Transcript Electric Potential - McMaster Physics and Astronomy

Day of Wrath
Tuesday June 16
9:30-11:30 am
CNH-104
30 MC Questions, Cumulative
Physics 1B03summer-Lecture 12
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Fluid Mechanics
• Pressure
• Buoyancy
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Buoyancy
The fluid exerts an upward force on
the object equal to the weight of fluid
displaced.
This force is result of pressure
differences in the fluid; the pressure is
greater at the bottom than at the top.
This is why objects can ‘float’: the
magnitude of the buoyant force equals
that of the force of gravity:
B = Fg
P1
h
P2
so:
B = mg = ρoVog
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Archimedes’s Principle: the magnitude of the buoyant
force always equals the weight of the fluid displaced by
the object.
Question: A boat filled with bricks floats in a swimming pool. If the
bricks are dumped overboard does the water level in the pool rise,
or fall?
?
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Totally Submerged Object
For an object submerged in a fluid with ρf the upward force is
B=ρfVog (=weight of fluid displaced) and so the net force is:
B – Fg = ρfVog - ρoVog
= (ρf – ρo)Vog
Floating Object
For a floating object, it displaces a volume of fluid equal to its
own volume, and so:
B = Fg
ρfVfg = ρoVog
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Example
A giant ice cube (r = 917 kg/m3) floats in a pail of cold water. If
the cube is 100.0 mm on each side, how far is the top surface of
the ice above the water?
When the ice melts, does the level of water in the pail rise or fall?
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Example
A beach ball of mass 0.05 kg and radius of 0.2 m is filled with air
(density = 1.29 kg/m3) and placed under water.
a) What is the net force on the ball?
b) What is the acceleration of the ball?
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Example:
How heavy a balloon can 100 litres of helium lift? (ρHe=0.18kg/m3)
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Example
A 10-kg rock (density 2500 kg/m3) is suspended in a large
bucket of water by a cord. What is the tension in the cord?
tension = ?
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10 min rest
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Fluid Dynamics
•
•
Equation of Continuity
Bernoulli’s equation and examples
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Fluid Dynamics
Approximations:
1) no viscosity (frictionless flow)
2) steady, “laminar” flow. If the flow is turbulent, mechanical
energy is lost (converted to thermal energy).
3) “incompressible” fluid. Sufficiently accurate for gases if
pressure differences are small.
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Streamlines
-the paths followed by particles in steady flow
-velocity is parallel to the streamline
- particles never cross streamlines; the streamlines mark out
imaginary “tubes of flow”
area A1
speed v1
area A2
speed v2
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Equation of Continuity
“Volume flow rate” (volume per unit time)
= (cross-sectional area)  (linear velocity)
“Mass flow rate” (mass per unit time)
= (density)  (volume flow rate)
So, if mass in = mass out, then
rAv = mass flow rate = constant
or
r1A1v1 = r2A2v2
for steady flow.
“Incompressible” fluids (density remains uniform): cancel out
density to get
Volume flow rate = constant
or
A1v1 = A2v2
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A fluid if flowing through a pipe of 10mm radius at a velocity of
10m/s. How fast will it be flowing if the pipe narrows to 5mm in
radius ?
radius
r1 = 10mm
radius
r2 = 5mm
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Bernoulli’s Equation: work and energy in fluids
Conditions: steady flow, incompressible fluid.
Look at energy balance along a streamline:
Change in (kinetic energy/volume)
+ change in (potential energy/volume)
= (net work by pressure)/volume
then,
or,
P1  12 rv12  rgy1 = P2  12 rv22  rgy2
P  12 rv 2  rgy = a constant along a streamline
Note: the above equation looks similar what we have
seen before if we replace ρ by m.
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Example
a) What is the velocity of the water
leaving the little hole
b) How far (horizontally) from the hole
does the water hit the ground?
d
h
x
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Example
What is the speed of the water leaving
the hole in the tank?
gauge pressure P0
h
v
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Example
Water moving at 10m/s through a 1m radius pipe at a pressure
of 50kPa. It then falls 50m and goes into a 0.3m radius
pipe. What is the water pressure at the bottom ?
h
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Exam Tips + Course Evaluations
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