Chapter 4 : Fluid Kinematics - Notes, Chemical Engineering Chemical Engineering Notes | EduRev

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Chemical Engineering : Chapter 4 : Fluid Kinematics - Notes, Chemical Engineering Chemical Engineering Notes | EduRev

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PROPRIETARY AND CONFIDENTIAL 
 
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Page 2


 
 
 
 
 
 
 
 
 
PROPRIETARY AND CONFIDENTIAL 
 
This Manual is the proprietary property of The McGraw-Hill 
Companies, Inc. (“McGraw-Hill”) and protected by 
copyright and other state and federal laws.  By opening and 
using this Manual the user agrees to the following 
restrictions, and if the recipient does not agree to these 
restrictions, the Manual should be promptly returned 
unopened to McGraw-Hill:  This Manual is being provided 
only to authorized professors and instructors for use in 
preparing for the classes using the affiliated textbook.  No 
other use or distribution of this Manual is permitted.  
This Manual may not be sold and may not be distributed 
to or used by any student or other third party.  No part of 
this Manual may be reproduced, displayed or distributed 
in any form or by any means, electronic or otherwise, 
without the prior written permission of McGraw-Hill.   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
PROPRIETARY MATERIAL.  © The McGraw-Hill Companies, Inc.  All rights 
reserved.  No part of this Manual may be displayed, reproduced or distributed in any 
form or by any means, without the prior written permission of the publisher, or used 
beyond the limited distribution to teachers and educators permitted by McGraw-Hill 
for their individual course preparation.  If you are a student using this Manual, you 
are using it without permission. 
Solution Manual, Chapter 4 – Fluid Kinematics 
Chapter 4 
Fluid Kinematics 
 
 
 
 
Introductory Problems 
 
4-1C 
Solution We are to define and explain kinematics and fluid kinematics.  
 
Analysis Kinematics means the study of motion. Fluid kinematics is the study 
of how fluids flow and how to describe fluid motion. Fluid kinematics deals with 
describing the motion of fluids without considering (or even understanding) the forces 
and moments that cause the motion. 
 
Discussion Fluid kinematics deals with such things as describing how a fluid 
particle translates, distorts, and rotates, and how to visualize flow fields. 
 
 
 
 
4-2 
Solution We are to write an equation for centerline speed through a nozzle, 
given that the flow speed increases parabolically.  
 
Assumptions 1 The flow is steady. 2 The flow is axisymmetric. 3 The water is 
incompressible. 
 
Analysis A general equation for a parabola in the x direction is 
General parabolic equation:  ()
2
ua bx c =+ - (1) 
We have two boundary conditions, namely at x = 0, u = u
entrance
 and at x = L, u = u
exit
. 
By inspection, Eq. 1 is satisfied by setting c = 0, a = u
entrance
 and b = (u
exit
 - u
entrance
)/L
2
. 
Thus, Eq. 1 becomes 
Parabolic speed: 
( )
exit entrance 2
entrance 2
uu
uu x
L
-
=+ 
 
 
(2) 
 
Discussion You can verify Eq. 2 by plugging in x = 0 and x = L. 
 
 
4-1 
 
PROPRIETARY MATERIAL.  © The McGraw-Hill Companies, Inc.  All rights 
reserved.  No part of this Manual may be displayed, reproduced or distributed in any 
form or by any means, without the prior written permission of the publisher, or used 
beyond the limited distribution to teachers and educators permitted by McGraw-Hill 
for their individual course preparation.  If you are a student using this Manual, you 
are using it without permission. 
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