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Consider the coating operation shown below. A solid substrate is pulled steadily with a velocity V through a die of length L and width W in the horizontal direction (positive x-direction). The space between the substrate surface and the die (h) contains a coating liquid which is an incompressible Newtonian fluid. The top surface of the die at y h is stationary. The pressure on the liquid at the die entrance at x = 0 is Po, while the pressure on the liquid at the die exit at x L is PL. Assume the liquid is in steady fully developed laminar flow in the die region, and L>h and W >>h. a) List assumptions and write the simplified forms of the continuity and Navier-Stokes equations. b) Write the boundary conditions to be used for solving the Navier-Stokes equation. c) Solve for the coating liquid velocity profile in the die region.

Consider the coating operation shown below. A solid substrate is pulled steadily with a velocity V through a die of length L and width W in the horizontal direction (positive x-direction). The space between the substrate surface and the die (h) contains a coating liquid which is an incompressible Newtonian fluid. The top surface of the die at y h is stationary. The pressure on the liquid at the die entrance at x = 0 is Po, while the pressure on the liquid at the die exit at x L is PL. Assume the liquid is in steady fully developed laminar flow in the die region, and L>h and W >>h. a) List assumptions and write the simplified forms of the continuity and Navier-Stokes equations. b) Write the boundary conditions to be used for solving the Navier-Stokes equation. c) Solve for the coating liquid velocity profile in the die region.

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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Parts a-c please.

Consider the coating operation shown below. A solid substrate is pulled steadily with a velocity V through a die of length L and width W in the horizontal direction (positive x-direction). The space between the substrate surface and the die (h) contains a coating liquid which is an incompressible Newtonian fluid. The top surface of the die at y = h is stationary. The pressure on the liquid at the die entrance at x = 0 is Po, while the pressure on the liquid at the die exit at x = L is PL. Assume the liquid is in steady fully developed laminar flow in the die region, and L>>h and W >>h. a) List assumptions and write the simplified forms of the continuity and Navier-Stokes equations. b) Write the boundary conditions to be used for solving the Navier-Stokes equation. c) Solve for the coating liquid velocity profile in the die region. d) Obtain an equation for the force required to pull the substrate through the die region. Coating Liquid y h / Substrate //
Transcribed Image Text:Consider the coating operation shown below. A solid substrate is pulled steadily with a velocity V through a die of length L and width W in the horizontal direction (positive x-direction). The space between the substrate surface and the die (h) contains a coating liquid which is an incompressible Newtonian fluid. The top surface of the die at y = h is stationary. The pressure on the liquid at the die entrance at x = 0 is Po, while the pressure on the liquid at the die exit at x = L is PL. Assume the liquid is in steady fully developed laminar flow in the die region, and L>>h and W >>h. a) List assumptions and write the simplified forms of the continuity and Navier-Stokes equations. b) Write the boundary conditions to be used for solving the Navier-Stokes equation. c) Solve for the coating liquid velocity profile in the die region. d) Obtain an equation for the force required to pull the substrate through the die region. Coating Liquid y h / Substrate //
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