Document Sample

Fluids Liquids and Gases Chapter 11 Density Density is the amount of mass in 1 m3. mass kg density Units : m3 volume m and m V V What is the mass of 5200 cm3 of 1060 kg/m3 blood? 3 kg 3 1m m V 1060 3 5200cm 5.51kg m 100cm Density Pressure Pressure is the force exerted by a fluid on an area of 1 m2. F P A N Unit: pascal Pa 2 m F PA Air pressure Standard atmospheric pressure at sea level is 101,300 Pa = 1 atmosphere = 1 atm Example How much force does the air exert on the liquid in the tube that has a 2 cm2 surface area? F PA 2 N 2 1m F 101,300 2 2cm 20.26 N m 100cm Pressure at depth in a liquid Pressure is the same everywhere at the same depth. Consider a block of liquid at rest. F Fbottom Ftop Fg 0 F Pbottom A Ptop A mg 0 Pbottom Ptop A mg V g Ah g hg Pbottom Ptop A A Pbottom P gh top pressure difference Pdepth gh Example 4 The Swimming Hole Points A and B are located a distance of 5.5 m beneath the surface of the water. Find the pressures at A and B. PA Psurface Pdepth Psurface gh pressure difference for 5.5m atmospheric pressure kg m PA 101,300 Pa 1000 3 9.8 2 5.5 m m s PA 155, 200 Pa A and B are at the same Psurface depth so their pressures are the same. Pdepth PB 155, 200 Pa Blood pressure What is the difference in blood pressure between a person's heart and their feet? Pdepth gh kg m Pdepth 1060 3 9.8 2 1.35m m s Pdepth 14, 024 Pa Pressure Points A, B, C, and D are all ... • At the same level. • In the same liquid . • At the same pressure. Barometer no air pressure A barometer is an instrument used to measure atmospheric pressure. PA Psurface Pdepth Psurface 0 Patmosphere 0 gh liquid mercury How tall would mercury be for Pdepth 101,300 Pa air pressure? kg m 101,300 Pa 13, 600 3 9.8 2 h m s air pressure h 0.760 m 760 mm A and B are at the same level so For water h = 10.3 m or about 34 feet. their pressures are the same. Absolute pressure and Gauge pressure Tire pressure is measured in customary units of psi. [ psi means pounds/inch2 ] Inside the tire the gauge pressure is 30 psi above normal atmospheric pressure. Outside the tire atmospheric pressure is 15 psi. Inside the tire the absolute pressure is 45 psi. 30 psi + 15 psi = 45 psi. Absolute pressure and Gauge pressure gas pressure Psurface PA Psurface Pdepth Pdepth PA is the absolute pressure at point A. Psurface is the atmospheric pressure Patmosphere . A and B are at the same level so Pdepth is how much higher the gas their pressures are the same. pressure is above atmospheric pressure. Pdepth is the gauge pressure. Open-tube manometer blood-pressure gauge Blood pressure cuff measures a patient's blood pressure in units of the height of mercury in a tube. Pdepth gh Psurface Pdepth Pair in the cuff Blood pressure is gauge pressure. Measuring blood pressure Blood pressure in the heart should be measured at the same horizontal level as the heart (usually at the upper arm). P 130 / 85 Pdepth 105 mm of Hg P 235/190 760 mm of Hg Pdepth 14,024 Pa 105 mm of Hg 101,300 Pa Pascal's principle Increasing the pressure at one place in an enclosed fluid increases the pressure by the same amount everywhere in the fluid. This principle explains the operation of all hydraulic systems. Hydraulic systems Force = Pressure Area Force on a piston is proportional to the piston area. Small piston Small force Large piston Large force Example 7 A Car Lift Find gauge pressure needed to raise the car. Find force needed at the small piston. Car and large piston weigh 20,000 N. Density of the hydraulic oil is 800 kg/m3. Height h is 2 m. Ignore the weight of the pistons. Flarge 20, 000 N PB 2 282,900 Pa Alarge 0.0707m Small piston r = 0.012 m PA PB (same level in same liquid) A = 4.52 x 10-4 m2 Fsmall Large piston PA Psurface Pdepth gh r = 0.15 m Asmall A = 0.0707 m2 Fsmall kg m PA 800 3 9.8 2 2m 4.52 104 m 2 m s Fsmall 282,900 Pa 4 15, 680 Pa 4.52 10 m 2 Fsmall 120.8 N Archimedes' principle The upward force that fluids exert on