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3 A constant-density Newtonian fluid is flowing as a thin film down a vertical wall in laminar flow; see Fig. 15.9.Find the velocity distribution and the volumetric flow rate per unit width of wall by using the Navier-Stokes equations (z component) on the assumptions that there is no flow in the x or y direction, that the z component of the velocity is zero at the solid wall, and that there is no shear stress at the liquid-air surface, and the flow is steady-state. (Waves may appear on the fluid surface in this situation; ignore that possibility for this problem). t Air Solid wall Thin liquid film Thickness Ax FIGURE 15.9 A thin liquid film flowing down a wall.

3 A constant-density Newtonian fluid is flowing as a thin film down a vertical wall in laminar flow; see Fig. 15.9.Find the velocity distribution and the volumetric flow rate per unit width of wall by using the Navier-Stokes equations (z component) on the assumptions that there is no flow in the x or y direction, that the z component of the velocity is zero at the solid wall, and that there is no shear stress at the liquid-air surface, and the flow is steady-state. (Waves may appear on the fluid surface in this situation; ignore that possibility for this problem). t Air Solid wall Thin liquid film Thickness Ax FIGURE 15.9 A thin liquid film flowing down a wall.

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
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### Problem 3 A constant-density Newtonian fluid is flowing as a thin film down a vertical wall in laminar flow; see Fig. 15.9. Find the velocity distribution and the volumetric flow rate per unit width of the wall by using the Navier-Stokes equations (z component) under the following assumptions: - There is no flow in the x or y direction. - The z component of the velocity is zero at the solid wall. - There is no shear stress at the liquid-air surface. - The flow is steady-state. (Note: Waves may appear on the fluid surface in this situation; ignore that possibility for this problem). ### Figure 15.9 #### Description: The diagram illustrates a thin liquid film flowing down a vertical solid wall. The components shown include: - **Solid Wall**: Represented as a vertical line on the left. - **Thin Liquid Film**: Depicted flowing adjacent to the solid wall and labeled as such. - **Thickness \(\Delta x\)**: Indicated by a horizontal arrow, showing the film's thickness perpendicular to the wall. - **Air**: Labeled to the right of the thin liquid film, indicating the surrounding environment.
Transcribed Image Text:### Problem 3 A constant-density Newtonian fluid is flowing as a thin film down a vertical wall in laminar flow; see Fig. 15.9. Find the velocity distribution and the volumetric flow rate per unit width of the wall by using the Navier-Stokes equations (z component) under the following assumptions: - There is no flow in the x or y direction. - The z component of the velocity is zero at the solid wall. - There is no shear stress at the liquid-air surface. - The flow is steady-state. (Note: Waves may appear on the fluid surface in this situation; ignore that possibility for this problem). ### Figure 15.9 #### Description: The diagram illustrates a thin liquid film flowing down a vertical solid wall. The components shown include: - **Solid Wall**: Represented as a vertical line on the left. - **Thin Liquid Film**: Depicted flowing adjacent to the solid wall and labeled as such. - **Thickness \(\Delta x\)**: Indicated by a horizontal arrow, showing the film's thickness perpendicular to the wall. - **Air**: Labeled to the right of the thin liquid film, indicating the surrounding environment.
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