Python code that implements the Buckingham-Pi theorem and return all sets of dimensionless groups
Clone the package from the github repository into the current directory
git clone https://github.com/saadgroup/BuckinghamPy.git .
Use pip tool to install the package in the active python evironment
pip install .
Consider a fluid with density R and viscosity V, pumped in a centrifugal pump with power input P, a volume flow rate Q, an impeller diameter E, and a rotational rate G.
The homogeneous function that relates all these variables is: f(R, V, P, Q, E, G) = 0
Using the fundamental units (M, L, T), find all the sets of dimensionless terms with the power input P being part of only one dimensionless term per set.
Using BuckinghamPy, we execute the following code:
from buckinghampy import BuckinghamPi
Example = BuckinghamPi()
Example.add_variable(name='R', units='M/L^(3)')
Example.add_variable(name='P', units='M*L^(2)/(T^3)', non_repeating=True)
Example.add_variable(name='V', units='M/(T*L)')
Example.add_variable(name='Q', units='L^(3)/T')
Example.add_variable(name='E', units='L')
Example.add_variable(name='G', units='1/T')
Example.generate_pi_terms()
Example.print_all()
or you can import the graphic user interface only in a Jupyter cell
from buckinghampy import BuckinghamPiGui
GUI=BuckinghamPiGui()