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a. 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). Solid wall Thin liquid film - Thickness Ax Air

a. 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). Solid wall Thin liquid film - Thickness Ax Air

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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3 A constant-density Newtonian fluid is flowing as a thin film down a vertical wall in laminar flow; see Fig. 15.9. a. 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). Solid wall * Air Thin liquid film Thickness Ax FIGURE 15.9 A thin liquid film flowing down a wall. b. Repeat the solution to Prob. 3a, showing both the velocity distribution and the volumetric flow rate, for the case in which the flow under the influence of gravity is between two parallel vertical plates, separated by the distance Ax. In Prob. 15.9 the pressure gradient in the flow direction was zero, because the film was open to the air, which is at practically a constant pressure. Here also, assume that the pressure gradient in the flow direction is zero, because the vertical plates must end somewhere, and the pressure at the top and the bottom of the space between them may be assumed to be the same. NOTE: I realize that you can find the solutions to 3 and 4 online if you just google it, but do try this on your own first... good collaborative problem..
Transcribed Image Text:3 A constant-density Newtonian fluid is flowing as a thin film down a vertical wall in laminar flow; see Fig. 15.9. a. 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). Solid wall * Air Thin liquid film Thickness Ax FIGURE 15.9 A thin liquid film flowing down a wall. b. Repeat the solution to Prob. 3a, showing both the velocity distribution and the volumetric flow rate, for the case in which the flow under the influence of gravity is between two parallel vertical plates, separated by the distance Ax. In Prob. 15.9 the pressure gradient in the flow direction was zero, because the film was open to the air, which is at practically a constant pressure. Here also, assume that the pressure gradient in the flow direction is zero, because the vertical plates must end somewhere, and the pressure at the top and the bottom of the space between them may be assumed to be the same. NOTE: I realize that you can find the solutions to 3 and 4 online if you just google it, but do try this on your own first... good collaborative problem..
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