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Pascal's Principle

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Pascal's Principle Pascal’s Principle What happens inside a fluid when pressure is exerted on it? Does pressure have a direction? Does it transmit a force to the walls or bottom of a container? Any change in the pressure of a fluid is transmitted uniformly in all directions throughout the fluid. Boyle’s Law • Boyle discovered that the volume of a gas is inversely proportional to the pressure. • Boyle’s Law: PV = constant • If the pressure increases, the volume decreases. • P1V1 = P2V2 • At higher altitude, the air density become smaller, i.e. larger volume, the air pressure become smaller. – This is the reason of the balloon inflation. Archimedes’ Principle • The average density of an object compared to a fluid determines whether the object will sink or float in that liquid. • The upward force that pushes objects back toward the surface in liquids is called the buoyant force. • Archimedes’ Principle: The buoyant force acting on an object fully or partially submerged in a fluid is equal to the weight of the fluid displaced by the object. • consider a block submerged in water, suspended from a string. – The pressure of the water pushes on the block from all sides. – Because the pressure increases with depth, the pressure at the bottom of the block is greater than at the top. – There is a larger force (F = PA) pushing up at the bottom than there is pushing down at the top. – The difference between these two forces is the buoyant force. F = mg = density*volume*g pressure = F/A = density*g*volume/A volume/A =height pressure = density*g*height = ρgh Pascal’s principle says: ρgh is the same everywhere and in all directions. Ch 9 CP 4 Wooden boat: 3m x 1.5m x 1m that carries five people. Total mass of boat and people equals 1200 kg. a) What is total weight? b) What is buoyant force required to float? c) What volume of water must be displaced to float? d) How much of the boat underwater? a) W = Mg = 1200 kg (9.8 m/s2) 1m W = 11760 N 3m b) Fnet = Fb – W = 0 Fb = 11760 N W F c) Fb = H2O Vg (see Ch 9 E 12) b Fb/H2Og = 11760N/(1000 kg/m3)(9.8 m/s2) = V = 1.2 m3 d) V = LWh = (3m)(1.5m)h = 1.2 m3 h = 0.27 m 3/2/2011 Physics 214 Fall 2010 5 2A-03 Vacuum Demos Effects of Vacuum on objects made largely of air or air pockets. Why do the Do the balloons burst in balloons burst in vacuum differently the vacuum ? then they normally burst ? Why do the What will happen when marshmallows the marshmallows are get bigger in returned to normal vacuum ? pressure ? Can you guess what happens when Shaving Cream is placed in vacuum ? AN AIR-POCKET/BALLOON WILL EXPAND WHEN THE PRESSURE IS REDUCED AND IT WILL DEFLATE WHEN THE PRESSURE IS INCREASED. SO BALLOONS WILL EXPAND AS THEY RISE IN THE ATMOSHPERE AND THE EXPANSION OF A PARTIALLY EVACUATED CAN IS USED IN BAROMETERS. 3/2/2011 Physics 214 Fall 2010 6 2B-04 Liquid Pressure Investigating Pressure in different directions within a liquid in equilibrium. What will happen to The increase in pressure ρgh is the reading on the measured by the difference in manometer as the height of the liquid in the U tube. sensor is rotated ? g h A B A B AT ANY GIVEN POINT IN A STATIONARY LIQUID, THE PRESSURE IS THE SAME IN ALL DIRECTIONS. 3/2/2011 Physics 214 Fall 2010 7 2B-05 Pressure Forces in Liquids An open ended cylinder kept shut by liquid pressure What happens as the submerged cylinder filled with There are two forces acting Air air is filled with water ? on the plate. It’s weight down and PA up. When PA exceeds the weight the PA cylinder stays intact In this situation the plate has to now support the Water weight of the water and when the weight of the water plus plate exceeds PA PA the cylinder opens THE LIQUID PRESSURE DEPENDS ONLY ON DEPTH P = ρgh. THE UPWARD FORCE DEPENDS ON THE AREA F = PA 3/2/2011 Physics 214 Fall 2010 8 2B-08 Buoyant Force Compare the Buoyant Force between two cylinders of equal volume and different mass. T T Scale reads Which object FB experiences the tension in cord: greater buoyant T = Mg – FB force, the heavier Mg = FB + T one or lighter one ? Mg Mg We find Fb to be exactly equal for both masses BUOYANT FORCE DOES NOT DEPEND ON THE MATERIAL OF THE OBJECT DISPLACING THE FLUID. THE BUOYANT FORCE DEPENDS ONLY ON THE VOLUME OF FLUID DISPLACED. 3/2/2011 Physics 214 Fall 2010 9 2B-09 Archimedes I T The fluid exerts a buoyant What happens to FB the reading on the force on the block, which upper scale when reduces the tension on the block is lowered the cord. The reading on into the beaker of the scale is lowered. water ? Mg T = Mg – FB Should anything Since the fluid exerts a force on the block, happen to the the block exerts an EQUAL and OPPOSITE reading on the lower scale ? force on the fluid. EVEN THOUGH THE BLOCK DOES NOT ‘TOUCH’ THE LOWER SCALE, THE FORCE ON THE FLUID DUE TO THE BLOCK IS TRANSMITTED TO THE SCALE. THE REDUCTION IN READING ON THE UPPER SCALE IS EXACTLY EQUAL TO THE INCREASE IN READING ON THE LOWER SCALE. IF THE CONTAINER WAS FULL SO THAT WHEN THE BLOCK WAS INSERTED THE VOLUME THE BLOCK DISPLACED SPILLS OUT OF THE CONTAINER THEN THE BOTTOM SCALE WOULD NOT CHANGE. 3/2/2011 Physics 214 Fall 2010 10 Quiz: Boat displaces 2.5 m3 of water. Density of water 3 H2O = 1000 kg/m . What is the mass of water displaced? What is the buoyant force? A). Mass = 2500 kg, buoyant force = 24500N B). Mass = 250 kg, buoyant force = 2450N C). Mass = 25 kg, buoyant force = 245N D). Mass = 2500 kg, buoyant force = 2450N E). Mass = 2500 kg, buoyant force = 245N F = W Mass of fluid displaced b FD (mFD) = volume x density of fluid. 3 3 MFD = VFDH2O = (2.5 m )(1000 kg/m ) = 2500 kg Buoyant force equals weight of fluid displaced. 2 Fb = WFD = mFD g = (2500 kg)(9.8 m/s ) = 24500 N 11.
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