Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

please answer question 1 . written if possible Consider the horizontal, laminar flow of a non-Newtonian fluid (K=2Pasn and n=0.35) that is subjected to a

please answer question 1 . written if possible

image text in transcribed

image text in transcribed

Consider the horizontal, laminar flow of a non-Newtonian fluid (K=2Pasn and n=0.35) that is subjected to a constant pressure gradient of 500Pa/m in a pipe of circular cross-section (radius R=5cm ). Performing a momentum balance on an annular fluid element (length dz and thickness dr) leads to the differential equation (DE) drd(rrz)=rdzdp where r is the radial coordinate. The no-slip boundary condition applies at the pipe wall, whereas the strain rate vanishes at r=0. The apparent viscosity for this fluid is related to its strain rate via ()=Kn1 where K and n are positive constants 1. Using the ODE given in the question i.e., Equation (4) above, solve (i.e., integrate) it simultaneously with the appropriate shear stress-shear strain relationship from r=0 to r=+R with r=0.5cm, where r=0 corresponds to the pipe centreline, to compute the velocity profile of the fluid. Of course, use Euler integration. Report the velocities in tabulated form at each node in SI units. Compute the RMSE. Consider the horizontal, laminar flow of a non-Newtonian fluid (K=2Pasn and n=0.35) that is subjected to a constant pressure gradient of 500Pa/m in a pipe of circular cross-section (radius R=5cm ). Performing a momentum balance on an annular fluid element (length dz and thickness dr) leads to the differential equation (DE) drd(rrz)=rdzdp where r is the radial coordinate. The no-slip boundary condition applies at the pipe wall, whereas the strain rate vanishes at r=0. The apparent viscosity for this fluid is related to its strain rate via ()=Kn1 where K and n are positive constants 1. Using the ODE given in the question i.e., Equation (4) above, solve (i.e., integrate) it simultaneously with the appropriate shear stress-shear strain relationship from r=0 to r=+R with r=0.5cm, where r=0 corresponds to the pipe centreline, to compute the velocity profile of the fluid. Of course, use Euler integration. Report the velocities in tabulated form at each node in SI units. Compute the RMSE

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Process Dynamics And Control

Authors: Dale E. Seborg, Thomas F. Edgar, Duncan A. Mellichamp, Francis J. Doyle

4th Edition

1119385561, 1119385563, 9781119285953, 978-1119385561

More Books

Students also viewed these Chemical Engineering questions

Question

Identify the issues that contribute to staff member frustration.

Answered: 1 week ago