Task 1 : Dimensional analysis and modeling Consider example 7.9 in slide 49, which
we solved in class about the dimensional
analysis of Friction in a Pipe:
1. Employ the “BuckinghamPy” AI tool to replicate
the dimensional analysis we covered in class,
using the Buckingham Pi Theorem. Compare
your findings with our analytical solutions.
Access the tool at: BuckinghamPy Tool.
2. For this practical application, consider a pipe prototype with a
diameter of 1.2 m and a roughness of 0.0046 cm, transporting
crude oil at 25°C (viscosity of 0.01 Pa.s and density of 835 kg/m3)
at a velocity of 3 m/s. Our goal is to construct a scale model that
preserves the fluid dynamic similarities to this prototype using a
cast iron pipe with a roughness of 0.025 cm, circulating water at
25°C (viscosity of 0.89E-03 Pa.s and density of 1000 kg/m3).
Develop a VBA function integrated into an Excel spreadsheet to
calculate potential water velocities for various pipe diameters in
this model. Graph the relationship between these variables and
apply polynomial regression to derive a functional relationship.
Notes (1): Consider the pipe diameter range from 2.5 cm to 25
cm with 0.5 cm step.
(2) You can also change the surface roughness of the pipe model
by changing the pipe material.
TASK 2 : Differential analysis of fluid flowConsider example 9-2 in slide 17, which we solved in class
about the Design of a Compressible Converging Duct; you
are requested to perform the following tasks:
Create a VBA function within an Excel spreadsheet that predicts
the various steam functions and streamlines between x = 0 and x =
2.0 m.
Plot the approximate shape of the duct, ignoring friction on the
walls.
With the VBA Function, predict how high the duct should be at
section (2), the exit of the duct. WHAT TO SUBMIT :
A short technical report shows the VBA and Excel spreadsheet
The excel spreadsheet used for your calculation