From general property balance equation to shear viscosity: Application of Laplace transforms technique

Differential equations have solutions which contains a number of unknown integration constants that can be found by applying appropriate boundary conditions. This rather tedious procedure was overcome by the application of Laplace transform techniques, where the unknown integration constants were evaluated during the process of solution by use of straightforward algebraic equations. In this study, the Laplace transform technique was used to solve the diffusivity equation of fluid flow. The technique was used to extract the kinematic viscosity, and then the dynamic viscosity was obtained. The Prandtl number of the fluid was used to generate the time domain of the motion in the container. The shear viscosity of water at a temperature of 293.15 K was determined to be 1.0006 cp, and this compares with the value obtainable from standard experimental procedure. From the analysis in this study, it is confirmed that the viscosity of water is a strong function of temperature.