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?

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?

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.9P: When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the...

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When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the weight of the sphere is balanced by the buoyant force and the frictional resistance of the fluid. Make a dimensional analysis of this problem and indicate how experimental data for this problem could be correlated. Neglect compressibility effects and the influence of surface roughness.
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