Fluid Flows and Bernoulli s Principle

Transcription

1 Fluid Flows and Bernoulli s Principle Sreamlines demonsraing laminar (smooh) and urbulen flows of an ideal fluid CELEBRATING EINSTEIN March 31 - April 23, 2017 ART, DANCE AND SYMPHONY PERFORMANCES Danced Lecure and Inerview Imaginaion is more imporan han knowledge. - Alber Einsein and we are jus beginning o deec hem now. You are invied o join our inerdisciplinary celebraion o undersand he beauy and significance of hese ransformaive discoveries abou our universe. LECTURES Fas Radio Burss: The Sory So Far Richard Price Duncan Lorimer, Cener for Graviaional Waves & Cosmology April 21, 7:30 p.m. March 31, 7:30 p.m. Danced Lecure and Inerview When Black Holes Collide! Graviaional Waves and Oher Shane Larson Tales from he Horizon April 22, 2 p.m. Zach Eienne, Cener for Graviaional Waves & Cosmology, April 22, 7:30 p.m. WVU Mah Deparmen April 7, 7:30 p.m. Danced Lecure and Inerview Janna Levin Einsein Unyielding: A Caalys in a New Berlin April 23, 2 p.m. Exra credi opporuniy Over 100 years ago, Einsein prediced graviaional waves, Kaherine Aaslesad, WVU Hisory Deparmen (up o 10 poins added o final exam grade) (his equaes o 2.5 poins added o your FINAL GRADE AVERAGE) April 10, 7:30 p.m. A Shou Across Time Communiy Symphony Beginning he Exploraion of he Universe wih Graviaional April 22, 4:30 p.m. Waves April 23, 4:30 p.m. Rainer Weiss, Massachuses Insiue of Technology April 13, 7 p.m. Einsein Arwork & Demonsraions April 21, 5 p.m. NANOGrav: Searching for Graviaional Waves wih Pulsars April 22, 4:30 p.m. Maura McLaughlin, Cener for Graviaional Waves and April 23, 12 p.m. Cosmology hp://einsein.wvu.edu/ DOCUMENTARIES April 18, 7:30 p.m. lile green men Pulsar Search Collaboraory Documenary Graviaional Wave Asronomy: Turning Imaginaion ino Discovery April 17, 7 p.m. Joan Cenrella, Goddard Space Fligh Cener LIGO, A Passion for Undersanding April 20, 3:30 p.m. April 19, 7 p.m. PLANETARIUM SHOWS SPACE RACE FUN RUN Einsein planearium nigh and roofop elescope observing April 22, 9 a.m. March 31, 8:30 p.m. April 19, 8:30 p.m. April 7, 8:30 p.m. April 20, 8:30 p.m. More evens and informaion: einsein.wvu.edu April 10, 8:30 p.m. Celebraing Einsein was originally produced by Monana WVU is an EEO/Affirmaive Acion Employer Minoriy/Female/Disabiliy/Veeran Sae Universiy and he exreme Graviy Insiue. Exra credi opporuniy (up o 10 poins added o final exam grade) (his equaes o 2.5 poins added o your FINAL GRADE AVERAGE) hp://einsein.wvu.edu/ Aend an even.* Wrie a repor: I will NOT ACCEPT any 1. Wha even did you aend? urned in afer 2. Wha were he main (physics/ APRIL 28! asronomy) ideas discussed? 3. Relae hem in some way o principles we learned in class. 4. Wha was he cooles hing you learned from he even? *space fun run excluded bu will be really cool! Velociy v Δx/ Thinking abou raes Acceleraion a Δv/ Volume flow rae Volume hrough a surface per ime

2 Raes and fluid flow Cows someimes ea small rocks and pariculaes! Waer (an ideal fluid ) moves rapidly, and waer/saliva help flush hese maerials from heir somachs. A drooly ruminan A cow swallows abou 100 Liers (0.1 m 3 ) of saliva each day. Assuming cow swallows i all, wha is he volume flow rae (volume per uni ime) of saliva ino he cow? Unis of volume flow rae: m 3 /s A. 0.1 m 3 /s B. 1.2 x 10-3 m 3 /s C. 1.2 x 10-6 m 3 /s Q94 Assumpions Today Non-viscous fluid (no inernal fricion.) Noe: Honey is viscous. Mud is viscous. Waer is no. Blood SHOULDN T be viscous! Densiy is consan. Fluid moion is seady. No urbulence in he fluid. Volume 1 Volume2 ime ime mass in mass ou Av Δx1 A1 Volume 1 Volume2 ime ime Δx2 A2 Av mass in Δx1 mass ou Δx2 Av A1 A2 Av

3 Coninuiy Equaion Flow rae is FASTER if pushed hrough a smaller cross-secional area. A1v1 A2v2 Wha do you do if your garden hose does no reach all of your plans? Physics! A1v1 A2v2 Aneurysms Is he blood flow faser in a normal blood vessel or in a blood vessel wih? saccular A. B. C. D. fusiform Q95 Normal blood vessel Aneurysm Same in healhy and aneurysed vessel No enough informaion o deermine Bernoulli s Principle If volume flow rae is consan, and conservaion of energy applies o fluids, hen P1 + 1/2 ρv12 + ρgy1 P2 + 1/2 ρv22 + ρgy2 P2, v2, y2 P1, v1, y1

4 An imporan consequence As a fluid goes hrough a region where i changes speed or heigh, he pressure of he fluid will change. lower P higher P As heigh increases, pressure decreases. higher P lower P CAREFUL!!! As speed increases, pressure decreases. Careful!.Couner-inuiive! Aneurysms Is he PRESSURE higher in a normal blood vessel or in region wih? saccular fusiform Q96 A. Normal blood vessel B. Aneurysm C. Same in healhy and aneurysed vessel D. No enough informaion o deermine Bernoulli s Mos Imporan Implicaion. A slow-moving fluid exers more pressure han a fas-moving fluid (depends also on elevaion of volume flow).

5 Consider a house wih a very hin (Δy ~ 0), fla roof of area square meers. During a hurricane wih winds of 140 mph (62.6 m/s), wha is he ne force on he roof? Ouside house v air 2 1 v air ~ 0 Inside house Densiy of air: kg/m 3 Consider a house wih a very hin (Δy ~ 0), fla roof of area square meers. During a hurricane wih winds of 140 mph (62.2 m/s), wha is he ne force on he roof? Ouside house v air 2 1 v air ~ 0 Inside house If he wind is blowing very hard ouside, Wha direcion does he ne force poin? A B C D Q97 Bernoulli s Mos Imporan Implicaion. A slow-moving fluid exers more pressure han a fas-moving fluid (depends also on elevaion of volume flow). Airplane wings! Faser air over Slower air under Higher pressure under he wing creaes LIFT!