Algebraic equations such as Bernoulli's relation, are dimensionally consistent, but what about differential equations? Consider, for example, the boundary-layer x-momentum equation, first derived by Ludwig Prandtl in 1904: ди ди ap ат ри — + pu Әх + pg: + дх ày ду where T is the boundary-layer shear stress and g, is the com- ponent of gravity in the x direction. Is this equation dimen- sionally consistent? Can you draw a general conclusion?

Question
Algebraic equations such as Bernoulli's relation,
are dimensionally consistent, but what
about differential equations? Consider, for example, the
boundary-layer x-momentum equation, first derived by
Ludwig Prandtl in 1904:
ди
ди
ap
ат
ри — + pu
Әх
+ pg: +
дх
ày
ду
where T is the boundary-layer shear stress and g, is the com-
ponent of gravity in the x direction. Is this equation dimen-
sionally consistent? Can you draw a general conclusion?
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Transcribed Image Text

Algebraic equations such as Bernoulli's relation, are dimensionally consistent, but what about differential equations? Consider, for example, the boundary-layer x-momentum equation, first derived by Ludwig Prandtl in 1904: ди ди ap ат ри — + pu Әх + pg: + дх ày ду where T is the boundary-layer shear stress and g, is the com- ponent of gravity in the x direction. Is this equation dimen- sionally consistent? Can you draw a general conclusion?

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