On Physically Similar Systems; Illustrations of the Use of Dimensional Equations¶
Buckingham, E. (1914). On Physically Similar Systems; Illustrations of the Use of Dimensional Equations. Physical Review, 4(4), 345-376.
Cited by¶
5 citations across 4 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Dimensional Analysis
- Dimensional Analysis is the constraint that (1) every physical quantity carries a dimensional signature expressed as a product of base dimensions (mass M, length L, time T, charge Q, temperature Θ, amount N, luminous intensity J), (2) any well-formed physical equation must be dimensionally homogeneous — every additive term, and both sides of any equality, must share identical dimensional signatures — (3) dimensionless ratios (Π-groups) formed by combining dimensional variables reveal the true number of independent parameters governing a phenomenon, often far fewer than the raw variable count suggests, and (4) the Buckingham π theorem
This sourceFirst complete formal statement of the Buckingham pi theorem; reduces an n-variable relation in k independent dimensions to (n-k) dimensionless groups; directly supports the pi-theorem formalization claim and the pendulum Buckingham-pi worked example.
- (1822), which established that physical laws must maintain dimensional consistency across all variables, and gained rigorous formalization through the work of Buckingham
This sourceIntroduces the 'pi' notation for dimensionless variables and the notion of physically similar systems; supports the claim that Buckingham (1914) gave the first complete statement of the pi theorem as a parameter-reduction method. (Same paper as buckingham-1914-core.)
- Dimensional Analysis is the constraint that (1) every physical quantity carries a dimensional signature expressed as a product of base dimensions (mass M, length L, time T, charge Q, temperature Θ, amount N, luminous intensity J), (2) any well-formed physical equation must be dimensionally homogeneous — every additive term, and both sides of any equality, must share identical dimensional signatures — (3) dimensionless ratios (Π-groups) formed by combining dimensional variables reveal the true number of independent parameters governing a phenomenon, often far fewer than the raw variable count suggests, and (4) the Buckingham π theorem
- Feature Engineering
Mechanisms¶
- Dimensional Consistency Check
- Prefer dimensionless groups. Where possible, recast the relationship into non-dimensional ratios so the exponent cannot smuggle in a units mismatch.
This sourceUses Buckingham's theorem to rewrite physical relations as dimensionless groups, exposing exponents that would otherwise encode inconsistent units.
- Prefer dimensionless groups. Where possible, recast the relationship into non-dimensional ratios so the exponent cannot smuggle in a units mismatch.
- Dimensional Scaling Test
Verification¶
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