Fluids Buoyancy - De Anza College

1 FluidsBuoyancyLana SheridanDe Anza CollegeApril 12, 2017 Last time pressure and depth Pascal s principle measurements of pressureOverview Buoyancy and archimedes principleManometerThe pressure being measured,P, can be compared to atmosphericpressureP0by measuring the height of the incompressible fluid inthe U-shaped tube. Buoyant Forces and archimedes s Principle Pressure MeasurementsDuring the weather report on a television news program, the barometric pressure is often provided. This reading is the current local pressure of the atmosphere, which varies over a small range from the standard value provided earlier. How is this pres-sure measured? One instrument used to measure atmospheric pressure is the common barom-eter, invented by Evangelista Torricelli (1608 1647). A long tube closed at one end is filled with mercury and then inverted into a dish of mercury (Fig. ). The closed end of the tube is nearly a vacuum, so the pressure at the top of the mer-cury column can be taken as zero.

2 In Figure , the pressure at point A, due to the column of mercury, must equal the pressure at point B, due to the atmo-sphere. If that were not the case, there would be a net force that would move mer-cury from one point to the other until equilibrium is established. Therefore, P0 5 rHggh, where rHg is the density of the mercury and h is the height of the mercury column. As atmospheric pressure varies, the height of the mercury column varies, so the height can be calibrated to measure atmospheric pressure. Let us determine the height of a mercury column for one atmosphere of pressure, P0 5 1 atm 5 3 105 Pa: mBased on such a calculation, one atmosphere of pressure is defined to be the pres-sure equivalent of a column of mercury that is exactly 0 m in height at 08C. A device for measuring the pressure of a gas contained in a vessel is the open-tube manometer illustrated in Figure One end of a U-shaped tube containing a liquid is open to the atmosphere, and the other end is connected to a container of gas at pressure P.

3 In an equilibrium situation, the pressures at points A and B must be the same (otherwise, the curved portion of the liquid would experience a net force and would accelerate), and the pressure at A is the unknown pressure of the gas. Therefore, equating the unknown pressure P to the pressure at point B, we see that P 5 P0 1 rgh. Again, we can calibrate the height h to the pressure P. The difference in the pressures in each part of Figure (that is, P 2 P0) is equal to rgh. The pressure P is called the absolute pressure, and the difference P 2 P0 is called the gauge pressure. For example, the pressure you measure in your bicycle tire is gauge uick Quiz Several common barometers are built, with a variety of Fluids . For which of the following Fluids will the column of fluid in the barometer be the highest? (a) mercury (b) water (c) ethyl alcohol (d) Buoyant Forces and archimedes s PrincipleHave you ever tried to push a beach ball down under water (Fig.)

4 , p. 424)? It is extremely difficult to do because of the large upward force exerted by the water on the ball. The upward force exerted by a fluid on any immersed object is called The total force on the dam is equal to the product of the average pressure and the area of the face of the dam:F5 PavgA5112rgH21Hw2512rgwH2which is the same result we obtained using ! 0PP0P0 ABhhABbFigure Two devices for measuring pressure: (a) a mercury barometer and (b) an open-tube manometer. continuedIfhis positive,P>P0, if negative ,P< P0is called thegauge training in their spacesuits:The total mass of NASA s EMU (extravehicular mobility unit) is178 kg. Why does training underwater make maneuvering in thesuits easier?1 Picture from apparent weight of submerged objects is less than its an object that would float, but is held underwater, its apparentweight is negative!There is an upward force on an object in a fluid called does this force exist? Where does it come from?

5 We know pressure depends on depth, so an object that s notcompletely flat will have different pressure on different parts of a rectangular object of heighthand base areaAwith itstop edge at a force on each of the four sides will be force on the bottom will be(P0+ g(h+d)) force on the top will be(P0+ gd) will be a net upward force from the pressuredifference!BuoyancyWhy does this force exist? Where does it come from?We know pressure depends on depth, so an object that s notcompletely flat will have different pressure on different parts of a rectangular object of heighthand base areaAwith itstop edge at a force on each of the four sides will be force on the bottom will be(P0+ g(h+d)) force on the top will be(P0+ gd) will be a net upward force from the pressuredifference!BuoyancyWhy does this force exist? Where does it come from?We know pressure depends on depth, so an object that s notcompletely flat will have different pressure on different parts of a rectangular object of heighthand base areaAwith itstop edge at a force on each of the four sides will be force on the bottom will be(P0+ g(h+d)) force on the top will be(P0+ gd) will be a net upward force from the pressuredifference!

