Interpretation: The equation for the laminar flow of a liquid between the 2 infinite parallel plates is to be proved.
Concept introduction: The flow in a liquid is said to be Laminar when the Reynold’s number is less than 2100. The equation for laminar flow can be derived by the force balance between the plates. The equation for the shear stress is a very useful measure here as it can help in achieving the final result. The shear stress equation is,
The notations used here are,
Answer to Problem 5.1P
The equation for the flow of a laminar liquid between two infinite parallel plates is,
Explanation of Solution
The two infinite parallel plates can be given as,
In the given diagram,
b = Distance between the plates
L = Length of plate in direction of flow
The force balance between the two plates is given as,
In the above expression,
Rearrange equation (2),
Substitute equation (1) in equation (3),
Integrate equation (4) with limits b/2 to y and 0 to u,
Solving the above integrand within the given limits we get,
The equation for the flow of a laminar liquid between two infinite parallel plates is,
Want to see more full solutions like this?
Chapter 5 Solutions
Unit Operations of Chemical Engineering
- Introduction to Chemical Engineering Thermodynami...Chemical EngineeringISBN:9781259696527Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark SwihartPublisher:McGraw-Hill EducationElementary Principles of Chemical Processes, Bind...Chemical EngineeringISBN:9781118431221Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. BullardPublisher:WILEYElements of Chemical Reaction Engineering (5th Ed...Chemical EngineeringISBN:9780133887518Author:H. Scott FoglerPublisher:Prentice Hall
- Industrial Plastics: Theory and ApplicationsChemical EngineeringISBN:9781285061238Author:Lokensgard, ErikPublisher:Delmar Cengage LearningUnit Operations of Chemical EngineeringChemical EngineeringISBN:9780072848236Author:Warren McCabe, Julian C. Smith, Peter HarriottPublisher:McGraw-Hill Companies, The