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# Pressure

Asked by 23rd April 2010, 9:23 PM

Please refer to the dimensional analysis for the solution.

The oscillations can be measured by frequency of oscillation.

T   PaρbEc   where, symbols have their usual meaning.

Writing in terms of dimensions,

[T] = [ML-1T-2]a[ML-3]b[ML2T-2]c

Comparing the exponents of M:

0 = a+b+c ... (1)

Comparing exponents of T:

1 = -2a-2c

a+c = -1/2     .... (2)

Comparing exponents of L:

0 = -a-3b+2c  ... (3)

Using (2) in (1) gives,

b = 1/2,

Hence (3) becomes,

a - 2c = -3/2    .........(4)

Solving (2) and (4), we find,

c = 1/3 and a = -5/6.

Hence,

T = Cρ1/2E1/3/P5/6

where C is a constant.

Regards,

Team,

TopperLearning.

Answered by Expert 23rd April 2010, 9:44 PM
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