Chapter 4 luids A luid a substance that can low (in contrast to a solid) Air Water luids comort to the boundaries o any container in which we put them, and do not maintain a ixed shape
density and pressure Density mass per unit volume m ρ V m mass o the object V its volume SI units: kg/m 3. Example: What is the mass o the air in the class room with dimensions m and 8 m and a height o 4 m. Density o air.9 kg/m 3 3 m ρv (.9kg / m )*(m *8m *4m) 495kg 3 density and pressure Pressure orce per unit area P A orce A area SI units: N/m Pascal (Pa) Other units: atm.0*0 5 Pa 760 torr 4.7 lb/in Example: What is the pressure orm a 60-kg person on the ground whose two eet cover an area o 500 cm. mg p A A ( 60kg)*(9.8m / s ) /(0.050m ) 000N / m 4
Checkpoint The pressure exerted on the ground by a man is greatest when: A) he stands with both eet lat on the ground B) he stands lat on one oot C) he stands on the toes o one oot D) he lies down on the ground E) all o the above yield the same pressure 5 luids at rest experimental acts A luid exerts a pressure in all directions. At any point at rest the pressure is the same in all directions The pressure increases with depth The orce due to luid pressure always acts perpendicular to any surace it is in contact with 6 3
Hydrostatic pressure The water is in static equilibrium ree-body diagram + mg p A and pa p A p A + ρa y y ) g ( p p + ρg( y ) y or pressure at depth h p p 0 + ρgh 7 Hydrostatic pressure gauge pressure Pressure at depth h p p 0 + ρgh p 0 the pressure due to atmosphere ρgh the pressure due to the liquid above level. The dierence between an absolute pressure and an atmospheric pressure and the gauge pressure 8 4
Checkpoint In a stationary homogeneous liquid: A) pressure is the same at all points B) pressure depends on the direction C) pressure is independent o any atmospheric pressure on the upper surace o the liquid D) pressure is the same at all points at the same level E) none o the above 9 Problem: A submarine Crew members attempt to escape rom a damaged submarine 0 m below the surace. What orce must be applied to a pop-out hatch, which is. m by 0.6 m, to push it out at that depth? Assume that the density o the ocean water is 05 kg/m 3. pa p ρgh ρgha 7.3 0 4 N 670 lb 0 5
Atmospheric pressure The pressure o the Earth s atmosphere varies with altitude. Atmospheric pressure at see level is about atm or.03*0 5 N/m 4.7 lb/in How does a human body withstand the enormous pressure on its surace? Living cells maintain an internal pressure that closely equals the external pressure. Pascal s principle A change in pressure applied to an enclosed incompressible luid is transmitted undiminished to every point o the luid and to the walls o its container Example Pascal s principle and the hydraulic lever A i i A 0 0 A 0 0 i Ai However V Ad A d i i 0 0 d0 di Ai / A0 with a hydraulic lever, a given orce applied over a given distance can be transormed to a greater orce applied over a smaller distance 6
Archimedes principle o buoyancy When a body is ully or partially submerged in a luid, a buoyant orce rom the surrounding luid acts on the body. The orce is directed upward and has a magnitude equal to the weight o the luid that has been displaced by the body b m g ρ Vg m mass o the luid that is displaced by the body 3 Archimedes principle o buoyancy (proo) P A b P A ( P P ) A ( P + ρ gh P ) A ρ gha ρ gv m g m g ρ Vg b the key the pressure increases with the depth 4 7
loating (condition) gravitational orce buoyancy orce g b or an object with a uniorm density ρ Vg ρ V submerged ρ V ρ V submerged g ρ ρ How do steel battleships loat? 5 Problem: Helium balloon What volume o helium is needed i a balloon is to lit a load o 80 kg (including the weight o the empty balloon (air density:.9 kg/m 3, helium density 0.79 kg/m 3 ) ( m + 80kg) g ( ρ V + 80kg) g ρ Vg V g b ρ Vg He air air He 80kg ρ ρ He air 60m 3 6 8
Checkpoint Two identical blocks o ice loat in water as shown. Then: A) block A displaces a greater volume o water since the pressure acts on a smaller bottom area B) block B displaces a greater volume o water since the pressure is less on its bottom C) the two blocks displace equal volumes o water since they have the same weight D) block A displaces a greater volume o water since its submerged end is lower in the water E) Block B displaces a greater volume o water since its submerged end has a greater area 7 Archimedes: Is the crown gold? Real story? Apparent weight in a luid weight weight app b Mass o the crown: 4.7 kg when submerged in water: 3.4 kg w' w ρ Vg w w' w ρ Vg w c ρ Vg ρ Vg c ρ ρ c then the density o the crown,300 kg/m 3 density o gold 9,300 kg/m 3 density o lead,300 kg/m 3 8 9
Thinking about physics rom http://www.amherst.edu/%7ephysicsqanda/ 9 A simple question? 0 0