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N kg m kg 1 2
Р [Pa]= М L T ;
m 2 m 2 s 2 m s 2
2
2
-2
dimension of work A=[N∙m]= kg∙m∙m /s = М∙L ∙T ;
dimension of dynamic viscosity coefficient
kg 1 1
μ [Pa∙s] М L T .
m s
To make the study of mechanical phenomenon it is enough
to use only three independent basic units of length, time and
mass. Dimension of any physical quantity can be represented as
the product raised to a degree of dimensions of basic physical
quantities.
For mechanical phenomena following formula is fair:
X L T M (2.1)
or
X L T M J (2.2)
,
where α, β, γ, δ, φ, ω, ε – some exponents.
When it is not possible to create a mathematical
problem (make a system of differential equations), then
criteria can be based on analysis of dimensions of physical
quantities with the appropriate dimension, which is expressed
through the basic units.
Method of analysis of dimensions is based on the
following. In case of practical implementation of method of
analysis of dimensions following two assumptions are
considered:
1) it is know in advance, on which process parameters
and variables depends physical quantity, which is being
studied;
2) connection between all important physical quantities
of studied process is expressed as degree polynomial.
In the simplest case, dimensions of physical quantities are
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