**A)** Using glycerin in a pipe of radius R=0.05 m and length L=20 m, run a case with Re= *_____.
This is your baseline Reynolds number. Run this for coarse, medium and fine resolution . For every case, save velocity profiles at the exit and velocity and pressure along the axis. Also, make note of the total pressure drop in the pipe for each case ran. Plot velocity profiles at the exit of the pipe and both velocity and pressure along the centerline. Discuss.

**B)** Run two additional cases for water and air with R=0.05 m and L=20 m. Set the velocity so that the Re is still equal to your baseline value for each fluid. Plot the exit velocity profile for each fluid (including the case from part A) and compare to the theoretical solution for laminar flow. Plot centerline velocity and pressure for each case. Discuss.

**C)** Using water with the same diameter and velocity as in part B, run cases with pipe lengths of L=1, 5 and 10 m. Plot exit velocity profiles (including the case from part B) and discuss.

**D)**Using glycerin with R=0.05 m and L=20 m, vary the velocity to run cases with Re=100, 200, 500 and 2000. Determine the entrance length for each case (including your baseline case) and plot as a function of Re. Discuss.

**Analysis:**

**1)** Create a table that shows the parameters for each case that you run (including at least density,
viscosity, pipe diameter, length, velocity, Reynolds number and total pressure drop). Using non- dimensional group theory, normalize the total pressure drop to determine a non-dimensional ****p that can be compared among the different cases.

**2)**Compute the non-dimensional pressure drop that you expect for each case from laminar pipe flow theory, including the effects of entrance losses. Add this information as a new column to the table from part 1. Discuss.

**3)**Numerically integrate the mass flux at the exit of your baseline case with fine mesh and show that the mass flow is approximately equal to that at the inlet of the pipe. Discuss any errors in this calculation.

**4)**Write a discussion of your results and analysis. Attach supporting plots and tables.

NOTES: You will need to normalize the velocity, radial and/or axial positions when making your plots so that the different cases can be logically compared in the same plots. When comparing results in parts A-D, you should combine profiles from different cases into a single plot so they can be directly compared.

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