partially or fully submerged objects is called a buoyant force. The buoyant force is equal to the weight of the fluid displaced by the object. Fbuoyant Fg displaced fluid mdisplace fluid g Fbuoyant fluidVolumedisplaced g Vg Example 9 A Swimming Raft How deep is the raft submerged? Pine wood 550 kg/m3 F 0 Fg Fbuoyant (equilibrium) 0 mraft g waterVsubmerged g 0 raftVraft g waterVsubmerged g waterVsubmerged raftVraft water Araft hsubmerged raft Araft hraft kg raft hraft 550 3 0.3m hsubmerged m 0.165m water 1000 3 kg m Example 9 A Swimming Raft Since the density of the raft was Pine wood 550 kg/m3 less than the density of the water, the submerged depth was less than the thickness of the raft. If the density of the raft were greater than the water, the raft would sink because it could not displace a weight of water equal to its own weight. kg raft hraft 550 3 0.3m m hsubmerged 0.165m water kg 1000 3 m Archimedes' principle The fluid in a charged battery has a higher density than the fluid in a discharged battery. Green ball floats when the fluid density is more than the ball density. Fluid dynamics: vocabulary Streamlines - paths of fluid particles Steady flow - constant velocity Unsteady flow - variable velocity Turbulent flow - erratically variable velocity Compressible - variable density (example: gases) Incompressible - constant density (example: liquids) Viscous flow - does not flow easily (example: honey) Non-viscous flow - flows easily (example: water) Ideal fluid - incompressible, non-viscous fluid (Our focus will be on the behavior of ideal fluids.) Mass flow rate Mass of fluid flowing past a point in one second is called the mass flow rate. The (blue) mass m with velocity v in section 1 will flow past the end of the tube in time Δt. mass Volume Avt mass flow rate Av time t t m kg Mass Flow Rate unit: s Continuous flow A single tube with wide and narrow sections has different velocities in each section, but the same mass flow rate. mass flow rate section 1 mass flow rate section 2 1 A1v1 2 A2 v2 continuity equation Continuous flow The density is the same throughout an incompressible fluid. 1 A1v1 2 A2 v2 (continuity equation) 1 2 (incompressible fluid) Therefore A1v1 A2v2 (volume flow rate) volume flow rate section 1 volume flow rate section 2 For an incompressible fluid, the volume flow rate is the same everywhere in the tube. Example 12 A Garden Hose Hose fills an 8 x 10-3 m3 bucket in cross sectional area 20 seconds. of 1.6x10-4 m2 Find the volume flow rate. Find the mass flow rate. cross sectional area Find the velocity for each example. of 0.8 x10-4 m2 volume 8 103 m3 m3 volume flow rate Q 4 104 time 20s s Q Av m3 4 4 10 Q s 2.5 m (wide area) v A 1.6 104 m 2 s m3 4 104 Q s 5m v 4 (narrow area) A 0.8 10 m 2 s Pressure changes along a flowing fluid Pdepth Pressure change provides Pressure change is due to the net force needed to the difference in depth in accelerate the fluid. the fluid. Pressure must drop to allow the fluid to speed up. Bernoulli's equation for an ideal fluid Bernoulli's equation describes the relationships between pressure, velocity, and height in a flowing fluid. P v gy1 P2 v gy2 1 1 2 2 1 1 2 2 2 Pressure Velocity Based on principles of work Height and mechanical energy. Applications for Bernoulli's equation P v gy1 P2 v gy2 1 1 2 2 1 1 2 2 2 Conceptual Example 14 Tarpaulins and Bernoulli’s Equation When the truck is stationary, the tarpaulin lies flat, but it bulges outward when the truck is speeding down the highway. Explain. Applications for Bernoulli's equation P v gy1 P2 v gy2 1 1 2 2 1 1 2 2 2 Applications for Bernoulli's equation P v gy1 P2 v gy2 1 1 2 2 1 1 2 2 2 Applications for Bernoulli's equation P v gy1 P2 v gy2 1 1 2 2 1 1 2 2 2 The End

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 25 |

posted: | 8/8/2012 |

language: | English |

pages: | 34 |

OTHER DOCS BY Um9k2f4W

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.