A thin rod of diameter d is pulled at constant velocity vo in the positive z-direction through a pipe of diameter D and length L. The fluid filling the space between the rod and pipe wall is an incompressible Newtonian liquid with density p and viscosity µ. Assume steady fully developed laminar flow for the fluid with no pressure gradient in the z-direction, dP/dz = 0. (a) Write the simplified form of the Navier-Stokes equation and the appropriate boundary conditions. (b) Derive an equation for the velocity profile in the liquid. (c) Obtain an equation for the force required to pull the rod through the pipe.

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
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A thin rod of diameter d is pulled at constant velocity v, in the positive z-direction through a pipe of diameter D
and length L. The fluid filling the space between the rod and pipe wall is an incompressible Newtonian liquid
with density p and viscosity u. Assume steady fully developed laminar flow for the fluid with no pressure
gradient in the z-direction, dP/dz= 0.
(a) Write the simplified form of the Navier-Stokes equation and the appropriate boundary conditions.
(b) Derive an equation for the velocity profile in the liquid.
(c) Obtain an equation for the force required to pull the rod through the pipe.
Transcribed Image Text:A thin rod of diameter d is pulled at constant velocity v, in the positive z-direction through a pipe of diameter D and length L. The fluid filling the space between the rod and pipe wall is an incompressible Newtonian liquid with density p and viscosity u. Assume steady fully developed laminar flow for the fluid with no pressure gradient in the z-direction, dP/dz= 0. (a) Write the simplified form of the Navier-Stokes equation and the appropriate boundary conditions. (b) Derive an equation for the velocity profile in the liquid. (c) Obtain an equation for the force required to pull the rod through the pipe.
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