Answered: Consider the steady fully developed…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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Transcribed Image Text:**Text:** Consider the steady fully developed laminar flow of an incompressible Newtonian liquid film down an inclined and very wide plane surface. The liquid film which is in contact with air has a thickness L and the surface has a width W (W >> L). a) Obtain the simplified forms of the continuity and Navier-Stokes equations. b) Write the boundary conditions for solving the Navier-Stokes equation. c) Solve for the velocity profile and volumetric flow rate. --- **Diagram Explanation:** The diagram depicts an inclined plane with a liquid film flowing over it. Key elements in the diagram include: - **Coordinate System**: The x-axis is along the plane surface, and the y-axis is perpendicular to the flow, pointing upwards through the film. - **Film Thickness (L)**: The thickness of the liquid film is denoted by L. - **Elemental Control Volume**: A rectangular control volume is indicated with dimensions Δx in the flow direction and Δy across the film thickness. - **Inclination Angle (θ)**: The plane is inclined at an angle θ with respect to the horizontal. - **Gravity (g)**: An arrow pointing downward indicates the direction of gravitational force acting on the liquid. This setup is used to analyze the behavior of the fluid flow and create mathematical models for flow dynamics using the given equations and conditions.

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