Presentation on theme: "L 13 Fluids : Statics fluids at rest"— Presentation transcript:
1 L 13 Fluids : Statics fluids at rest More on fluids.How can a steel boat float.A ship can float in a cup of water!Today’s weatherHurricane Rita: in
2 Variation of pressure with depth in a liquid Anybody the does scuba diving knows that the pressure increases as then dive to greater depthsThe increasing water pressure with depth limits how deep a submarine can gocrush depth 2200 ft
3 The deeper you go, the higher the pressure hypothetical volume of water inside a larger volume.PTopAdensity = mass/volume = mass/Volor mass = VolPBottomAW
4 Forces in a STATIC fluid (at rest) W is the weight = mg of this volumeFTOP is the force on the top of the volume exerted by the fluid above it pushing downFBOTTOM is the force on the volume due to the fluid below it pushing upFor this volume not to move (Static fluid) we must have thatFBOTTOM = FTOP + mgAHWFTOPFBOTTOM
5 Variation of pressure with depth FBOTTOM - FTOP = mg = (density x Vol) x gFBOTTOM - FTOP = A H gSince pressure is Force / area, Force = P x APBottom A – PTop A = A H g, orrhoPBottom – PTop = H gThe pressure below is greaterthan the pressure above.
6 Why does P increase with depth? the block on the bottomsupports all the blocksabove itthis layer of fluid mustsupport all the fluid above it
7 Pressure in a fluid increases with depth h The pressure at the surface isatmospheric pressure, 105 N/m2Po = PatmPressure at depth hP(h) = Po + rghr = density (kg/m3)= 1000 kg/m3 for waterhP(h)
8 How much does P increase At the surface of a body of waterthe pressure is 1 atm= 100,000 PaAs we go down into the water,at what depth does the pressuredouble, from 1 atm to 2 atm or 200,000 PaWant g h = 100,000 Pa1000 kg/m3 x 10 x h = 100,000So h = 10 meters or about 30 feet100,000 Pah
9 Pressure is always perpendicular to the surface of an object
11 Pressure increaseswith depth, so thespeed of water leakingfrom the bottom hole islarger than that from thehigher ones.
12 Problem: how much does 1 gallon of water weigh? At 20 C the density of water is 998 kg/m3there are 264 gallons in one liter, so the volume of 1 gal is 1/264 m3the mass of 1 gal of water is then 998 kg/m3 x (1/264) m3/gal = 3.79 kg/galweight = mass x g = 3.79 kg x 9.8 m/s2 = 37.1 N x pounds/N = 8.3 pounds
13 Measuring atmospheric pressure - Barometers Inverted closedtube filled withliquidThe column of liquid isheld up by the pressure ofthe liquid in the tank. Nearthe surface this pressureis atmospheric pressure, sothe atmosphere holds theliquid up.PATMPATMPliquid
14 Barometric pressureAtmospheric pressure can support a column of water 10.3 m high, or a column of mercury (which is 13.6 times as dense as water) 30 incheshigh the mercury barometerToday’s weather
15 Pascal’s PrincipleIf you apply pressure to an enclosed fluid, that pressure is transmitted equally to all parts of the fluidIf I exert extra pressure on the fluid with a piston, the pressure in the fluid increases everywhere by that amountCartesian diver
16 Pascal’s VasesThe fluid levels are the same in all each tube irrespective of their shape
17 A hydraulic car lift Pressure is F x A At the same depth the pressures are the sameso F1 /A1 = F2 /A2, orwith a little force you can lift a heavy object!the jack
18 Water pumpsA ground level pump can only be used to cause water to rise to a certain maximum height since it uses atmospheric pressure to lift the waterfor deeper wells the pump must be located at the bottom
19 Pressure depends only on depth DamThe pressure at the bottom of the lake is higher than at the topThe dam must be thicker at its baseThe pressure does not depend on how far back the lake extends
20 Blood PressureThe blood pressure in your feet can be greater than the blood pressure in your head depending on whether a person is standing or reclining
21 Buoyancy – why things float TITANICThe trick is to keep the water on the outside of the ship, andto avoid hitting icebergs (which also float), andare easy to miss since 90 % of it is submerged.
22 Buoyant Force submerged object that has a mass density ρO The density of thewater is ρWPTopAF = P AhPBottomAW
23 Buoyant forceThe water pushes down on the top of the object, and pushes up on the bottom of the objectThe difference between the upward force and the downward force is the buoyant force FBsince the pressure is larger on the bottom the buoyant force is UP
24 Archimedes principlethe pressure difference is ρW g h, so the buoyant force isFB = P x A = ρW g h A= ρW g (volume of object)= ρW (volume of object) g= mass of displaced water x gFB = weight of displaced waterThis is Archimedes principleAhobject
25 Archimedes principle The buoyant force on an object in a fluid equals the weight of thefluid which it displaces.this works for objects in waterhelium balloons (density of He = 0.18 kg/m3)hot air balloons the density ofhot air is lower than the density of coolair so the weight of the cool air that isdisplaced is larger than the weightof the balloon
26 Will it float?The object will float if the buoyant force is enough to support the object’s weightThe object will displace just enough water so that the buoyant force = its weightIf it displaces as much water as possible and this does not match its weight, it will sink.Objects that have a density less than water will always float.