Chapter 5 Dimensional Analysis and Similarity
5.1 Solution: For kerosene at 20C, take = 804 kg/m3 and = 0.00192 kg/ms. The only unknown in the transition Reynolds number is the fluid velocity: Re tr 2
MEC516/BME516:
Fluid Mechanics I
Chapter 5: Dimensional Analysis &
Similarity
Part 5
David Naylor, 2014
Department of Mechanical
& Industrial Engineering
David Naylor
Overview
Re
Discussion of some
MEC516/BME516:
Fluid Mechanics I
Chapter 5: Dimensional Analysis &
Similarity
Part 2
David Naylor, 2014
Department of Mechanical
& Industrial Engineering
David Naylor
Overview
Dimensional Analysis
MEC516/BME516:
Fluid Mechanics I
Chapter 5: Dimensional Analysis &
Similarity
Part 1
David Naylor, 2014
Department of Mechanical
& Industrial Engineering
David Naylor
Overview
An Introduction to Sim
MEC516/BME516:
Fluid Mechanics I
Chapter 5: Dimensional Analysis &
Similarity
Part 3
David Naylor, 2014
Department of Mechanical
& Industrial Engineering
David Naylor
Dimensional Analysis Example
So
MEC516/BME516:
Fluid Mechanics I
Chapter 5: Di mensional Analysis &
Similarity
Part 8
David Naylor, 2014
Department of Mechanical
& Industrial Engineering
David Naylor
Overview
The Ipsen Method: An
MEC516/BME516:
Fluid Mechanics I
Chapter 5: Dimensional Analysis &
Similarity
Part 6
David Naylor, 2014
Department of Mechanical
& Industrial Engineering
David Naylor
Overview
Theory of Models and
Note Title
0' 1.56 The device in Fig. P156 is called a cone-plate viscome-
ter [29]. The angle of the cone is very small, so that sin
6 z 0, and the gap is lled with the test liquid. The .
torque M
Welcome to
MEC516/BME516:
Fluid Mechanics I
David Naylor, 2014
Image from www.freeimages.com
Engineering Applications of Fluid Mechanics:
HVAC e.g. furnaces, air-conditioners, ducting systems
Image
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Department of Mechanical and Industrial Engineering
Obtained from Ryerson's
Mechanical
Engineering
MEC
516/BME
516Course Union (MECU) www.ryemecu.com
Fluids Mecha
Obtained from Ryerson's Mechanical Engineering Course Union (MECU)-www.ryemecu.com
Ryerson University
Department of Mechanical and Indnstrial Engineering
Meichaillics I
MEC 516 Fluid Mechanics
MidtE'r
Obtained from Ryerson's Mechanical Engineering Course Union (MECU)-www.ryemecu.com
RYERSON UNIVERSITY
DEPARTMENT OF MECHANICAL AND INDUSTRIAL ENGINEERING
MEC 516IBME 516
FLUID MECHANICS I
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MEC516 - Fluid Mechanics I Laboratory
Department of Mechanical Engineering
TABLE OF CONTENTS
Page
Table of Contents . 1
1. Measurement of Dynamic Viscosity . 3
2. Reynolds Apparatus and Pipe Friction
Sept. 1, 2014
A student asked the following very insightful question:
In your solution, for y=h the shear stress is negative and for y= -h the shear stress is positive. Does that mean
the shear stress
MEC516/BME516:
Fluid Mechanics I
Chapter 5: Dimensional Analysis &
Similarity
Part 4
David Naylor, 2014
Department of Mechanical
& Industrial Engineering
David Naylor
Overview
Solved Example Dimens
MEC516/BME516:
Fluid Mechanics I
Chapter 5: Dimensional Analysis &
Similarity
Part 7
David Naylor, 2014
Department of Mechanical
& Industrial Engineering
David Naylor
Overview
Some Typical Model St
1%
ML
LU
Example: Consider steady fully developed ow between two
innite parallel xed plates, separated by distance 2h. It can be
shown that the velocity distribution is parabolic, and is given by:
uty
Print Name:
SOLUTIO NS
Section # Student ID:
RYERSON UNIVERSITY
Department of Mechanical and Industrial Engineering
MEC Slé/BME 516
Fluids Mechanics
Common Midterm Test
Friday, Oct 17, 2014
4:10 to 6:
Lecture 10: MEC516 FLUID MECHANICS I
2012
1/5
Buoyancy
Archimedes laws of buoyancy:
1. A body immersed in a fluid experiences a vertical buoyant force equal to the weight of the fluid
it displaces.
FB
Lecture 18: MEC516 FLUID MECHANICS I
2012
1/2
Bernoullis Equation
V2
g z (mechanical energy), to a streamline in a
2
steady, frictionless and incompressible flow, the mechanical energy will remain c
Lecture 7: MEC516 FLUID MECHANICS I
2012
1/2
Manometers (continued)
Examples
1) Inclined manometer:
a
R
A
p B p a 1 h1 y 2 y R sin (abs)
or p B 1 h1 y 2 y R sin (gage)
Substituting for y gives:
a
a
Lecture 3: MEC516 FLUID MECHANICS I
2012
1/3
Dimensions & Units
A dimension is the measure by which a physical variable is expressed quantitatively.
e.g.: length is a dimension [associated with] dista
Lecture 6: MEC516 FLUID MECHANICS I
2012
1/2
Pressure Variation in an Incompressible Fluid with a constant or
For a fluid, which is homogeneous and incompressible, its or is constant.
Integrating Eq.
Lecture 9: MEC516 FLUID MECHANICS I
2012
1/3
Example
A concrete gate is used to keep water level of a river upstream.
L 3 2 4 2 5 ft
hinge
l = 3 ft
h1 = 3 ft
h
SG = 1
h2 = 4 ft
4 ft
SG = 1
Gate with 5
Lecture 4: MEC516 FLUID MECHANICS I
2012
1/2
Chapter 2: Pressure Distribution in a Fluid
Hydrostatics or fluid statics is a study of fluid at rest or static.
Lets consider a differential volume of flu
MEC516 Fluid Mechanics I
2012
An example on buoyancy
King Hiero of Syracuse wanted to know whether his new golden crown was really made of pure
gold (SGgold = 19.3). Archimedes discovered the buoyancy
Lecture 9: MEC516 FLUID MECHANICS I
2012
1/3
Example
A concrete gate is used to keep water level of a river upstream.
L 3 2 4 2 5 ft
hinge
l = 3 ft
h1 = 3 ft
h
SG = 1
h2 = 4 ft
4 ft
SG = 1
Gate with 5
Lecture 5: MEC516 FLUID MECHANICS I
2012
1/2
Basic Equation of Fluid Statics
Lets consider a small volume (element) of fluid in a static fluid.
Note: Static fluid has no shear stress ( = 0), because t