Some Applications of Cubic Equations in Engineering

Cubic equations have many applications in engineering, three of them are discussed in this paper. There are many equations of states for real gases but the cubic equations are the simplest ones and are sufficiently accurate for a limited range of temperatures and pressures. Degree of dissociation of chemical equilibrium for carbon dioxide and water can be written as cubic equations. Slope of a simply supported beam loaded by a continuous load is also represented as a cubic equation. Cubic equations can be solved exactly using Cardano’s formula. They can also solve numerically; Newton-Raphson method is a popular choice. Although a cubic equation has three roots, only real roots are valid in real applications discussed in this paper. Even there may be only one root that can be used; two other roots will be discarded. There are many ways a cubic equation solved but the simplest one is to solve it manually using a scientific calculator. Software and programming languages are better if there are many equations to be solved repeatedly.