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Transcript
Fluids Fluids • • • • • Pressure Fluids at rest Archimedes’ principle Fluids in motion Bernoulli’s principle 1 Fluids Demonstration: Cups and Balloons Fluids Fluid – Anything that flows •Water •Oil •Air •Jellybeans? 2 Fluids Fluids can be: Static Dynamic Fluids can not be directly pushed or pulled. They can only be moved by PRESSURE Static Fluids Density (ρ) m Mass (kg ) ρ= ⇒ v Volume(m3 ) ρwater=1000 kg/m3 To convert from g/cm3 to kg/m3 you must multiply by 1000 3 Static Fluids Pressure=Force/Area P= Force( N ) Area (m 2 ) Pascal (Pa) is the unit of pressure The smaller the area the greater the pressure Can you think of other common units??? Static Fluids A cube and a spherical ball are made of the same material and have the same mass. Which exerts the larger pressure on the floor? 4 Static Fluids Describe how a gas exerts pressure on the walls of its container. Static Fluids Why does the pressure in a tire increase as you add more air? 5 Static Fluids Demonstration: Dixie Cups Static Fluids Some Perspective on Pressure Air Pressure= 1.01 ⋅105 Pa or 14.7 PSI Tire Pressure= 3.03 ⋅10 Pa 5 Full SCUBA TANK= or 45PSI 2.06 ⋅107 Pa or 3000 PSI Ocean Bottom= 1.1 ⋅10 Pa or >16000 PSI 8 6 Static Fluids Example: The “foot print” of a car tire is approx. 150 cm2. The pressure in each tire is 3.03x105 Pa. What is the weight of the car? Static Fluids Day 1 HW: 7 Static Fluids Demonstration: Vacuum Cannon Static Fluids Vacuum Cannon…how it works 8 Static Fluids Demonstrations •Suction Cups •Magdeburg Hemispheres •Balloon in Bell Jar •Alarm in Bell Jar Static Fluids Pascal's Principle (hydraulic principle) Any INCREASE (or decrease) in pressure to a confined fluid is transmitted undiminished throughout the fluid Assume the fluid is quasistatic 9 Static Fluids Pascal's Principle examples: •Hydraulic Jacks •Squeezing Toothpaste •Bulldozers and Backhoes •Automotive Breaks Small Area= small input force Large Area=large output force F = PA Static Fluids Pascal's Principle Equation 10 Static Fluids Example: A Hydraulic jack for a car has an output piston diameter of 5.0 cm and an input piston diameter of 1.0 cm. You want to lift a 8000 N car. How much force must be applied to the input piston? Pressure Measurement The change in height relates directly to the gauge pressure using P = ρ hg 11 Pressure Measurement Static Fluids Q: Which container has the greatest fluid pressure at the bottom of the container? h 12 Static Fluids Q: Which container has the greatest fluid pressure at the bottom of the container? Static Fluids Example: You are driving on a rainy day and hydroplane into a puddle that is barely deep enough to cover the roof of your car (approx. 1.6 meters). Determine the minimum force necessary to open your car door. The door has an area of approximately 1 square meter. 13 Static Fluids Homework: Static Fluids – Buoyant Force Buoyant Force -An upward pointing force exerted on a body immersed in a fluid. -Caused by the increasing pressure with increasing depth 14 Static Fluids – Buoyant Force Buoyant Force Static Fluids – Buoyant Force Example: Determine the apparent weight of a 3000 N treasure chest filled with gold coin. The chest is airtight and 40 cm on a side. Fbuoy N Fg 15 Static Fluids – Buoyant Force Example: What volume of helium is needed if a balloon is to lift a load of 180 kg (including the weight of the empty balloon) Fbuoy FgHe Fgload Static Fluids – Archimedes’ Principle Archimedes’ Principle The buoyant force is equal to the weight of the displaced fluid. If you want something to float in water you must make its effective density less than the density of water. Eureka!! 16 Static Fluids – Archimedes’ Principle Archimedes’ Principle Lab: Buoyant Force w/ force sensor Static Fluids – Archimedes’ Principle Activity – Penny Barge 17 Fluids in Motion Fluid Dynamics •The study of moving fluids •Only consider Laminar flow Laminar – Layers Turbulent – Mixing of layers Equation of Continuity Av is another way of expressing volume/time The equation of continuity is really a statement of conservation of matter…what goes in must come out! 18 Equation of Continuity Moving Fluids – Bernoulli’s Equation Bernoulli’s Equation is just another restatement of conservation of energy. P1 + 12 ρ v12 + ρ gy1 = P2 + 12 ρ v22 + ρ gy2 GPE at location 1 Kinetic Energy location 1 Pressure at location 1 More accurately, work done as a result of a pressure difference P1-P2 19 Example 1: Heating Duct – Eqtn of Continuity What area must a heating duct have if air moving 3.0 m/s along it can replenish the air every 15 minutes in a room of volume 300 m3? Assume the air’s density remains constant. Example 2: Blood Flow – Eqtn of Continuity In humans, blood flows from the heart into the aorta, from which it passes into the major arteries. These branch into arterioles, which in turn branch into capillaries. The blood returns to the heart via the veins. The radius of the aorta is about 1.2 cm, and the blood passing through it has a speed of about 40 cm/s. A typical capillary has a radius of about 4 x 10-4 cm, and blood flows through it at a speed of about 5x10-4 m/s. Estimate the number of capillaries that are in the body. 20 Example 2: Blood Flow – Eqtn of Continuity (continued) Example 3: Bernoulli’s Equation Water circulates throughout a house in a hot-water heating system. If the water is pumped at a speed of 0.50 m/s through a 4.0 cm diameter pipe in the basement under a pressure of 3 atm, what will be the flow speed and pressure in a 2.6 cm diameter pipe on the second floor 5.0 m above? Assume the pipes do not divide into branches. 21 Example 3: Bernoulli’s Equation Example 3: Bernoulli’s Equation 22 Torricelli’s Theorem Predicts the speed a fluid will shoot come out of a pipe Assumes the height of the water doesn’t change appreciably ie. V2=0 The pressure at the top and bottom of the container is the same (1 atm) Moving Fluids – Bernoulli’s Principle Bernoulli’s Principle Where fluid flow is fast, pressure is low Where fluid flow is slow, pressure is high Activities: Dime in cup Ping Pong Ball and coffee stir “two sheets to the wind” Ball in stream of water Bernoulli, Mexican and movies?? 23 Fluids in Motion Physics of Flight Physics of baseball Physics of Chimneys Physics of Sailboats Fluids in Motion B A C Where is the pressure the greatest, at point A, B or C? 24