This document defines fluids and key fluid dynamics concepts like density, pressure, buoyancy, and Bernoulli's principle. It discusses how fluids are classified as liquids or gases based on their ability to flow and change shape. Density is defined as mass per unit volume. Pressure increases with depth in a fluid. Archimedes' principle and buoyant force are explained. Bernoulli's principle states that as fluid speed increases, pressure decreases, conserving total energy in the system.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
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Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
How to Make a Field invisible in Odoo 17Celine George
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The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
2. Define a Fluid
Matter is normally classified in one of three
groups
Solid, Liquid, Gas
Liquids share a commonality with gases in
that they can flow and alter their shape as
they flow
Solids do not share this property, they cannot
flow nor can they readily change their shape;
solids are not fluids
3. Definite Volume
Even though both liquids and gases are
fluids, they have a distinct difference
Liquids have a definite volume
Say you have a one gallon gasoline can full of
fuel
If you pour the entire can into a lawn mower fuel
tank, there will still be one gallon of gasoline
4. Indefinite Volume
Gases have neither definite volume or shape
When a gas is poured, not only does it
change its shape to fit the new container, the
gas expands to fill the new container
5. Density and Buoyant Force
Have you ever felt uncomfortable in a
crowded room? Probably because there
were too many people for the amount of
space; the density of people was too high
Density is how much there is of a quantity in
a given amount of space
The quantity can be anything from people to cars
to mass or energy
6. Density and Buoyant Force
Mass density is mass per unit volume of a
substance
When we talk about a fluid’s density, we are
really talking about mass density
Mass density is represented by the Greek
letter rho (ρ)
capital V for volume
The SI unit for mass density is kg/m3
ρ =
m
V
7. Pressure
Solids and liquids tend to be incompressible
Their density change very little with changes
in pressure
Gases are not completely incompressible
meaning their volumes are greatly affected by
pressure
That is why there is no standard density for
gas as there is for solids and liquids
8. Buoyant Force
Have you noticed that heavy objects seem
lighter under water
It is much easier to pick up a person in a
swimming pool than on dry ground
That is because the water exerts an upward force
on objects that are partially or completely
submerged
The upward force is called the buoyant force
9. Buoyant Force
Have you ever laid on a raft in a pool
You and the raft experience a buoyant force,
which keeps both you and the raft afloat
Because the buoyant force acts in the opposite
direction as the force of gravity, objects
submerged in a fluid such as water have a net
force on them that is smaller than their weight
10. Buoyant Force
This means they appear to weigh less in
water
The weight of an object immersed in a fluid is the
object’s apparent weight
11. Archimedes’ Principle
Imagine you fill a bucket to the top and drop
in a brick
What happens? Why?
The total volume of water that overflows is the
displaced volume of water. The volume of the
water is equal to the volume of the portion of the
brick that is underwater
12. Archimedes’ Principle
The magnitude of the buoyant force acting on
the brick is known as Archimedes’ Principle
Any object completely or partially submerged in a
fluid experiences an upward buoyant force equal
in magnitude to the weight of fluid displaced by
the object
Archimedes’ principle can be written as
F m gB f=
13. Archimedes’ principle
Whether an object will float or sink depends
of the net force acting on it
This net force is the object’s apparent weight
and can be calculated as follows
F F F objectnet B g= − ( )
14. Archimedes’ principle
Now apply Archimedes Principle, using mo to
represent the mass of the object
Rewrite using that idea
F m g m gnet f o= −
F V V gnet f f o o= −( )ρ ρ
15. Archimedes’ principle
A floating object cannot be denser than the
liquid in which it floats
The expression for the net force on an object
floating on the surface gives the following
result
Or:
F V V gnet f f o o= = −0 ( )ρ ρ
ρ
ρ
f
o
o
f
V
V
=
16. Archimedes’ principle
We know the displaced volume of fluid can
never be greater than the volume of the
object
That means for an object to float the object’s
density must be less than the displaced
fluid’s density
If the volume of the object is equal to the
volume of displaced liquid, the entire object is
submerged
17. Floating Objects
For floating objects, the buoyant force equals
the object’s weight
Imagine a raft with cargo floating on a river
Two forces act on the raft and the cargo
The downward force of gravity
The upward buoyant force
Because the raft is floating, the raft is in
equilibrium and the two forces are balanced
18. Floating Objects
This means for floating objects the force of
gravity is equal to the buoyant force
As in
Notice for a floating object, the buoyant force
can be found by using the first condition of
equilibrium, Archimedes’ principle would be
overkill in such a situation
F m gB o=
19. Apparent Weight
The apparent weight of a submerged object
depends of density
Think of or raft from earlier
Imagine a hole is punched in the raft
The raft and cargo eventually sink below the water’s
surface
The net force on the raft and cargo is the difference
between the buoyant force and the weight of the raft
and cargo
20. Apparent Weight
As the volume of the raft decreases, the volume of
displaced water also decreases, as does the
magnitude of the buoyant force
This is shown with
After the raft becomes completely submerged, the two
volumes are equal
Notice that both the direction and the magnitude of the
net force depend on the difference between the
density of the object and the density of the fluid in
which it is immersed
F V V gnet f f o o= −( )ρ ρ
F Vgnet f o= −( )ρ ρ
21. Apparent Weight
If the object’s density is greater than the fluid density,
the net force is negative (downward) and the object
sinks
If the object’s density is less than the fluid density, the
net force is positive and the object rises to the surface
and floats
If the densities are the same, the object floats, but
underwater
A simple relationship between the weight of a
submerged object and the buoyant force on the object
can be found by considering their ratios as follows
m g
F
o
B
o
f
=
ρ
ρ
23. Pressure
You experience pressure everyday
When you dive to the bottom of a swimming pool
When you drive up a large hill
When you ride in a airplane
24. Pressure
Pressure is force per unit area
The fluids above are exerting force against your
eardrums, so your ears want to ‘pop’ to adjust for
the pressure change
Pressure is measure of how much force is applied
of a given area. It can be written as
P
F
A
=
25. Pressure
The SI unit of pressure is the N/m2 which is
called a Pascal (Pa)
A Pascal is a very small amount of pressure.
