Pemodelan Aliran Fluida Bidang Miring pada Lapisan Tipis

Abstract

Fluid flow can be expressed as a partial differential equation. This study presents a deduction of fluid flow modelling on an inclined plane. The fluid flow is assumed to be incompressible and irrotational. Modelling fluid flow in the incline involves various equations: the continuity equation, the Navier-Stokes equation, the power equation, and the pressure equation. The Navier-Stokes, power-law, and pressure equations are transformed into dimensionless forms and then solved by substituting the power-law and pressure equations into the Navier-Stokes equation. Reynold’s number is assumed to be very small, so we can omit it in the Navier-stokes equation. Further, the Navier-Stokes equation that has been built is transformed into dimensional form. In constructing a fluid flow model on an inclined plane, free surface kinematic equations are also needed, which produce differential equations, so that models and solutions for fluid flow on an inclined plane are obtained in thin layers. This model is in the form of a first-order quasi-linear equation. We obtain that the solution is a function of the position of the fluid flowing at a certain time which also depends on the fluid type.