Download States of Matter Density Pressure Buoyancy and Archimedes` Principle

EF 152
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Lec 4-5
States of Matter
Density
Gas
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Solid
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In a gas, the molecules are far apart
and the forces between them are very
small
In a solid, the molecules are very close
together, and the form of the solid
depends on the details of the forces
between them; that form is often a
lattice. Solids resist changes in shape.
Liquid
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In a liquid, the molecules are also
close together and resist changes in
density, but not in shape.
Pressure is force per unit area:
F
P=
A
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The pressure in a static fluid at
any point must be the same in all
directions.
Pressure increases with depth,
due to the force of gravity:
P1 = Po + ρgh
ρ=
m
V
Varies slightly with temperature and pressure.
Specific gravity of a substance is the density
of that substance divided by the density of
water at 4.0oC. SG = ρ
ρWater
Fluids (gasses and liquids),
cannot support a tensile or
shear load.
Pressure
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Density is mass per unit volume:
Buoyancy and Archimedes’ Principle
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Assume block is in equilibrium.
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Then upward forces must equal downward forces.
Upward force: pressure from fluid
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Downward force: atmospheric pressure plus weight
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Therefore
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Fup = Fdown
P2 − P1 = − ρg ( y2 − y1 )
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EF 152
Lec 4-5
Buoyancy and Archimedes’ Principle
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Archimedes’ Principle: The buoyant force on an
immersed object equals the weight of displaced fluid.
FBouyant = ρ w gVsubmerged
Hydrodynamics – Fluids in Motion
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Assumptions
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Continuity Equation
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Conservation of Mass
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For a given time t. the amount of “stuff” (mass) that passes
by someone at 1 must equal the amount of “stuff” mass that
masses by someone at two.
m1 = m2
ρA1Δl1 = ρA2 Δl2
ρA1v1t = ρA2 v2t
ρA1v1 = ρA2 v2
v1 A1 = v2 A2
The fluid is incompressible.
The temperature does not vary.
The flow is steady, so that the velocity and
pressure do not depend on time.
The flow is laminar rather than turbulent.
The flow is irrotational, so there is no circulation.
There is no viscosity in the fluid.
Bernoulli’s Equation
If a fluid is incompressible and has no
viscosity, energy is conserved. Therefore,
the work done on a “piece” of fluid is equal to
the change in its kinetic energy.
1
1
P1 + ρv12 + ρgy1 = P2 + ρv22 + ρgy2
2
2
1
⇒ P + ρv 2 + ρgy = constant
2
v=0
P2 − P1 = − ρg ( y2 − y1 )
y1 = y2
1
1
P1 + ρv12 = P2 + ρv22
2
2
2
EF 152
Lec 4-5
Lift
Real Fluids
1
1
Pb − Pt = ρvt2 − ρvb2
2
2
Viscosity
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Viscosity acts like a drag or frictional
force; it slows flow speed relative to a
surface.
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v is the average speed or slipstream speed.
If a wing has a width w and tip-to-tip span S
L = wSρKv 2
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K is a constant << 1
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Venturi Tube / Meter
⎡⎛ A ⎞ 2 ⎤
1
P2 − P1 = ρv12 ⎢⎜⎜ 1 ⎟⎟ − 1⎥
2
⎢⎣⎝ A2 ⎠
⎥⎦
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There are 8 problems worth 12 points each and graded on a
0, 3, 6, 8, 10 12 scale.
There are two questions per page and they MAY or MAY
NOT be related to each other.
If they are related to each other, you can use any and all the work that
you write out for your solution to the first problem for the solution of the
second problem on that page.
‰ You DO NOT need to redraw Coordinate Systems, FBDs, etc.
You can bring one sheet of notes (i.e., a “cheat sheet”)
‰ Must be on Engineering paper
‰ Front side ONLY
‰ In YOUR handwriting
‰ Put your name at top
‰ Anything you want to write
‰ You are to turn it in with the exam
‰ NO other books, notes, etc. are allowed.
Q=
πR 4 (P1 − P2 )
8ηL
Viscous (Poiseuille) Flow
Reynolds Number
ρ
Re = vL
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η
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Exam 4
You must show ALL work on ALL problems
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Coordinate system on all problems
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Final answers must have the correct SF
Vector symbols and answers when required
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Final answers must have correct and consistent units
Watch unit conversions and unit consistency
Significant Figures (SF)
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Provide generic versions of the equations
Units
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Make sure they are easily read, everything is labeled and the are complete
Equations
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When needed and not provided
FBD on all problems that need them
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ηvA
y
Turbulence.
Exam 4 – Friday, Oct 26
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Top: non-viscous velocity profile.
Bottom: same flow with viscosity.
F=
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Non – Viscous Flow
Use over bars or over arrows (hats for unit vectors)
Vector answers must be in either I j notation or magnitude and direction
format. Some questions may specify which format.
etc.
A cover sheet with Material Data, Useful Constants and Formulas will be provided.
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