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[Problem Specification|FLUENT - Laminar Pipe Flow Problem Specification]\\
[1. Create Geometry in GAMBIT|FLUENT - Laminar Pipe Flow Step 1]\\
[2. Mesh Geometry in GAMBIT|FLUENT - Laminar Pipe Flow Step 2]\\
[3. Specify Boundary Types in GAMBIT|FLUENT - Laminar Pipe Flow Step 3]\\
[4. Set Up Problem in FLUENT|FLUENT - Laminar Pipe Flow Step 4]\\
[5. Solve\!|FLUENT - Laminar Pipe Flow Step 5]\\
[6. Analyze Results|FLUENT - Laminar Pipe Flow Step 6]\\
[7. Refine Mesh|FLUENT - Laminar Pipe Flow Step 7]\\  {color:#ff0000}{*}Problem 1{*}{color}\\
[Problem 2|FLUENT - Laminar Pipe Flow Problem 2]
{panel}

h2. Problem 1


h4. Problem

a) Consider the problem solved in this tutorial. At the exit of the pipe,          we can define the error in the calculation of the centerline velocity          as:

{latex}
\large
$$
{\varepsilon} = {\mid U_c - U_{exact} \mid}
$$
{latex}


where _U{~}{_}{_}c{~}_ is the centerline          value from FLUENT and _U{~}{_}{_}exact{~}_ is the exact          analytical value for fully-developed laminar pipe flow. We expect the          error to take the form:

{latex}
\large
$$
{\varepsilon} = {K \Delta r^p }
$$
{latex} 


where the coefficient _K_ and the power _p_ depend upon the          method . Consider the solutions obtained on the 100x5, 100x10, and 100x20          meshes. Using MATLAB, perform a linear least squares fit of:

!ps1eq3.jpg!

to obtain the coefficients _K_ and _p_. You can look up the          value of _U{_}{_}exact_ from any introductory textbook          in fluid mechanics such as _Fluid Mechanics_ by F. White. Explain          why your values make sense.

b) Repeat the above exercise using the "first-order upwind"          scheme for the momentum equation. Contrast the value of _p_ obtained          in this case with the previous one and explain your results briefly         (2-3 sentences).

h4. Hints

Note that the first or second order discretization applies only to the         convective terms in the Navier-Stokes equations. The viscous terms are         always second order accurate.

Go to [Problem 2|FLUENT - Laminar Pipe Flow Problem 2]\\

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