Fluid Flows and Bernoulli’s Principle
5
Fluid Flows and Bernoulli’s Principle Streamlines demonstrating laminar (smooth) and turbulent flows of an ideal “fluid” WVU is an EEO/Affirmative Action Employer — Minority/Female/Disability/Veteran Celebrating Einstein was originally produced by Montana State University and the eXtreme Gravity Institute. More events and information: einstein.wvu.edu LECTURES “Fast Radio Bursts: The Story So Far” Duncan Lorimer, Center for Gravitational Waves & Cosmology March 31, 7:30 p.m. “When Black Holes Collide! Gravitational Waves and Other Tales from the Horizon” Zach Etienne, Center for Gravitational Waves & Cosmology, WVU Math Department April 7, 7:30 p.m. “Einstein Unyielding: A Catalyst in a New Berlin” Katherine Aaslestad, WVU History Department April 10, 7:30 p.m. “Beginning the Exploration of the Universe with Gravitational Waves” Rainer Weiss, Massachusetts Institute of Technology April 13, 7 p.m. “NANOGrav: Searching for Gravitational Waves with Pulsars” Maura McLaughlin, Center for Gravitational Waves and Cosmology April 18, 7:30 p.m. “Gravitational Wave Astronomy: Turning Imagination into Discovery” Joan Centrella, Goddard Space Flight Center April 20, 3:30 p.m. ART, DANCE AND SYMPHONY PERFORMANCES Danced Lecture and Interview Richard Price April 21, 7:30 p.m. Danced Lecture and Interview Shane Larson April 22, 2 p.m. April 22, 7:30 p.m. Danced Lecture and Interview Janna Levin April 23, 2 p.m. “A Shout Across Time” Community Symphony April 22, 4:30 p.m. April 23, 4:30 p.m. Einstein Artwork & Demonstrations April 21, 5 p.m. April 22, 4:30 p.m. April 23, 12 p.m. PLANETARIUM SHOWS Einstein planetarium night and rooftop telescope observing March 31, 8:30 p.m. April 7, 8:30 p.m. April 10, 8:30 p.m. April 19, 8:30 p.m. April 20, 8:30 p.m. DOCUMENTARIES “little green men” Pulsar Search Collaboratory Documentary April 17, 7 p.m. “LIGO, A Passion for Understanding” April 19, 7 p.m. SPACE RACE FUN RUN April 22, 9 a.m. CELEBRATING EINSTEIN March 31 - April 23, 2017 Over 100 years ago, Einstein predicted gravitational waves, and we are just beginning to detect them now. You are invited to join our interdisciplinary celebration to understand the beauty and significance of these transformative discoveries about our universe. “Imagination is more important than knowledge.” - Albert Einstein http://einstein.wvu.edu/ Extra credit opportunity (up to 10 points added to final exam grade) (this equates to 2.5 points added to your FINAL GRADE AVERAGE) http://einstein.wvu.edu/ Attend an event.* Write a report: 1. What event did you attend? 2. What were the main (physics/ astronomy) ideas discussed? 3. Relate them in some way to principles we learned in class. 4. What was the coolest thing you learned from the event? Extra credit opportunity (up to 10 points added to final exam grade) (this equates to 2.5 points added to your FINAL GRADE AVERAGE) *space fun run excluded but will be really cool! I will NOT ACCEPT any turned in after APRIL 28! v = Δx/t Velocity a = Δv/t Acceleration = Volume through a surface per time Volume flow rate Thinking about rates…
Transcript of Fluid Flows and Bernoulli’s Principle
Fluid Flows and Bernoulli’s Principle
Streamlines demonstrating laminar (smooth) and turbulent flows of an ideal “fluid”
WVU is an EEO/Affirmative Action Employer — Minority/Female/Disability/VeteranCelebrating Einstein was originally produced by Montana
State University and the eXtreme Gravity Institute.
More events and information: einstein.wvu.edu
LECTURES
“Fast Radio Bursts: The Story So Far”Duncan Lorimer, Center for Gravitational Waves & Cosmology
March 31, 7:30 p.m.
“When Black Holes Collide! Gravitational Waves and Other Tales from the Horizon”Zach Etienne, Center for Gravitational Waves & Cosmology,
WVU Math Department
April 7, 7:30 p.m.
“Einstein Unyielding: A Catalyst in a New Berlin” Katherine Aaslestad, WVU History Department
April 10, 7:30 p.m.
“Beginning the Exploration of the Universe with Gravitational Waves”Rainer Weiss, Massachusetts Institute of Technology
April 13, 7 p.m.
“NANOGrav: Searching for Gravitational Waves with Pulsars”Maura McLaughlin, Center for Gravitational Waves and
Cosmology
April 18, 7:30 p.m.
“Gravitational Wave Astronomy: Turning Imagination into Discovery”Joan Centrella, Goddard Space Flight Center
April 20, 3:30 p.m.
ART, DANCE AND SYMPHONY PERFORMANCESDanced Lecture and InterviewRichard Price
April 21, 7:30 p.m.
Danced Lecture and Interview Shane Larson
April 22, 2 p.m.
April 22, 7:30 p.m.
Danced Lecture and Interview Janna Levin
April 23, 2 p.m.
“A Shout Across Time” Community Symphony
April 22, 4:30 p.m.
April 23, 4:30 p.m.
Einstein Artwork & DemonstrationsApril 21, 5 p.m.
April 22, 4:30 p.m.
April 23, 12 p.m.
