Assignment #6 Solution Set
Problem 1
Pressure driven flow of an incompressible Newtonian fluid through the annular gap between two coaxial cylinders:
The Governing equation:
dp
1 d dv z
r
dz
r dr dr
A. General solution (with integration constants C1 and
CHEMICAL ENGINEERING 2O04
Assignment #4
Dr. D. Latulippe
Out: March 5th
Due: March 16th

QUESTION 1
The cross section of a noncircular duct is shown in the
attached figure. Ethylene glycol (at 25 oC) is being
transported through the shaded region betwee
Student Name: _ ID#_
CHEMICAL ENGINEERING 2O04
Fluid Mechanics Test 1
DAY CLASS
Duration 120 minutes
McMaster University Term Test
D.R. Latulippe
Thursday February 12th, 2015
The test includes 4 questions + 1 bonus question in 7 pages (the last page is i
1
INTRODUCTION TO FLUID
MECHANICS
Department of Chemical Engineering
CHEM ENG 2O04
Course Notes
Fundamentals
Fox & McDonald
1.5 to 1.6
2.4 to 2.5
Appendices A2, A3, G
2
Dimensions & Units
3
Dimensional Consistency
All physical equations must be dimension
1
INTRODUCTION TO FLUID
MECHANICS
Department of Chemical Engineering
CHEM ENG 2O04
Course Notes
Conservation of Momentum Part II
NavierStokes Equations
Fox & McDonald
2.3, 2.6, 5.4, & 7.5
2
Velocity Fields (from PDF_01 notes)
For a given flow situation,
1
INTRODUCTION TO FLUID
MECHANICS
Department of Chemical Engineering
CHEM ENG 2O04
Course Notes
Unidirectional Laminar
Viscous Flow Part I
Fox & McDonald
5.4, 8.1 8.3, + many more examples
2
Unidirectional Laminar Viscous Flow
Fluid moves in one directio
1
INTRODUCTION TO FLUID
MECHANICS
Department of Chemical Engineering
CHEM ENG 2O04
Course Notes
THE BERNOULLI EQUATION Part I
Fox & McDonald
4.1, 4.8, 6.4, 8.6 8.8
PIPEFLO
Tutorials 1  5
2
BERNOULLI EQUATION
aka Total Mechanical Energy Balance
Mechanica
1
INTRODUCTION TO FLUID
MECHANICS
Department of Chemical Engineering
CHEM ENG 2O04
Course Notes
TURBOMACHINERY Part I
Fox & McDonald
10.1 to 10.4
PIPEFLO
Tutorials 8, 9, & 10
Radial
Flow
Axial
Flow
2
Mixed Flow
Types
Turbomachinery: Transfers energy betw
1
INTRODUCTION TO FLUID
MECHANICS
Department of Chemical Engineering
CHEM ENG 2O04
Course Notes
TURBOMACHINERY Part II
Fox & McDonald
10.1 to 10.4
PIPEFLO
Tutorials 8, 9, & 10
2
Radial flow pumps
Flow enters at the eye of the
pump
Flow is forced outwar
INTRODUCTION TO FLUID
MECHANICS
Department of Chemical Engineering
CHEM ENG 2O04
Course Notes
Flow Similarity
Fox & McDonald
7.6
Similarity for Modelling of Prototypes
Predicting prototype performance from model observations
A prototype can be scaled do
1
INTRODUCTION TO FLUID
MECHANICS
Department of Chemical Engineering
CHEM ENG 2O04
Course Notes
THE BERNOULLI EQUATION Part II
Fox & McDonald
8.6 8.8
PIPEFLO
Tutorials 1  5
2
hlT accounts for total energy loss
Need to account for:
1. Irreversible conver
1
INTRODUCTION TO FLUID
MECHANICS
Department of Chemical Engineering
CHEM ENG 2O04
Course Notes
Conservation of Momentum Part I
Linear Momentum Equation
Fox & McDonald
4.4
2
Momentum Equation
Start with Newtons second law:
F =
THREE types of forces:
Surf
1
INTRODUCTION TO FLUID
MECHANICS
Department of Chemical Engineering
CHEM ENG 2O04
Course Notes
Velocity Flow Profiles
Laminar vs Turbulent
Fox & McDonald
2.2, 2.6
7.5
8.1, 8.5
2
Classification of Fluid Motions
Fig. 2.13
3
Reynolds Number
The forces enc
1
INTRODUCTION TO FLUID
MECHANICS
Department of Chemical Engineering
CHEM ENG 2O04
Course Notes
Unidirectional Laminar Viscous Flow
Part III (Unsteadystate)
2
Flow near a wall that is set in motion
A semiinfinite quantity of a
viscous fluid is contact
1
INTRODUCTION TO FLUID
MECHANICS
Department of Chemical Engineering
CHEM ENG 2O04
Course Notes
Unidirectional Laminar
Viscous Flow Part II
Fox & McDonald
5.4, 8.1 8.3, + many more examples
2
Pressure driven, fullydeveloped,
laminar flow in a pipe
For c
Student Name: _ ID#_
CHEMICAL ENGINEERING 2O04
Fluid Mechanics Test 2
DAY CLASS
Duration 120 minutes
McMaster University Term Test
D.R. Latulippe
Thursday March 19th, 2015
The test includes 4 questions + 1 bonus question in 10 pages (the last two pages a
Q. 1
Given: Ethylene glycol at 25 oC.
= 1100 kg/m3
= 1.62102 Pas
a) Given: Q = 0.16 m3/s
Where Dh is the hydraulic diameter, and
, P is the wetted perimeter.
The net flow area the area difference between the square and the circle:
The wetted perimeter
Assignment 3 E1
E2
E3
E4
E5
E6
Assignment 4 E1
E2
E3
E4
Problem 8.49 At r = 0.707R, the velocity equals the average velocity
Problem 8.70 The maximum Q for laminar flow is 0.452 cm 3/s
The required pressure drop is 235 kPa
Problem 8.79 The head loss is 1.
CHEMICAL ENGINEERING 2O04
Assignment #5
Dr. D. Latulippe
Out: March 20th
Due: March 30th