6 BuoyancyWhy does this force exist? Where does it come from?We know pressure depends on depth, so an object that s notcompletely flat will have different pressure on different parts of a rectangular object of heighthand base areaAwith itstop edge at a force on each of the four sides will be force on the bottom will be(P0+ g(h+d)) force on the top will be(P0+ gd) will be a net upward force from the pressuredifference!BuoyancyHow big will the upward force be?Fbuoy=Fup Fdown= (P0A+ g(h+d)A) (P0A+ gd A)= ghA= gVobjbecause the volume of the submerged block isVobj= that Vobj=mf, themass of the displaced fluid.(We are assuming is constant.)BuoyancyHow big will the upward force be?Fbuoy=Fup Fdown= (P0A+ g(h+d)A) (P0A+ gd A)= ghA= gVobjbecause the volume of the submerged block isVobj= that Vobj=mf, themass of the displaced fluid.(We are assuming is constant.)BuoyancyHow big will the upward force be?Fbuoy=Fup Fdown= (P0A+ g(h+d)A) (P0A+ gd A)= ghA= gVobjbecause the volume of the submerged block isVobj= that Vobj=mf, themass of the displaced fluid.

7 (We are assuming is constant.) Buoyancy and archimedes PrincipleArchimedes PrincipleThe buoyant force on an object is equal to the weight of the fluidthat the object , if a brick falls to the bottom of a pool it must push anamount water equal to its volume up and out of the and archimedes PrincipleFor a fully submerged object the buoyant force is:Fbuoy= fVobjgwhere fis the mass density of the fluid andVobjis the volume ofthe object. fVobjis the mass of the water moved aside by the and archimedes PrincipleAn object that floats will displace less fluid than its entire a floating object:Fbuoy= fVsubgwhereVsubis the volume of the part of the object underneath thefluid level and FloatingWill a particular object sink or float in a particular fluid? If the object isless densethan the fluid it will float. If the object ismore densethan the fluid it will sink. If the object and the fluid have the same density if will neitherfloat or sink, but drift at and FloatingSince therelativedensity of the object to the fluid determineswhether it will sink or float, we sometimes use the notion ofspecific specific gravity of an object relates its density to the density ofwater (or occasionally other liquids):Specific gravity,SGof a sample is the ratio of its density to that of sample waterOften referenced in brewing!

8 Sinking and FloatingA floating object displaces a mass of fluid equal to its own mass!(Equivalently, a weight of fluid equal to its own weight.)This also means that fVsub= ships are often compared by theirdisplacements, theweight (or mass, depending on context) of water they Enterprisewas an aircraft carrier (now decommissioned).Displacement: 94,781 tonnes (metric tons), fully tonne = 1000 kgWhat is the mass of the fully loaded USS Enterprise in kgs?m=94,781,000 kgAnother Problem1 Your friend of mass 100 kg can just barely float in fresh her approximate m32 Hewitt, page ships are often compared by theirdisplacements, theweight (or mass, depending on context) of water they Enterprisewas an aircraft carrier (now decommissioned).Displacement: 94,781 tonnes (metric tons), fully tonne = 1000 kgWhat is the mass of the fully loaded USS Enterprise in kgs?m=94,781,000 kgAnother Problem1 Your friend of mass 100 kg can just barely float in fresh her approximate m32 Hewitt, page ships are often compared by theirdisplacements, theweight (or mass, depending on context) of water they Enterprisewas an aircraft carrier (now decommissioned).

9 Displacement: 94,781 tonnes (metric tons), fully tonne = 1000 kgWhat is the mass of the fully loaded USS Enterprise in kgs?m=94,781,000 kgAnother Problem1 Your friend of mass 100 kg can just barely float in fresh her approximate m32 Hewitt, page ships are often compared by theirdisplacements, theweight (or mass, depending on context) of water they Enterprisewas an aircraft carrier (now decommissioned).Displacement: 94,781 tonnes (metric tons), fully tonne = 1000 kgWhat is the mass of the fully loaded USS Enterprise in kgs?m=94,781,000 kgAnother Problem1 Your friend of mass 100 kg can just barely float in fresh her approximate m32 Hewitt, page Quiz are shipwrecked and floating in the middleof the ocean on a raft. Your cargo on the raft includes a treasurechest full of gold that you found before your ship sank, and theraft is just barely afloat. To keep you floating as high as possible inthe water, should you(i) leave the treasure chest on top of the raft,(ii) secure the treasure chest to the underside of the raft, or(iii) hang the treasure chest in the water with a rope attached tothe raft?

10 (Assume throwing the treasure chest overboard is not an optionyou wish to consider.)Aoption (ii) is the bestBoption (iii) is the bestCoptions (ii) and (iii) would be the same, better than (i)DAll would be the same2 Serway & Jewett, page Quiz are shipwrecked and floating in the middleof the ocean on a raft. Your cargo on the raft includes a treasurechest full of gold that you found before your ship sank, and theraft is just barely afloat. To keep you floating as high as possible inthe water, should you(i) leave the treasure chest on top of the raft,(ii) secure the treasure chest to the underside of the raft, or(iii) hang the treasure chest in the water with a rope attached tothe raft?(Assume throwing the treasure chest overboard is not an optionyou wish to consider.)Aoption (ii) is the bestBoption (iii) is the bestCoptions (ii) and (iii) would be the same, better than (i) DAll would be the same2 Serway & Jewett, page in AirBuoyancy in air works the same way as in liquids:Fbuoy= fVobjgIf an object is less dense than air, it will float , in the atmosphere, the density of air varies with in Air1 Photo by Derek Jensen, in AirBy roughly how much is your weight reduced by the effects of theair you are submerged in?