PLANETARIUM SHOWS
Einstein planetarium night and rooftop telescope observing
March 31, 8:30 p.m.
April 7, 8:30 p.m.
April 10, 8:30 p.m.
April 19, 8:30 p.m.
April 20, 8:30 p.m.
DOCUMENTARIES “little green men”
Pulsar Search Collaboratory Documentary
April 17, 7 p.m.
“LIGO, A Passion for Understanding”
April 19, 7 p.m.
SPACE RACE FUN RUN April 22, 9 a.m.
CELEBRATINGEINSTEINMarch 31 - April 23, 2017
Over 100 years ago, Einstein predicted gravitational waves,
and we are just beginning to detect them now.
You are invited to join our interdisciplinary celebration
to understand the beauty and significance of these transformative discoveries about our universe.
“Imagination is more important than knowledge.” - Albert Einstein
http://einstein.wvu.edu/
Extra credit opportunity
(up to 10 points added to final exam grade)
(this equates to 2.5 points added to your FINAL GRADE
AVERAGE)
http://einstein.wvu.edu/Attend an event.*
Write a report:1. What event did you attend?2. What were the main (physics/
astronomy) ideas discussed?3. Relate them in some way to principles
we learned in class.4. What was the coolest thing you
learned from the event?
Extra credit opportunity(up to 10 points added to final exam grade)
(this equates to 2.5 points added to your FINAL GRADE AVERAGE)
*space fun run excluded but will be really cool!
I will NOT ACCEPT any
turned in after APRIL 28!
v = Δx/tVelocity
a = Δv/tAcceleration
= Volume through a surface per time
Volume flow rate
Thinking about rates…
Rates and fluid flow
A drooly ruminant
Cows sometimes eat small rocks and particulates! Water (an “ideal fluid”) moves rapidly, and water/saliva help flush these
materials from their stomachs.
A cow swallows about 100 Liters (0.1 m3) of saliva each day. Assuming cow swallows it all, what is the volume flow rate
(volume per unit time) of saliva into the cow?
A. 0.1 m3/s B. 1.2 x 10-3 m3/s C. 1.2 x 10-6 m3/s
Units of volume flow rate:
m3/sQ94
• Non-viscous fluid (no internal friction.)Note: Honey is viscous. Mud is viscous. Water is not. Blood SHOULDN’T be viscous!
• Density is constant.
• Fluid motion is steady.
• No turbulence in the fluid.
Assumptions Today
Rate of mass in
=Rate of
mass out
timeVolume
timeVolume 21 =
A1
Δx1
A2
Δx2
Rate of mass in
=Rate of
mass out
timeVolume
timeVolume 21 =
A1
Δx1
A2
Δx2
AvtxA=
ΔAv
txA=
Δ
AvtxA=
ΔAv
txA=
Δ
“Continuity” Equation
Flow rate is FASTER if pushed through a smaller cross-sectional area.
A1v1 = A2v2
What do you do if your garden hose does not reach all of your plants?
A1v1 = A2v2
Physics!
AneurysmsIs the blood flow faster in a normal blood
vessel or in a blood vessel with aneurysm?
saccular aneurysm
fusiform aneurysm
A. Normal blood vesselB. AneurysmC. Same in healthy and aneurysed vesselD. Not enough information to determine
Q95
Bernoulli’s PrincipleIf volume flow rate is constant,
and conservation of energy applies to fluids, then…
P1 + 1/2 ρv12 + ρgy1 =
P2 + 1/2 ρv22 + ρgy2
P1, v1, y1
P2, v2, y2
As height increases, pressure decreases.
higher P
lower P
As speed increases, pressure decreases.
higher P lower P
An important consequenceAs a fluid goes through a region where it changes
speed or height, the pressure of the fluid will change.
P1 + 1/2 ρv12 + ρgy1 =
P2 + 1/2 ρv22 + ρgy2
CAREFUL!!!
Careful!….Counter-intuitive!
P1 + 1/2 ρv12 + ρgy1 =
P2 + 1/2 ρv22 + ρgy2
AneurysmsIs the PRESSURE higher in a normal blood
vessel or in region with aneurysm?
saccular aneurysm
fusiform aneurysm
A. Normal blood vesselB. AneurysmC. Same in healthy and aneurysed vesselD. Not enough information to determine
Q96
Bernoulli’s Most Important Implication.
A slow-moving fluid exerts more pressure than a fast-moving fluid
(depends also on elevation of volume flow).
Consider a house with a very thin (Δy ~ 0), flat roof of area 148.6 square meters. During a hurricane with winds of 140
mph (62.6 m/s), what is the net force on the roof?
12
vair
vair~ 0
Inside house
Outside house
P1 + 1/2 ρv12 + ρgy1 =
P2 + 1/2 ρv22 + ρgy2
Density of air: 1.225 kg/m3
If the wind is blowing very hard outside, What direction does the net force point?
A B C D
Q97
12
vair
vair~ 0
Inside house
Outside house
P1 + 1/2 ρv12 + ρgy1 =
P2 + 1/2 ρv22 + ρgy2
Consider a house with a very thin (Δy ~ 0), flat roof of area 148.6 square meters. During a hurricane with winds of 140
mph (62.2 m/s), what is the net force on the roof?
Bernoulli’s Most Important Implication.
A slow-moving fluid exerts more pressure than a fast-moving fluid
(depends also on elevation of volume flow).
Airplane wings!
Faster air over
Slower air under
Higher pressure under the wing creates LIFT!
