Another aftereffect of the Buckingham ПЂ assumption of dimensional assay is that the anatomic assurance amid a assertive amount (say, n) of variables can be bargain by the amount (say, k) of absolute ambit occurring in those variables to accord a set of p = n в€’ k independent, dimensionless quantities. For the purposes of the experimenter, altered systems that allotment the aforementioned description by dimensionless abundance are equivalent.
Example[edit]
The ability burning of a stirrer with a accustomed appearance is a action of the body and the bendability of the aqueous to be stirred, the admeasurement of the stirrer accustomed by its diameter, and the acceleration of the stirrer. Therefore, we accept n = 5 variables apery our example.
Those n = 5 variables are congenital up from k = 3 dimensions:
Length: L (m)
Time: T (s)
Mass: M (kg)
According to the ПЂ-theorem, the n = 5 variables can be bargain by the k = 3 ambit to anatomy p = n в€’ k = 5 в€’ 3 = 2 absolute dimensionless numbers, which are, in case of the stirrer:
Reynolds amount (a dimensionless amount anecdotic the aqueous breeze regime)
Power amount (describing the stirrer and aswell involves the body of the fluid)
Example[edit]
The ability burning of a stirrer with a accustomed appearance is a action of the body and the bendability of the aqueous to be stirred, the admeasurement of the stirrer accustomed by its diameter, and the acceleration of the stirrer. Therefore, we accept n = 5 variables apery our example.
Those n = 5 variables are congenital up from k = 3 dimensions:
Length: L (m)
Time: T (s)
Mass: M (kg)
According to the ПЂ-theorem, the n = 5 variables can be bargain by the k = 3 ambit to anatomy p = n в€’ k = 5 в€’ 3 = 2 absolute dimensionless numbers, which are, in case of the stirrer:
Reynolds amount (a dimensionless amount anecdotic the aqueous breeze regime)
Power amount (describing the stirrer and aswell involves the body of the fluid)
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