Suppose that in a coating process a solid sheet immersed in a liquid is pulled steadily at velocity U through a slot in a die, as shown in the figure. The die dimensions are such that there is a liquid gap of thickness H on each side of the sheet. Far downstream from the die the coating has a final thickness H... The pressure in the upstream liquid is ambient (P = Po) and gravitational and surface tension effects are negligible. The die length is L and the system width is W. The liquid is Newtonian and Re is such that the flow is laminar. Liquid P = Po X Die Liquid Solid Sheet Liquid Die H Gas P = Po Width = W | H₂ U (a) Assuming fully developed flow, determine vx(y) for the liquid in the upper gap. Be sure to use the coordinates shown. (b) Determine the force required to pull the sheet through the die. You may assume that the shear force on the sheet in the upstream liquid (x < 0) is negligible.
Suppose that in a coating process a solid sheet immersed in a liquid is pulled steadily at velocity U through a slot in a die, as shown in the figure. The die dimensions are such that there is a liquid gap of thickness H on each side of the sheet. Far downstream from the die the coating has a final thickness H... The pressure in the upstream liquid is ambient (P = Po) and gravitational and surface tension effects are negligible. The die length is L and the system width is W. The liquid is Newtonian and Re is such that the flow is laminar. Liquid P = Po X Die Liquid Solid Sheet Liquid Die H Gas P = Po Width = W | H₂ U (a) Assuming fully developed flow, determine vx(y) for the liquid in the upper gap. Be sure to use the coordinates shown. (b) Determine the force required to pull the sheet through the die. You may assume that the shear force on the sheet in the upstream liquid (x < 0) is negligible.
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:Suppose that in a coating process a solid sheet immersed in a liquid is pulled
steadily at velocity U through a slot in a die, as shown in the figure. The die
dimensions are such that there is a liquid gap of thickness H on each side of the
sheet. Far downstream from the die the coating has a final thickness H... The
pressure in the upstream liquid is ambient (P = Po) and gravitational and surface
tension effects are negligible. The die length is L and the system width is W. The
liquid is Newtonian and Re is such that the flow is laminar.
Liquid
P = Po
X
Die
Liquid
Solid Sheet
Liquid
Die
H
Gas
P = Po
Width = W
Hoo
U
(a) Assuming fully developed flow, determine vx(y) for the liquid in the upper gap. Be
sure to use the coordinates shown.
(b) Determine the force required to pull the sheet through the die. You may assume
that the shear force on the sheet in the upstream liquid (x < 0) is negligible.
(c) Assuming that H is given, determine H...
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