The Physical Basis of Dimensional Analysis

In: Science

Submitted By Roushdy
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Procedure of Creating Dimensionless Groups

1. List all Variables that are included in the problem 2. Express each variable in terms of basic dimension 3. Determine the required number of pi terms 4. Select a number of repeating variables 5. Form a pi term by multiplying one of the non repeating variable by the product of repeating variables each raised to an exponent that will make the combination dimensionless 6. Repeat step 5 7. Check all the resulting pi terms 8. Express the final form as a relationship among the pi terms and think about what it means

Recapitulation

1. A base quantity is a property that is defined in physical terms by two operations: a comparison operation, and an addition operation. The comparison operation is a physical procedure for establishing whether two samples of the quantity are equal or unequal; the addition operation defines what is meant by the sum of two samples of that property.

2. Base quantities are properties for which the following concepts are defined in terms of physical operations: equality, addition, subtraction, multiplication by a pure number, and division by a pure number. Not defined in terms of physical operations are: product, ratio, power, and logarithmic, exponential, trigonometric and other special functions of physical quantities.

3. A base quantity can be measured in terms of an arbitrarily chosen unit of its own kind and a numerical value.

4. A derived quantity of the first kind is a product of various powers of numerical values of base quantities. A derived quantity is defined in terms of numerical value (which depends on base unit size) and does not necessarily have a tangible physical representation.

5. The dimension of any physical quantity, whether base or derived, is a formula that defines how the numerical value of the quantity changes when the base…...

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