Dimensional Analysis Theory

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Dimensional analysis is routinely used to check the plausibility of derived equations and computations. It is also used to form reasonable hypotheses about complex physical situations that can be tested by experiment or by more developed theories of the phenomena, and to categorize types of physical quantities and units based on their relations to or dependence on other units, or their dimensions if any. In physics and all science, dimensional analysis is the practice of checking relations among physical quantities by identifying their dimensions. The dimension of any physical quantity is the combination of the basic physical dimensions that compose it. Some fundamental physical dimensions are length, mass, time, and electric charge. All other physical quantities can be expressed in terms of these fundamental physical dimensions. Detailed discussion of the dimensional analysis is depicted in the chapter on dimensional analysis.
For the present investigation the various process variables for structural subassembly manufacturing and the corresponding dimensional indices as well as unit of measurement are worked out. Dimensional analysis is carried out to formulate dimensional equations, ensuing relationship between dependent Pie terms and independent Pie terms.
4.11 Formulation of Pie terms for independent variables:
Various independent variables are grouped based on logical thinking by considering the similarities between variables. The groups are then used for formulation of Pie terms. One such identified group of variable belongs to the anthropometric data of operator. It is with alleviate to create the group of parameters such as body dimensions of the operator. So the first Pie term is related to anthropometric data of the o...

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...Length ( mm)
L

In terms of MLT Indices

Π6 = (M0L1T0 x M0L1T0 )
( M0L1T0 x M0L1T0)

Breadth ( mm)
B

Thickness (mm)
T

Part Weight (gm)
Wt

Machinable length
Mc.len

Machine criticality
Mc_criticality

4.12 Formulation of Pie terms for dependent variables:
The factors are arranged in numerator and denominator so as to cancel off the units and make it dimensionless, Pie term related to cycle time required for activity:

Similarly factors are arranged for human energy spent in doing the activity:
Π8 = Pulse ÷ rmvbits
Table 4.15: Description of Pi terms for dependent variables
Pi term related to Cycle time
Cycle time
Machine operation time
Tc
To

In terms of MLT Indices
Π7 = ( M0L0T1 )
( M0L0T1 )
Pi term related to Human energy input
Pulse
rmvbits
Pulse
rmvbits
Π8 = Pulse ÷ rmvbits
In terms of MLT Indices
Π8 = ( M0L0T0 )
( M0L0T0 )

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