py-dimensional-analysis

This Python package addresses physical dimensional analysis. In particular, py-dimensional-analysis calculates from a given system of (dimensional) variables those products that yield a desired target dimension.

The following example illustrates how the variables mass, force, time and pressure must relate to each other in order to produce the dimension length*time.

import danalysis as da

si = da.standard_systems.SI         # predefined standard units
s = da.Solver(
    {
        'a' : si.M,                 # [a] is mass
        'b' : si.L*si.M*si.T**-2,   # [b] is force (alt. si.F)
        'c' : si.T,                 # [c] is time
        'd' : si.Pressure           # [d] is pressure
    },
    si.L*si.T                       # target dimension
)
print(s.solve())

Which prints

Found 2 variable products of variables
{
        a:Q(M),
        b:Q(L*M*T**-2),
        c:Q(T),
        d:Q(L**-1*M*T**-2)
}, each of dimension L*T:
        1: [a*c**-1*d**-1] = L*T
        2: [b**0.5*c*d**-0.5] = L*T

This library is based on (Szirtes 2007), and also incorporates ideas and examples from (Santiago 2019; Sonin 2001).

Solver

The solver is based on the Buckingham’s π theorem. For more information, see (Szirtes 2007).

References

Santiago, Juan G. 2019. A First Course in Dimensional Analysis: Simplifying Complex Phenomena Using Physical Insight. MIT Press.

Sonin, Ain A. 2001. “Dimensional Analysis.” Technical report, Massachusetts Institute of Technology. http://web.mit.edu/2.25/www/pdf/DA_unified.pdf.

Szirtes, Thomas. 2007. Applied Dimensional Analysis and Modeling. Butterworth-Heinemann.