Consider a polymer (with density p and viscosity µ) flowing in between two parallel plates in a vertical position. Both plates are stationary at x = 0 and x = h. A downward pressure gradient is applied (-dp/dz) which is constant across the z-direction, which is also aided by gravity acting on the negative z-direction. g LH" a. Starting with the Navier-Stokes equations, find the simplified equation that defines the fluid velocity vz. State your assumptions to achieve this simplified equation. b. If h=4.0 cm and the liquid has a p = 1640 kg/m³ and a viscosity µ = 1.5 Pa's, what is the maximum downward velocity, Vz, max, when - d = 22,000 Pa/m. dz ---Be careful here - make sure you consider which direction your pressure gradient is in!
Consider a polymer (with density p and viscosity µ) flowing in between two parallel plates in a vertical position. Both plates are stationary at x = 0 and x = h. A downward pressure gradient is applied (-dp/dz) which is constant across the z-direction, which is also aided by gravity acting on the negative z-direction. g LH" a. Starting with the Navier-Stokes equations, find the simplified equation that defines the fluid velocity vz. State your assumptions to achieve this simplified equation. b. If h=4.0 cm and the liquid has a p = 1640 kg/m³ and a viscosity µ = 1.5 Pa's, what is the maximum downward velocity, Vz, max, when - d = 22,000 Pa/m. dz ---Be careful here - make sure you consider which direction your pressure gradient is in!
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:Consider a polymer (with density p and viscosity µ) flowing in between two parallel plates in a
vertical position. Both plates are stationary at x = 0 and x = h. A downward pressure gradient is
applied (-dp/dz) which is constant across the z-direction, which is also aided by gravity acting on
the negative z-direction.
g
LH"
a. Starting with the Navier-Stokes equations, find the simplified equation that defines the
fluid velocity vz. State your assumptions to achieve this simplified equation.
b. If h=4.0 cm and the liquid has a p = 1640 kg/m³ and a viscosity μ = 1.5 Pa's, what is the
maximum downward velocity, Vz, max, when = 22,000 Pa/m.
dp
dz
---Be careful here - make sure you consider which direction your pressure gradient is in!
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