QUESTION 1
For this problem you will use PIPEFLO to model a simple piping system for a bathroom and understand how
flushing a toilet affects the flow rate of water
CHEMICAL ENGINEERING 2O04
Assignment #6
Dr. D. Latulippe
Out: March 30th
Due: April 8th

QUESTION 1
In class, we looked at pressure driven flow of an incompressible Newtonian fluid (INF) through the
annular gap between two coaxial cylinders (see figure b
ChE 2O04 tutorial section
Check the
appropriate box
T02 Tuesdays 9:30 11:20
T01 Thursdays 8:30 10:20
T03 Thursdays 3:30 5:20
<Date>
Dr. D. R. Latulippe
Department of Chemical Engineering
McMaster University
Attached is my submission for the <first, second
CHEMICAL ENGINEERING 2O04
Assignment #3
Out: February 13th
Due: March 2nd
Dr. D. Latulippe

QUESTION 1
Water at 10 oC is flowing through a 4 schedule 40 smooth horizontal pipe at an average velocity of
1.2 m/s.
a) Based on the given information, do you e
CHEMICAL ENGINEERING 2O04
Assignment #2
Out: January 28th
Due: February 9th
Dr. D. Latulippe

QUESTION 1
a. Using Excel and the data in Appendix A of the textbook, plot the surface tension (mN/m) of
water versus temperature (oC).
b. Two colleagues propos
CHEMICAL ENGINEERING 2O04
Assignment #4
Dr. D. Latulippe
Out: March 5th
Due: March 16th

Extra problems (from 8th edition textbook) for selfstudy DO NOT hand in the solutions to
these problems with your assignment:
Problem 8.146
E1
Problem 8.161
E2
Prob
CHEMICAL ENGINEERING 2O04
Assignment #1
Out: January 14th 2014
Due: January 26th 2014
Dr. D. Latulippe

QUESTION 1
a. Using Excel and the data in Appendix A of the textbook, plot the change in water viscosity
(Pas) with temperature from 10 to 80 oC.
b. F
1
INTRODUCTION TO FLUID
MECHANICS
Department of Chemical Engineering
CHEM ENG 2O04
Course Notes
Introduction
Fox & McDonald
1.2 to 1.5
2.1 to 2.3
Appendix A1
2
Fluid Mechanics
What is a fluid?
Substance that deforms continuously under the application of
A single length of 2 schedule 40 wrought iron pipe is
used to convey 1200 cm3/s of cold lake water (~ 4 oC)
uphill. The pipe is 20 m in length and inclined at an
angle of 25o with the horizon.
a. Draw a schematic of the process including labels for the tw
CHEMICAL ENGINEERING 2O04
Tutorial #2
Dr. D. Latulippe
Tutorial Problem 1
The viscosity of an electrolyte solution depends on the concentration of dissolved salt as shown in the
table below for sodium chloride in water at 25 oC
Concentration (mol/L)
0
0.0