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Algebraic equations such as Bernoulli's relation, Eq. (1) of Ex. 1.3, are dimensionally consistent, but what about differential equations? Consider, for example, the bound- ary-layer x-momentum equation, first derived by Ludwig Prandtl in 1904: du - _ap + pv- ду du pu- P8x ax ду where 7 is the boundary-layer shear stress and g, is the component of gravity in the x direction. Is this equation dimensionally consistent? Can you draw a general con- dusion?

Algebraic equations such as Bernoulli's relation, Eq. (1) of Ex. 1.3, are dimensionally consistent, but what about differential equations? Consider, for example, the bound- ary-layer x-momentum equation, first derived by Ludwig Prandtl in 1904: du - _ap + pv- ду du pu- P8x ax ду where 7 is the boundary-layer shear stress and g, is the component of gravity in the x direction. Is this equation dimensionally consistent? Can you draw a general con- dusion?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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S Algebraic equations such as Bernoulli's relation, Eq. (1) of Ex. 1.3, are dimensionally consistent, but what about differential equations? Consider, for example, the bound- ary-layer x-momentum equation, first derived by Ludwig Prandtl in 1904: ди pu- du pv- ду + pgx + ax ду where 7 is the boundary-layer shear stress and g, is the component of gravity in the x direction. Is this equation dimensionally consistent? Can you draw a general con- cusion?
Transcribed Image Text:S Algebraic equations such as Bernoulli's relation, Eq. (1) of Ex. 1.3, are dimensionally consistent, but what about differential equations? Consider, for example, the bound- ary-layer x-momentum equation, first derived by Ludwig Prandtl in 1904: ди pu- du pv- ду + pgx + ax ду where 7 is the boundary-layer shear stress and g, is the component of gravity in the x direction. Is this equation dimensionally consistent? Can you draw a general con- cusion?
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