Question

Explain with example the use of dimensional analysis ‘to find the conversion factor

between the units of the same physical quantity in two different systems of units’.​

Answer 1

Answer:

Dimensions and units are commonly confused, even though the solution to all engineering problems must include units. Dimensions are physical quantities that can be measured, whereas units are arbitrary names that correlate to particular dimensions to make it relative (e.g., a dimension is length, whereas a meter is a relative unit that describes length). All units for the same dimension are related to each other through a conversion factor (e.g., 2.54 cm is exactly equal to 1 in). There are seven base dimensions that can be combined to describe all of the other dimensions of interest in engineering and physics, among other disciplines. In fluid mechanics, we generally pick length, mass, time, and temperature as base dimensions. This makes force a function of length, mass, and time (i.e., force is equal to mass multiplied by length all divided by time squared). Others define force as one of their base dimensions and define mass by dividing force by the gravitational acceleration. This is one of the major differences between the standard English unit system and metric unitsystem. Those who choose to use metric units make use of the units kilogram, meter, and second to define the Newton. In contrast, those that use the English units use the units pound, foot, and second to define the slug.

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