Bernoulli

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Bernoullis Principle Lecturer Professor
Stephen T. Thornton
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Reading Quiz
A sitting persons blood pressure is measured on
the arm, at approximately the same level as the
heart. How would the results differ if the
measurement were made on the persons leg instead?
A) blood pressure would be lower B) blood
pressure would not change C) blood pressure
would be higher D) not enough information given
to determine
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Reading Quiz
A sitting persons blood pressure is measured on
the arm, at approximately the same level as the
heart. How would the results differ if the
measurement were made on the persons leg instead?
A) blood pressure would be lower B) blood
pressure would not change C) blood pressure
would be higher D) not enough information
given to determine.
Assuming that the flow speed of the blood does
not change, then Bernoullis equation indicates
that at a lower height, the pressure will be
greater.
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Last Time

• Pascals Principle
• Buoyancy
• Archimedes Principle
• Mass flow equation of continuity

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Today

• Bernoulli equation/principle
• Applications of Bernoulli principle
• Read all remaining sections of chapter

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Conceptual Quiz

• Water flows through a 1-cm diameter pipe
  connected to a -cm diameter pipe. Compared to
  the speed of the water in the 1-cm pipe, the
  speed in the -cm pipe is higher (or lower) by

A) one-quarter B) one-half C) the same D)
double E) four times
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Conceptual Quiz

• Water flows through a 1-cm diameter pipe
  connected to a -cm diameter pipe. Compared to
  the speed of the water in the 1-cm pipe, the
  speed in the -cm pipe is higher (or lower) by

A) one-quarter B) one-half C) the same D)
double E) four times
The area of the small pipe is less, so we know
that the water will flow faster there. Because A
? r2, when the radius is reduced by one-half, the
area is reduced by one-quarter, so the speed must
increase by four times to keep the flow rate (A ?
v) constant.
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Bernoullis Equation (or Principle)

• It is basically a conservation of energy.
• Was derived using work-energy theorem.
• Works for fluids (gases and liquids).
• We ignore friction.

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Bernoullis equation, first version

• At constant height, h1 h2 ,
• This may seem odd, because it says
• as the pressure increases, the speed decreases
  within the fluid.
• Remember high v, low P and vice versa!!

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(No Transcript)
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Answer A A1v1 A2v2 High v, low P.
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Conceptual QuizBlood flows through a coronary
artery that is partially blocked by deposits of
plaque along the artery wall. Through what part
of the artery is the volume flow of blood the
largest?  A) The narrow part. B) The wide
part before the deposits. C) The wide part
after the deposits. D) The volume flow is
the same in all parts.
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Answer D

• The volume and mass flow must not change
  throughout or else blood would pile up somewhere
  along the artery.

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Conceptual QuizThe pressure in which part of
the coronary artery is the least? A) The narrow
part.B) The wide part before the
deposits.C) The wide part after the
deposits.D) The pressure is the same in all
parts.
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Answer A

• The pressure will be least where the speed is the
  greatest. That will be in the narrow part of the
  artery.

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The Bernoulli Effect on a Sheet of Paper
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Wings are designed to cause air to flow faster
over top of the wing. Causes pressure
differential resulting in lift.
True for birds and airplane wings, but not the
whole story!
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Force on a Roof Due to Wind Speed
Roof might blow off during hurricane!
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Air Circulation in a Prairie Dog Burrow
Lower P
Higher P
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An Atomizer Fast air (low pressure) causes
fluid to rise in tube.
Do demo
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Pitot tube used to measure the speed of airplanes.
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Conceptual QuizSoft top SUV drives fast. What
happens to soft top?
A) Soft top bows up. B) Soft top is
flat. C) Soft top bows down.
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Answer A

• Air speed on top is high, so pressure is low.
  Air speed inside SUV is very low, so pressure is
  normal. Pressure results in force pushing up.

High speed, low pressure.
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Do lots of demos (curve ball next slide)
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Why does a baseball or softball curve?
ball
Throw curveballs.
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Fluid Emerging from a Hole in a Container
See next slide.
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Calculate speed of water coming out.
0
Do demo
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Maximum Height of a Stream of Water
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Hurricane. A hurricane-force wind of 200 km/h
blows across the face of a storefront window.
Estimate the force on the 2.0 m x 3.0 m window
due to the difference in air pressure inside and
outside the window. Assume the store is airtight
so the inside pressure remains at 1.0 atm. (This
is why you should not tightly seal a building in
preparation for a hurricane).
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Fluid Flow Through a Tube
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Do toilet paper apparatus demo
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Conceptual Quiz
A) have more than ¾ submerged B) stay at the
same place C) have less than ¾ submerged D)
sink to the bottom E) float up a little

• An object floats in water with of its volume
  submerged. When more water is poured on top of
  the water, the object will

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Conceptual Quiz
A) have more than ¾ submerged B) stay at the
same place C) have less than ¾ submerged D)
sink to the bottom E) float up a little

• An object floats in water with of its volume
  submerged. When more water is poured on top of
  the water, the object will

We already know that density of the object is
of the density of water, so it floats in water
(i.e., the buoyant force is greater than its
weight). When covered by more water, it must
therefore float to the top.
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Conceptual Quiz
How is the smoke drawn up a chimney affected
when there is a horizontal wind blowing outside?
A) smoke rises more rapidly in the chimney B)
smoke is unaffected by the wind blowing C)
smoke rises more slowly in the chimney D)
smoke is forced back down the chimney
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Conceptual Quiz
How is the smoke drawn up a chimney affected
when there is a horizontal wind blowing outside?
A) smoke rises more rapidly in the chimney B)
smoke is unaffected by the wind blowing C)
smoke rises more slowly in the chimney D)
smoke is forced back down the chimney
Due to the speed of the wind at the top of the
chimney, there is a relatively lower pressure up
there as compared to the bottom. Thus, the smoke
is actually drawn up the chimney more rapidly,
due to this pressure difference.