Fluid Mechanics 3502 Day 1, Spring...

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Fluid Mechanics 3502 Day 1, Spring 2019 Syllabus Introduction Fluid Properties Part I Instructor Dr. Michele Guala, CEGE. Department UMN Office hours: (Tue-Thu) CEGE 162 9:30-10:30 ?1:30-2? Tue Thu CEGE phone (612) 626-7843 (Mon,Wed,Fr) SAFL, 2 Third Ave. SE, office 382, Phone (612)-625-9108 Class webpage http://personal.cege.umn.edu/~guala/webpage_CE3502_mic/index.html

Transcript of Fluid Mechanics 3502 Day 1, Spring...

Page 1: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

Fluid Mechanics 3502 Day 1, Spring 2019

Syllabus

Introduction

Fluid Properties Part I

Instructor Dr. Michele Guala, CEGE. Department UMN

Office hours: (Tue-Thu) CEGE 162 9:30-10:30 ?1:30-2?

Tue Thu CEGE phone (612) 626-7843

(Mon,Wed,Fr) SAFL, 2 Third Ave. SE, office 382, Phone (612)-625-9108

Class webpage http://personal.cege.umn.edu/~guala/webpage_CE3502_mic/index.html

Page 2: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

Introduction: Fluid Mechanics

To design and manage these systems we need to know :

• The STATE of the Fluid --- Usually PRESSURE (p ) and VELOCITY (u,v,w) at TEMPERATURE (T)

• The interaction of the fluid with its surroundings (Force, Torque, Boundary conditions)

Storing-

Moving-

Using-

Page 3: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

e.g., Density, Specific Weight, Viscosity

1. Knowing Fluid Properties

Response to shear stress

Four steps necessary to solve Fluid Mechanics problems

Page 4: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

e.g., Density, Specific Weight, Viscosity

1. Knowing Fluid Properties

Response to shear stress

Four steps necessary to solve Fluid Mechanics problems

2. Understanding Forces in Fluids and on their boundaries

e.g., Pressure force, Surface tension Lift & Drag

drag

Page 5: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

e.g., Density, Specific Weight, Viscosity

1. Knowing Fluid Properties

Response to shear stress

Four steps necessary to solve Fluid Mechanics problems

2. Understanding Forces in Fluids and on their boundaries

e.g., Pressure force, Surface tension Lift & Drag

drag

3. Using Conservation Equations

Mass Energy Momentum

u(x,t)

n

For example, For an arbitrary fixed volume in a steady flow field u

Net flow out of volume = A

dAnu = 0

Page 6: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

e.g., Density, Specific Weight, Viscosity

1. Knowing Fluid Properties

Response to shear stress

Four steps necessary to solve Fluid Mechanics problems

2. Understanding Forces in Fluids and on their boundaries

e.g., Pressure force, Surface tension Lift & Drag

drag

3. Using Conservation Equations

Mass Energy Momentum

Conservation of Mass (Volume) For steady state

Q -- volume flow rate Sum of Qin = sum of Qout

Red=control volume

Page 7: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

e.g., Density, Specific Weight, Viscosity

1. Knowing Fluid Properties

Response to shear stress

Four steps necessary to solve Fluid Mechanics problems

2. Understanding Forces in Fluids and on their boundaries

e.g., Pressure force, Surface tension Lift & Drag

drag

3. Using Conservation Equations

Mass Energy Momentum

mgh

2

21 mv

Conservation of Energy (Bernoulli—If losses are neglected, e.g., steady state )

2mv2

1mgh

Page 8: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

e.g., Density, Specific Weight, Viscosity

1. Knowing Fluid Properties

Response to shear stress

Four steps necessary to solve Fluid Mechanics problems

2. Understanding Forces in Fluids and on their boundaries

e.g., Pressure force, Surface tension Lift & Drag

drag

3. Using Conservation Equations

Mass Energy Momentum

What is resistance force Fr ?

Net External Force = rate of change of momentum

Conservation of Momentum

rcjcj F)VV)(VV(A

Newton's 2nd Law Review Dynamics -Statics

Fr

Page 9: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

e.g., Density, Specific Weight, Viscosity

1. Knowing Fluid Properties

Response to shear stress

Four steps necessary to solve Fluid Mechanics problems

2. Understanding Forces in Fluids and on their boundaries

e.g., Pressure force, Surface tension Lift & Drag

drag

3. Using Conservation Equations

Mass Energy Momentum

h

Fx

IN1

IN2

OUT1

OUT2

Fy

Page 10: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

e.g., Density, Specific Weight, Viscosity

1. Knowing Fluid Properties

Response to shear stress

Four steps necessary to solve Fluid Mechanics problems

2. Understanding Forces in Fluids and on their boundaries

e.g., Pressure force, Surface tension Lift & Drag

drag

3. Using Conservation Equations

Mass Energy Momentum

4. Using Dimensional Analysis

Page 11: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

Fluid Properties – Part 1

Solid-Liquid-Gas

Solid under shear vs Liquid under Shear

Specific Weight

Compressible vs. Non-Compressible

Viscosity

Newtonian vs. Non-Newtonian Fluids

Surface Tension

Vapor Pressure

Page 12: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

Fluid Properties – Part 1

Solid-Liquid-Gas

Solid under shear vs Liquid under Shear

Specific Weight

Compressible vs. Non-Compressible

Viscosity

Newtonian vs. Non-Newtonian Fluids

Surface Tension

Vapor Pressure

Page 13: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

Some properties of fluids

• Solid – Fluid Solid – liquid – gas

– How to best distinguish between them?

