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A liquid film with constant thickness d is flowing down a sloped surface due to gravity. The top surface is exposed to air at atmospheric pressure. Assume the z- direction goes into and out of the page and all fluid properties are constant for the z-direction (i.e., z- component can be ignored). a. Simplify the Navier-Stokes equations in the x and y direction. Determine the equation for the pressure within the falling film. b. Determine the equation that describes the velocity profile, vx, within the film. P Air Ө c. If the flowrate per unit length in the z-direction (Q) is 25.0 m²/s, the slope has an incline of 0 = 35° and the fluid has the following properties (p = 1000. kg/m³, µ = 7.20 kg/m-s), determine the thickness of the film in cm. d. Determine an expression for the shear stress at the sloped surface. HINT: Set up your x and y coordinates so that x is in the direction of flow and y is perpendicular to the flow. It will make this problem much simpler to solve.

A liquid film with constant thickness d is flowing down a sloped surface due to gravity. The top surface is exposed to air at atmospheric pressure. Assume the z- direction goes into and out of the page and all fluid properties are constant for the z-direction (i.e., z- component can be ignored). a. Simplify the Navier-Stokes equations in the x and y direction. Determine the equation for the pressure within the falling film. b. Determine the equation that describes the velocity profile, vx, within the film. P Air Ө c. If the flowrate per unit length in the z-direction (Q) is 25.0 m²/s, the slope has an incline of 0 = 35° and the fluid has the following properties (p = 1000. kg/m³, µ = 7.20 kg/m-s), determine the thickness of the film in cm. d. Determine an expression for the shear stress at the sloped surface. HINT: Set up your x and y coordinates so that x is in the direction of flow and y is perpendicular to the flow. It will make this problem much simpler to solve.

Introduction to Chemical Engineering Thermodynamics
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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A liquid film with constant thickness d is flowing down a sloped surface due to gravity. The top surface is exposed to air at atmospheric pressure. Assume the z- direction goes into and out of the page and all fluid properties are constant for the z-direction (i.e., z- component can be ignored). a. Simplify the Navier-Stokes equations in the x and y direction. Determine the equation for the pressure within the falling film. b. Determine the equation that describes the velocity profile, vx, within the film. Air Ꮎ c. If the flowrate per unit length in the z-direction (Q) is 25.0 m²/s, the slope has an incline of 0 = 35° and the fluid has the following properties (p = 1000. kg/m³, µ= 7.20 kg/m-s), determine the thickness of the film in cm. d. Determine an expression for the shear stress at the sloped surface. HINT: Set up your x and y coordinates so that x is in the direction of flow and y is perpendicular to the flow. It will make this problem much simpler to solve.
Transcribed Image Text:A liquid film with constant thickness d is flowing down a sloped surface due to gravity. The top surface is exposed to air at atmospheric pressure. Assume the z- direction goes into and out of the page and all fluid properties are constant for the z-direction (i.e., z- component can be ignored). a. Simplify the Navier-Stokes equations in the x and y direction. Determine the equation for the pressure within the falling film. b. Determine the equation that describes the velocity profile, vx, within the film. Air Ꮎ c. If the flowrate per unit length in the z-direction (Q) is 25.0 m²/s, the slope has an incline of 0 = 35° and the fluid has the following properties (p = 1000. kg/m³, µ= 7.20 kg/m-s), determine the thickness of the film in cm. d. Determine an expression for the shear stress at the sloped surface. HINT: Set up your x and y coordinates so that x is in the direction of flow and y is perpendicular to the flow. It will make this problem much simpler to solve.
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