of the Navier-Stokes equation.
  • #1
Varidius
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Homework Statement


An incompressible, viscous fluid is placed between horizontal, infinite, parallel
plates. The two plates move in opposite directions with constant velocities U1 and U2. The pressure gradient in the x-direction is zero and the only body force is due to the fluid weight. Use the Navier‐Stokes equations to derive an expression for the velocity distribution between the plates. Assume laminar flow.


Homework Equations


Obviously the "standard" Navier-Stokes Equation

Can anyone help me, I've never been properly able to understand and utilise the Navier-Stokes Equation?
 
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  • #2
Maybe this link can be helpful for you:

http://www.engineering.uiowa.edu/~fluids/Posting/Schedule/Quiz/Quiz8.pdf
 
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Related to Navier Stokes Equation to create a Velocity Profile

1. What is the Navier-Stokes Equation?

The Navier-Stokes Equation is a set of mathematical equations that describe the motion of a fluid. It takes into account factors such as velocity, pressure, and viscosity to calculate the behavior of the fluid.

2. How is the Navier-Stokes Equation used to create a velocity profile?

The Navier-Stokes Equation can be used to create a velocity profile by solving for the velocity at different points within a fluid. This can be done using numerical or analytical methods, and the resulting velocity profile can then be used to understand the behavior of the fluid.

3. What is a velocity profile?

A velocity profile is a graphical representation of the velocity of a fluid at different points within the fluid. It shows how the velocity changes as a function of distance or time, and is often used to analyze the behavior of fluids in pipes or channels.

4. Why is creating a velocity profile important?

Creating a velocity profile is important because it allows us to understand the behavior of fluids in different scenarios. It can help us predict the flow of fluids in pipes, channels, or around objects, and is crucial in many engineering and scientific applications.

5. What factors affect the velocity profile of a fluid?

The velocity profile of a fluid can be affected by a number of factors, including the shape and size of the channel or pipe, the viscosity of the fluid, and the boundary conditions of the system. Other factors such as turbulence, pressure gradients, and external forces can also play a role in determining the velocity profile.

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