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Problem 3: Velocity profile for Non-Newtonian Fluid in a Pipe The stress rate of shear for a non-Newtonian fluid flowing inside a pipe with a radius Ro is given by: dv T= K Equation (*) dr Where K and n are constants. (a) Sketch the system above and show the coordinates and the origin point. (b) Find the relationship between velocity and the radial positionr for this incompressible fluid at steady state. Hint: Combine the equation above with the equation below. You also need to manipulate the equation such as the dv/dr will be on one side and the rest of the stuff on the other side. Solve the resulting differential equation with the B.C. of at r=Ro, Vx=0. Po-Pr 2L (c) Derive the expression for Vx-max. (d) Derive the expression for Vx-av. (e) Calculate the shear rate equation (*) at r=Ro (f) Calculate the drag force acting on the Ro surface

Problem 3: Velocity profile for Non-Newtonian Fluid in a Pipe The stress rate of shear for a non-Newtonian fluid flowing inside a pipe with a radius Ro is given by: dv T= K Equation (*) dr Where K and n are constants. (a) Sketch the system above and show the coordinates and the origin point. (b) Find the relationship between velocity and the radial positionr for this incompressible fluid at steady state. Hint: Combine the equation above with the equation below. You also need to manipulate the equation such as the dv/dr will be on one side and the rest of the stuff on the other side. Solve the resulting differential equation with the B.C. of at r=Ro, Vx=0. Po-Pr 2L (c) Derive the expression for Vx-max. (d) Derive the expression for Vx-av. (e) Calculate the shear rate equation (*) at r=Ro (f) Calculate the drag force acting on the Ro surface

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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Problem 3: Velocity profile for Non-Newtonian Fluid in a Pipe The stress rate of shear for a non-Newtonian fluid flowing inside a pipe with a radius Ro is given by: dv. T = K Equation (*) - rx dr Where K and n are constants. (a) Sketch the system above and show the coordinates and the origin point. (b) Find the relationship between velocity and the radial position r for this incompressible fluid at steady state. Hint: Combine the equation above with the equation below. You also need to manipulate the equation such as the dv/dr will be on one side and the rest of the stuff on the other side. Solve the resulting differential equation with the B.C. of at r=Ro, Vx=0. Po-Pr %3D 2L (c) Derive the expression for Vx-max. (d) Derive the expression for Vx-av. (e) Calculate the shear rate equation (*) at r=Ro (f) Calculate the drag force acting on the Ro surface
Transcribed Image Text:Problem 3: Velocity profile for Non-Newtonian Fluid in a Pipe The stress rate of shear for a non-Newtonian fluid flowing inside a pipe with a radius Ro is given by: dv. T = K Equation (*) - rx dr Where K and n are constants. (a) Sketch the system above and show the coordinates and the origin point. (b) Find the relationship between velocity and the radial position r for this incompressible fluid at steady state. Hint: Combine the equation above with the equation below. You also need to manipulate the equation such as the dv/dr will be on one side and the rest of the stuff on the other side. Solve the resulting differential equation with the B.C. of at r=Ro, Vx=0. Po-Pr %3D 2L (c) Derive the expression for Vx-max. (d) Derive the expression for Vx-av. (e) Calculate the shear rate equation (*) at r=Ro (f) Calculate the drag force acting on the Ro surface
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