A force balance in a particular fluid flow is combined with Newton’s second law to yield the following equation: ρ d 2 z dt 2 + a dz dt + bz = c where ρ, z, and t are dimensional variables with the following dimensions: ρ [ML−3 ], z [L], and t [T]. (a) Determine the dimensions of the system parameters a, b, and c. (b) If standard SI units are to be used in the given equation and values of ρ, z, and t are provided in g/cm3 , mm, and h, what conversion factors must be applied to these variables before they are used in the equation?
A force balance in a particular fluid flow is combined with Newton’s second law to yield the following equation: ρ d 2 z dt 2 + a dz dt + bz = c where ρ, z, and t are dimensional variables with the following dimensions: ρ [ML−3 ], z [L], and t [T]. (a) Determine the dimensions of the system parameters a, b, and c. (b) If standard SI units are to be used in the given equation and values of ρ, z, and t are provided in g/cm3 , mm, and h, what conversion factors must be applied to these variables before they are used in the equation?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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A force balance in a particular fluid flow is combined with Newton’s second law to yield the following equation: ρ d 2 z dt 2 + a dz dt + bz = c where ρ, z, and t are dimensional variables with the following dimensions: ρ [ML−3 ], z [L], and t [T]. (a) Determine the dimensions of the system parameters a, b, and c. (b) If standard SI units are to be used in the given equation and values of ρ, z, and t are provided in g/cm3 , mm, and h, what conversion factors must be applied to these variables before they are used in the equation?
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