Air pressure at sea level is about 105 Pa which is
1 atm
The total air pressure in a typical automobile tire
is about 300000 Pa or 3 atm.
26. Fluids Exert Pressure
When you use a bicycle pump to put air into a
tire, you apply force on the piston, which
exerts a force on the gas inside the tire.
The gas pushes back on the piston and on the
walls of the tire.
The pressure is the same throughout the volume
of the gas
27. Hydraulic Pressure
An important use of fluid pressure is the
hydraulic press
Garages can use a motor to generate a large
force over a small area to provide a force to equal
a large area, such as lifting a car
F
A
F
A
1
1
2
2
=
28. Pressure and Depth
Pressure varies with depth in a fluid
As a submarine dives into the water the pressure
of the water against the hull of the sub increases.
Water pressure increases with depth because the
water at a given depth must support the weight of
the water.
The weight of the entire column of water above an
object exerts force on the object.
29. Pressure and Depth
The column of water exerting force has a
volume equal to Ah were A is the cross
sectional area and h is the depth.
The pressure at a depth caused by the
weight of a volume of water can be calculated
as
P
F
A
mg
A
Vg
A
Ahg
A
hg= = = = =
ρ ρ
ρ
30. Gauge Pressure
This pressure is referred to as gauge
pressure. It is NOT the total pressure at this
depth because atmospheric pressure is
applying pressure at the surface.
Absolute pressure P is calculated
Po is atmospheric pressure
P P hgo= + ρ
31. Atmospheric Pressure
Atmospheric pressure is pressure from above
The weight of the air pushing down on the earth
and the bodies on earth is known as atmospheric
pressure.
Atmospheric pressure is actually quite large,
assuming a SA of 2 m2, ATM is 200,000 N.
How can our bodies withstand such an
incredible force without being crushed?
Bodies are in equilibrium, fluids inside push back
with the same force creating a state of balance
33. Ideal Fluid
Ideal fluid model simplifies fluid flow analysis
Many fluid features are considered by studying an
ideal fluid
No real world fluid is an ideal fluid, but an ideal
fluid does showcase many properties of real world
fluids
34. Idea Fluid
We assume an ideal fluid is incompressible,
meaning the density always remains constant
We also assume an ideal fluid is nonviscous
Viscosity refers to the amount of internal friction in
a fluid
A fluid with a high viscosity tries to bond with its
container and flows more slowly than a low
viscous fluid
35. Ideal Fluid
Another property of an ideal fluid is ideal flow
We assume the velocity, density and pressure at
every point in the fluid is constant.
This is known as non-turbulent flow, there can be
no undertows or rip currents present in the
moving fluid
36. Conservation Laws of Fluids
If a fluid flows into a pipe, the mass that flows
into the pipe must equal the mass exiting the
pipe, even if the diameter of the pipe changes
x2
x1
V2
V1
A2
A1
37. Conservation Laws in Fluids
This can be shown as
Recall and
and recall
Both the time interval and density remain
constant though (ideal fluid), so they are
cancelled and we are left with
m m1 2=
m V= ρ V A x= ∆
ρ ρ1 1 1 2 2 2A x A x∆ ∆= v
d
t
=
ρ ρ1 1 1 1 2 2 2 2A v t A v t=
A v A v1 1 2 2=
38. Conservation Laws in Fluids
This is referred to as the continuity equation
where A shows two different cross sectional
areas and v shows two different velocities
A v A v1 1 2 2=
39. Conservation Laws in Fluids
As the cross sectional area increases, the
velocity slows, and as the cross sectional
area decreases, the velocity increases to flow
the same volume of water
The flow rate remains constant regardless
the diameter of the pipe
40. Conservation Laws in Fluids
The expressions for conservation of energy in
fluids differs slightly from our previous form
studied in chapter 5
The reason is that fluids also exert pressure,
so the conservation equation must take into
account the pressure of the fluids
A change in pressure can be related to the
transfer of energy into or out of the volume.
We must account for this energy.
41. Conservation Laws in Fluids
As a fluid moves through a pipe of varying
cross sectional area and elevation, the
pressure and speed can change, but the total
energy does not.
Bernoulli’s equation explains such a situation
constant, that is to say conservedP v gh+ + =
1
2
2
ρ ρ
42. Conservation Laws in Fluids
We can set up a version of the equation to
compare the energy of a fluid at two different
points in a pipe
P v gh P v gh1 1
2
1 2 2
2
2
1
2
1
2
+ + = + +ρ ρ ρ ρ
43. Special Case 1
Lets say the fluid is not moving and the initial
height is zero
a pressure function of depth
P P gh1 2 2= + ρ
44. Special Case 2
Lets say a fluid is flowing through a horizontal
pipe with restriction
Since
This expression implies that if at some
point in the flow, then
P v P v1 1
2
2 2
21
2
1
2
+ = +ρ ρ
h h1 2=
v v2 1>
P P2 1<
45. Bernoulli’s Principle
Swiftly moving fluids exert less pressure than
slowly moving ones.
Reason why a curve ball curves, a plane can
fly, a soccer player can ‘bend it like Beckham’
and why homes are ripped to shreds during
hurricanes and tornadoes