Bernoulli’s Principle
Lecturer:
Professor Stephen T. Thornton
Reading Quiz
A sitting person’s 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 person’s leg instead?
A)
B)
C)
D)
blood pressure would be lower
blood pressure would not change
blood pressure would be higher
not enough information given to
determine
Reading Quiz
A sitting person’s blood
pressure is measured on the
A) blood pressure would be lower
arm, at approximately the
same level as the heart. How B) blood pressure would not change
would the results differ if the C) blood pressure would be higher
measurement were made on D) not enough information given to
determine.
the person’s leg instead?
Assuming that the flow speed of the blood does not change, then
Bernoulli’s equation indicates that at a lower height, the pressure
will be greater.
Last Time
Pascal’s Principle
Buoyancy
Archimedes Principle
Mass flow – equation of continuity
Today
Bernoulli equation/principle
Applications of Bernoulli principle
Read all remaining sections of chapter
Conceptual Quiz
Water flows through a 1-cm diameter pipe
connected to a
1
2
-cm diameter pipe.
Compared to the speed of the water in the
1-cm pipe, the speed in the
higher (or lower) by
1
2
-cm pipe is
A) one-quarter
B) one-half
C) the same
D) double
E) four times
Conceptual Quiz
A) one-quarter
Water flows through a 1-cm diameter pipe
connected to a
1
2
B) one-half
-cm diameter pipe.
C) the same
Compared to the speed of the water in the
1-cm pipe, the speed in the
1
2
D) double
-cm pipe is
E) four times
higher (or lower) by
v1
v2
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.
Bernoulli’s 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.
1 2
P   v   gy
2
is a constant
1 2
1 2
P1   v1   gy1  P2   v2   gy2
2
2
Bernoulli’s equation, first version
At constant height, h1 = h2 ,
1 2
1 2
P1   v1  P2   v2
2
2
1 2
or P   v is constant.
2
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!!
Answer: A
A1v1 = A2v2
High v, low P.
Conceptual Quiz:
Blood 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.
Before
After
Answer: D
The volume and mass flow must not
change throughout or else blood would
pile up somewhere along the artery.
Conceptual Quiz:
The pressure in which part of the coronary
artery is the least?
A)
B)
C)
D)
The narrow part.
The wide part before the deposits.
The wide part after the deposits.
The pressure is the same in all parts.
Before
After
Answer: A
The pressure will be least where the
speed is the greatest. That will be in
the narrow part of the artery.
Before
After
The Bernoulli Effect on a Sheet of Paper
Do demo
Wings are designed to cause air to flow
faster over top of the wing. Causes
pressure differential resulting in lift.
High speed, low pressure
Low speed, high pressure
True for birds and airplane wings, but not the whole story!
Force on a Roof Due to Wind Speed
Very high speed, low pressure
Very low speed, normal pressure
Roof might blow off
during hurricane!
Air Circulation in a Prairie Dog Burrow
Lower P
Higher P
An Atomizer – Fast air (low pressure)
causes fluid to rise in tube.
Do demo
Pitot tube
used to measure
the speed of
airplanes.
Conceptual Quiz:
Soft top SUV drives fast. What happens to
soft top?
A) Soft top bows up.
B) Soft top is flat.
C) Soft top bows down.
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.
Do lots of demos
(curve ball next slide)
Why does a baseball or softball curve?
Increased air speed.
Lower pressure.
v
F
Spinning ball drags air
ball
Lower air speed.
Higher pressure
Throw
curveballs.
Fluid Emerging from a Hole in a Container
See next slide.
Calculate speed of water coming out.
0
1 2
1 2
P1   v1   gy1  P2   v2   gy2
2
2
We have P1  Pat  P2
v1  0 and y1  y2  h
1 2
So  gh   v2
2
v2  2 gh
known as Toricelli's Law
Do demo
Maximum Height of a Stream of Water
v  2gh
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).
No friction
Fluid Flow
Through a Tube
With friction
Do toilet paper apparatus demo
Conceptual Quiz
An object floats in water with
3
4
of its volume submerged.
A) have more than ¾ submerged
B) stay at the same place
When more water is poured
C) have less than ¾ submerged
on top of the water, the
D) sink to the bottom
object will:
E) float up a little
Conceptual Quiz
An object floats in water with
3
4
A) have more than ¾ submerged
of its volume submerged.
B) stay at the same place
When more water is poured on
C) have less than ¾ submerged
top of the water, the object will:
D) sink to the bottom
E) float up a little
3
We already know that density of the object is 4 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.
Conceptual Quiz
How is the smoke
drawn up a chimney
affected when there is
a horizontal wind
blowing outside?
A)
B)
C)
D)
smoke rises more rapidly in the chimney
smoke is unaffected by the wind blowing
smoke rises more slowly in the chimney
smoke is forced back down the chimney
Conceptual Quiz
How is the smoke
drawn up a chimney
affected when there is
a horizontal wind
blowing outside?
A)
B)
C)
D)
smoke rises more rapidly in the chimney
smoke is unaffected by the wind blowing
smoke rises more slowly in the chimney
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.