Question

prove dimensionally that surface tension depends directly on force and inversely proportional to length​

Answer 1

Answer:

1. WHAT IS DIMENSIONAL ANALYSIS?

Dimensional analysis is a means of simplifying a physical problem by appealing to

dimensional homogeneity to reduce the number of relevant variables.

It is particularly useful for:

 presenting and interpreting experimental data;

 attacking problems not amenable to a direct theoretical solution;

 checking equations;

 establishing the relative importance of particular physical phenomena;

 physical modelling.

Example.

The drag force F per unit length on a long smooth cylinder is a function of air speed U,

density ρ, diameter D and viscosity μ. However, instead of having to draw hundreds of

graphs portraying its variation with all combinations of these parameters, dimensional

analysis tells us that the problem can be reduced to a single dimensionless relationship

c f (Re) D 

where cD is the drag coefficient and Re is the Reynolds number.

In this instance dimensional analysis has reduced the number of relevant variables from 5 to

2 and the experimental data to a single graph of cD against Re.

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