– Certain properties, and response to container boundaries

• Mass, density, weight, and the “specifics”

Page 14: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

Solid-Liquid and Gas – response to stationary boundaries

Liquid will maintain its volume (mostly) but change its shape according to that of the container.

Surface Tension can be important.

If no force is applied, a solid will always retain its shape

Solid

Fluid – liquid or gas

Fluid – liquid or gas

Gas will always change its volume to completely fill its container No Surface Tension.

Summary (See Table 1.1)

Solid– retains shape & volume

Liquid– retains volume & deforms

Gas– retains mass, not volume or shape

Fluids

Page 15: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

Imagine an elastic solid held between two plates-and then applying a shear force to the top plate

Then imagine a long aquarium and a wooden block floating on the surface – let us apply a force to that block.

Bottom layer does not move—The NO SLIP condition

Solid-Liquid and Gas – response to forces at the boundaries

Top layer of fluid moves with velocity of the block

A solid resists to an applied force, only if it deforms. When the force decays, the solid returns to its initial position. the force per unit area is a shear stress = F/ Area

E.g., in a linear elastic solid, resistance is proportional to the amount of deformation (shear or strain). think about a spring

A fluid resists to the applied forces only if it flows (Newtonian fluids): the deformation rate, also known as the shear rate, within the fluid, represent a spatial variation of the fluid velocity. Deformation alone does not create a stress opposing to motion (there is no memory of the initial location of fluid parcels, no crystals matrix...).

E.g., in a Newtonian fluid, resistance is proportional to the shear rate.

variation in angular displacement dx/dy

variation in fluid velocity (dx/dt)/dy = dv/dy or temporal variation of the strain

y

x

Page 16: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

Dimensions, Units, etc.

• Length : L meter [m] 1m=3.281 ft

• Mass : M kilogram [kg] 1kg=2.2 lbm

• Time : t seconds [s]

• Temperature: T Kelvin [K] K=(F-32)/1.8+273.15

• gravity g = 9.81 m/s2 = 32.3 ft/s2

• density water(T) ~1000kg/m3 = 62.4 lbm/ft3

• density air (T) ~ 1 kg/m3

Page 17: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

Continuum Assumption We discuss the fluid behavior as observed in the range of scale typical of classical mechanics This is the macroscopic averaged behavior of a vast number of molecules. We define the fluid density:

𝜌 = ∆𝑀

∆𝑉 =

𝑀

𝑉

to be independent of ∆𝑉 In the case of water the continuum assumption is valid down to a cube of about L = 10-4 mm, = 10-7 m. In air (standard condition) L = 10-3 mm Note that the no-slip condition must apply when the continuum approach is valid (otherwise molecular dynamics) Note also that very large scales L may require additional care due to variation in density within the (very large ) Volume continuity is respected only if we account for variation in density as well: e.g. atmospheric flows are continuous, but fluid properities vary within

Page 18: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

Dimensions

Primary dimension: M L t

Secondary dimensions: e.g. F = ma ; [N] = [kg m s-2] = 𝐾𝑔 𝑚

𝑠2

Important: 1) always provide Eng. solutions with units, e.g. v = 3 m/s 2) always check that equations are dimensionally consistent

LHS (left hand side) = RHS e.g. L = L0 + v t + 𝑔𝑡2

2

3) often describe physical processes in dimensionless groups

e.g. Reynolds number = 𝑣 𝐿

ν

4) often present experimental results in dimensionless form e.g. pipe flow U/Uc = 0.3 at y/D=0.1

Page 19: Fluid Mechanics 3502 Day 1, Spring 2019personal.cege.umn.edu/~guala/webpage_CE3502_mic/notes/day01.pdf · 1. Knowing Fluid Properties Response to shear stress Four steps necessary

Some guidelines on proper scientific writing and homework preparation

1) make a sketch, assign variable names and reference system

2) Define the boundary conditions provide initial values of the known variables

3) Briefly state what is the question of the problem and mark the unknown variable

(INTRODUCTION)

4) Describe how you want to approach the problem and present the equations you intend to

use

5) List the assumptions that are needed to simplify the problem consistently with the above

equations (METHOD)

6) Briefly describe each step of your calculation, using both symbolic variables and actual

numbers

7) Make sure that units are always consistent in the equations and in the resulting variables

8) When required, provide figures or graphs that support your statements. Make sure that

figure axis are defined (variable name and units) and that in the figure caption all the

variable names and symbols used in the axis or legend are briefly described in words.

(RESULTS)

9) Highlight the final numerical result and, when required, explain in words the outcome of

your work/laboratory experimentation (CONCLUSION)