BuckinghamPy

Taking the leg work out of dimensional analysis.

What to do

Import the module as buckinghampy.

import buckinghampy as bp

Create some parameters. For instance, I can create a parameter with

diameter = bp.Param('D', dim=[0,1])

Here D is the parameter's symbol and dim is the dimension of the parameter. The dimension array is represented by a vector where each index location corresponds to a base dimension.

 dimensional vector: [ M L t T N I J ]
 1 Mass (ex. kilogram, k)
 2 Length (ex. meter, m)
 3 Time (ex. second, s)
 4 Temperature (ex. Kelvin, K)
 5 Quantity (ex. moles, mol)
 6 Current (ex. ampere, A)
 7 Luminous intensity (ex. candela, cd)

For convenience, common parameter archetypes are available using ptype. For example, I could have defined the diameter as

diameter = bp.Param('D', ptype='length')

After a number of parameters have been created, join them in a list.

paramList = [diameter, density, viscosity, velocity]

Then run the dimensional analysis to get the resulting list of Pi-Groups and then print the list.

pgl = bp.run(paramList)
bp.pprint(pgl)

Example: Pipe flow pressure drop

A common early example for dimensional analysis: find the important non-dimensional parameters for pressure drop due to flow in a pipe.

# Important parameters
DeltaP = bp.Param('DeltaP', dim=[1,-2,-2])
diameter = bp.Param('D', ptype='length')
relruf = bp.Param('eps', ptype='length')
density = bp.Param('rho', ptype='density')
viscosity = bp.Param('mu', ptype='viscosity')
velocity = bp.Param('V', ptype='velocity')

# Create list of parameters
paramList = [DeltaP, diameter, relruf, density, viscosity, velocity]
repeatingList = [diameter, density, velocity]

Here I am specifying the repeating variables to use, but I could not specify and let the module figure it out. Additionally, I could pass the optional argument depParam=DeltaP to bp.run to tell the module that DeltaP is the dependent parameter and should not be included in the repeating variable list.

# Run nondimensionalization process
pgl = bp.run(paramList, repeatingList)
bp.pprint(pgl)

The output of bp.pprint is

Pi-Group 1:  (D) (DeltaP) (rho)^-1 (V)^-2 
Pi-Group 2:  (D) (eps)^-1 
Pi-Group 3:  (D) (V) (rho) (mu)^-1 

For some more examples, see demo.py.