Moving Fluids
Fluid Flow Continuity
• The volume per unit time of a liquid flowing in a pipe is
constant throughout the pipe.
• V = Avt
–
–
–
–
V: volume of fluid (m3)
A: cross sectional areas at a point in the pipe (m2)
v: speed of fluid flow at a point in the pipe (m/s)
t: time (s)
• A1v1 = A2v2
– A1, A2: cross sectional areas at points 1 and 2
– v1, v2: speed of fluid flow at points 1 and 2
• http://library.thinkquest.org/27948/bernoulli.ht
ml
Sample problem
• A pipe of diameter 6.0 cm has fluid flowing through it at 1.6 m/s. How
fast is the fluid flowing in an area of the pipe in which the diameter is
3.0 cm? How much water per second flows through the pipe?
Natural Waterways
Flash flooding can be explained by fluid flow continuity.
Sample problem
The water in a canal flows 0.10 m/s where the canal is 12 meters deep
and 10 meters across. If the depth of the canal is reduced to 6.5 meters
at an area where the canal narrows to 5.0 meters, how fast will the
water be moving through this narrower region? What will happen to the
water if something prevents it from flowing faster in the narrower
region?
Artificial Waterways
Flooding from the
Mississippi River
Gulf Outlet was
responsible for
catastrophic flooding
in eastern New
Orleans and St.
Bernard during
Hurricane Katrina.
Fluid Flow Continuity in
Waterways
Mississippi River Gulf
Outlet levees are
overtopped by Katrina’s
storm surge.
A hurricane’s
storm surge can
be “amplified” by
waterways that
become narrower
or shallower as
they move inland.
Bernoulli’s Theorem
• The sum of the pressure, the potential energy per
unit volume, and the kinetic energy per unit volume
at any one location in the fluid is equal to the sum of
the pressure, the potential energy per unit volume,
and the kinetic energy per unit volume at any other
location in the fluid for a non-viscous incompressible
fluid in streamline flow.
• All other considerations being equal, when fluid
moves faster, the pressure drops.
Bernoulli’s Theorem
• P +  g h + ½ v2 = Constant
– P : pressure (Pa)
–  : density of fluid (kg/m3)
– g: gravitational acceleration constant (9.8 m/s2)
– h: height above lowest point (m)
– v: speed of fluid flow at a point in the pipe (m/s)
Sample Problem
• Knowing what you know about Bernouilli’s principle, design an
airplane wing that you think will keep an airplane aloft. Draw a
cross section of the wing.
Bernoulli’s Principle and Hurricanes
• In a hurricane or tornado, the high winds
traveling across the roof of a building can
actually lift the roof off the building.
• http://video.google.com/videoplay?docid=
6649024923387081294&q=Hurricane+Roof
&hl=en
Applications of Fluids Concepts
Storm Surges in Hurricanes
– http://www.nhc.noaa.gov/aboutsshs.shtml
– http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/
hurr/home.rxml
– http://science.howstuffworks.com/hurricane.htm
– http://www.nd.edu/~adcirc/katrina.htm
Bernoulli Effect in Design
• http://en.wikipedia.org/wiki/Lift_(force)
• http://scienceworld.wolfram.com/physics/topics/Aer
odynamics.html
• http://user.unifrankfurt.de/~weltner/Flight/PHYSIC4.htm
• http://www.bbc.co.uk/dna/h2g2/A517169
• http://www-history.mcs.standrews.ac.uk/Mathematicians/Bernoulli_Daniel.ht
ml
Building for Hurricanes
• http://www.campcastaway.com/
• http://www.bbc.co.uk/dna/h2g2/A517169
Building in the Wetlands
• http://www.campcastaway.com/
• http://www.bbc.co.uk/dna/h2g2/A517169
Hydrostatic Pressure: Dams
• http://www.pbs.org/wgbh/buildingbig/dam/b
asics.html
• http://en.wikipedia.org/wiki/Dam
– (This has information on failed dams at end of
article).
• http://www.hooverdamtourcompany.com/bui
ld.html
• http://www.dur.ac.uk/~des0www4/cal/dams/
foun/press.htm
Hydrostatic Pressure: Levees
• http://www.innovtg.com/Levees.htm
• http://www.wired.com/news/technology/0
,68746-0.html