Physics 5B L Lecture 33 JJanuary 13 13 2012 Chapter 13 Fl Fluids Ch t 13 id What fraction of an iceberg s volume is above water Density of sea water is 1025 kg m3 Density of pure fresh water ice is 920 kg m3 2 Another ice cube riddle A cube of fresh fresh water ice is floating in a glass of salty sea water that is filled upp exactlyy to the rim As the ice melts Density of sea water is 1025 kg m3 wate overflows water ove ows the t e rim B no water overflows and the water level doesn tt change doesn change C the water level drops A 3 Explanation A cube of fresh fresh water ice is floating in a glass of salty sea water that is filled upp exactlyy to the rim Density of sea water is 1025 kg m3 The weight of the ice cube is equal to the buoyant force it is floating Archimedes principle the buoyant force is equal to the weight of salt water displaced the amount that would fill the dashed red box So the weight of the ice is equal to the weight of displaced salt water Therefore the ice melts into fresh water of weight exactly equal to the weight of the displaced salt water But a given mass of fresh water will take up more volume than the same mass of salt water so the melted fresh water takes up more than the dashed red volume and therefore overflows the glass 4 Laminar Flow Streamlines 5 Laminar Flow vs Turbulence 6 Contradiction A fluid with near zero viscosity frictional drag will not easily l exhibit h b llaminar flow fl IInstead d the h flflow willll bbe turbulent especially if the fluid is moving fast But the equations that we will use e g Bernoulli Bernoulli ss equation hold only for laminar flow and neglect viscosity What this means is that our results that ignore viscosity must be approximate in practice Reynolds Number R Turbulent Flow 2v r If R is large large then the flow about the object of size r will be turbulent 7 Continuity steady steady flow flow A four lane highway merges down to a two lane highway The officer in the police car observes 8 cars passing every second second at 30 mph mph How many cars does the officer on the motorcycle observe passing every second A 4 B 8 C 16 How fast must the cars in the two lane section be going A 15 mph B 30 mph C 60 mph 818 As the incompressible fluid moves from the thick section of pipe into the thin section section it must assuming steady flow The fluid must accelerate in order to get the same rate of flow in the thin section as in the thick section maintain i t i constant t t velocity l it B accelerate increase speed C decelerate decrease speed A A 9 Continuity Equation 1 A1v1 2 A2v2 Mass of fluid passing Point 1 each second Mass of fluid passing Point 2 each second Special case incompressible fluid for which 1 2 10 A1 V1 A2 V2 11 Considering the answer to the previous question and recalling Newton s Newton s second law what happens to the pressure of the fluid as it moves from the thick section to the thin section P1 P2 B P1 P2 C P2 P1 A The only force present to accelerate the water to higher velocity is the pressure so P1 must be greater than P2 in order to ggive a net force and acceleration in the direction of the flow 12 Pressure vs Velocityy in Laminar Flow For an incompressible fluid A1v1 A2v2 Continuity Equation p1 1 1v12 p2 1 2v22 2 2 Bernoulli s Equation 13 Illustration of Laminar Flow Note in a real situation with viscosity the velocity will be near zero close to the wall of the pipe and highest in the center center not constant across the diameter However the continuity equation and Bernoulli s equation still hold along any individual streamline 14 Venturi Demo 15 Venturi Flowmeter A 1 0 cm diameter venturi flowmeter is inserted in a 2 0cm d diameter pipe carrying water a What is the flow speed v in the pipe if the pressure difference between the venturi and the unconstricted pipe is 17 kPa b What is the volume flow rate in cubic meters per second 16 Concept Quiz If I gently tl bl blow air i between b t the light bulbs what will they do A Move together B Move apart C Remain as they are 17