QS Study

Necessity of Dimensional Equations

The importance of dimensional equation in physics is enormous. Its importance’s are discussed below:

(1) One form of unit can be converted into another form of unit.

(2) Accuracy of an equation can be verified.

(3) Equation of different quantifies can be formed.

(4) Unit of a physical quantity can be determined.

(5) Solution of a physical problem can be found out.

(6) To derive the relation between various physical quantities.

(7) To check the correctness of a physical relation.

Limitations of Dimensional Equations

Although dimensional equations have many applications, they have some limitations as well. e.g.

(1) We form dimensional equations on the basis of the three Dimensional quantities L, M and T. But, if an unknown quantity is dependent on more than these three quantities, then we cannot form dimensional equation for that unknown quantity. For example, dimensional equation of thermal conductivity cannot be expressed only by L, M and T, as it depends on another quantity i.e., on temperature.

(2) Besides, by dimensional process we cannot find out the value of dimensionless quantity i.e., of constant.

(3) If a quantity is dependent on trigonometric or exponential functions, this method cannot be used.

(4) It cannot be used if the physical quantity is dependent on more than three unknown variables.

(5) In some cases, it is difficult to guess the factors while deriving the relation connecting two or more physical quantities.