L 13 Fluid Statics [2] More on fluids. How can a steel boat float. A ship can float in a cup of water! Today s weather
The deeper you go the higher the pressure P Top A hypothetical volume of water inside a larger volume. P Bottom A W
Forces in a STATIC fluid (at rest) H F BOTTOM F TOP A W W is the weight = mg of this volume F TOP is the force on the top of the volume exerted by the fluid above it pushing down F BOTTOM is the force on the volume due to the fluid below it pushing up For this volume not to move (Static fluid) we must have that F BOTTOM = F TOP + mg
Variation of pressure with depth F BOTTOM -F TOP = mg = (density x Vol) x g RHO F BOTTOM -F TOP = ρ A H g Since pressure is Force / area, Force = P x A P Bottom A P Top A = ρ A H g, or P Bottom P Top = ρ H g, The pressure below is greater than the pressure above.
How much does P increase At the surface of a body of water the pressure is 1 atm = 100,000 Pa h As we go down into the water, at what depth does the pressure double, from 1 atm to 2 atm or 200,000 Pa Want ρ g h = 100,000 Pa 1000 kg/m 3 x 10 x h = 100,000 So h = 10 meters or about 30 feet 100,000 Pa
this layer of fluid must support all the fluid above it the block on the bottom supports all the blocks above it
Measuring atmospheric pressure - Barometers Inverted closed tube filled with liquid P ATM P ATM The column of liquid is held up by the pressure of the liquid in the tank. Near the surface this pressure is atmospheric pressure, so the atmosphere holds the liquid up. P liquid
Barometric pressure Atmospheric 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 inches high the mercury barometer Today s weather
Pascal s Vases The fluid levels are the same in all each tube irrespective of their shape
Pressure depends only on depth Dam The pressure at the bottom of the lake is higher than at the top The dam must be thicker at its base The pressure does not depend on how far back the lake extends
Blood Pressure The blood pressure in your feet can be greater than the blood pressure in your head depending on whether a person is standing or reclining
Water pumps A 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 water for deeper wells the pump must be located at the bottom
Pascal s Principle If you apply pressure to an enclosed fluid, that pressure is transmitted equally to all parts of the fluid If I exert extra pressure on the fluid with a piston, the pressure in the fluid increases everywhere by that amount Cartesian diver
A hydraulic car lift Pressure is F x A At the same depth the pressures are the same so F 1 /A 1 = F 2 /A 2, or A F F A 2 = 2 1 1 with a little force you can lift a heavy object! the jack
Buoyancy why things float The trick is to keep the water on the outside of the ship, and to avoid hitting icebergs (which also float), and are easy to miss since 90 % of it is submerged.
Buoyant Force submerged object that has a mass density ρ O P Top A h P Bottom A W The density of the water is ρ W
Buoyant force The water pushes down on the top of the object, and pushes up on the bottom of the object The difference between the upward force and the downward force is the buoyant force F B since the pressure is larger on the bottom the buoyant force is UP
Archimedes principle the pressure difference is ρ W g h, so the buoyant force is F B = P x A = ρ W g h A = ρ W g (volume of object) = ρ W (volume of object) g h = mass of displaced water x g weight of displaced water This is Archimedes principle A object
Will it float? The object will float if the buoyant force is enough to support the object s weight The object will displace just enough water so that the buoyant force = its weight If 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.
Floating objects lighter object heavier object
Oil Tankers empty tanker full tanker