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.html

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 problemThe 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

A hurricane’s storm surge can be “amplified” by waterways that become narrower or shallower as they move inland.

Mississippi River Gulf Outlet levees are overtopped by Katrina’s storm surge.

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.uni-frankfurt.de/~weltner/Flight/PHYSIC4

.htm• http://www.bbc.co.uk/dna/h2g2/A517169• http://www-history.mcs.st-andrews.ac.uk/Mathemat

icians/Bernoulli_Daniel.html

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/basics.html

• http://en.wikipedia.org/wiki/Dam– (This has information on failed dams at end of

article).• http://www.hooverdamtourcompany.com/buil

d.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