Zhang deduced the similarity criteria of physical and mechanical parameters by dimensional analysis in the perspective of mechanics, resulting in the similarity criteria which cover geometrical, load and material properties, but the relationship between stress and gas pressure is unknown (Zhang et al. 2016).
To study the distribution law of the flow velocity along perforated pipes, influence factors such as the pipe laying slope, the length diameter ratio and the orifice rate were considered by dimensional analysis, and the influence of the flow velocity distribution index on the velocity distribution along the perforated pipe was analyzed by combining theoretical calculations with experiments.
Based on precise experimental observation and by utilizing dimensional analysis of the energy conservation equation, a new criterion is herein proposed for the condition in which the quasi-steady assumption is valid and for that in which it is not.
As a result, these laws provide satisfactory physical explanations for the measured lengths and shapes, beyond the fact that the derived formulae are constrained by the dimensional analysis of the parameters units.
It was developed from interviews with patients using a grounded theory approach, and the instrument was psychometrically tested using factor analysis [ 25], and further validated by a dimensional analysis of all items using structural equation modelling [ 26].
Ebtehaj et al. (2014) presented a regression-based equation to determine the densimetric Froude number (Fr) by dimensional analysis with a wide range of data as follows: Fr = frac{V}{{sqrt {g (s - 1 )d} }} = 4. 4 9;C_{V}^{ 0. 2 1} left( {frac{d}{R}} right)^{ - 0. 5 4}.
The wear rate (mm3/m) calculated for each load and sliding speed combination was used to state the dimensional equation in terms of wear rate parameter, interface parameter (X) and thermal parameter (Y) defined by dimensional analysis approach to quantify the influence of interactive tribological and materials parameters on the wear system under study.
A simple scaling law to quantitatively correlate the droplet size and process variables was developed by dimensional analysis and used to predict the diameter of particles produced under a given set of conditions.
They can be simplified by dimensional analysis.
The equivalence of measurement of energy per unit area to force per unit length can be proven by dimensional analysis.
