Physics 201 : Lecture 23 Fluids Density Pressure Variation of pressure with depth 9/14/2018 Physics 201, UW-Madison
Solid-Liquid-Gas Fluids have no definite volume Fluids have no definite shape For fluids molecules are in constant random motion In solids the molecules vibrate around fixed locations The molecules exert forces on each other 9/14/2018 Physics 201, UW-Madison
Density Density = Mass/Volume = M / V units = kg/m3 Densities of common things (kg/m3) Water 1000 ice 917 (floats on water) blood 1060 (sinks in water) lead 11,300 copper 8890 mercury 13,600 aluminum 2700 wood 550 air 1.29 helium 0.18 Iron or steel 7800 (but, a steel battle ship floats) 9/14/2018 Physics 201, UW-Madison 1
Lecture 23 : Preflight 1 Density of substance in gaseous phase is always lower than that in its solid phase. 1. Yes 2. No This is indeed true -- molecules are far apart in gaseous phase than in liquid phase. 9/14/2018 Physics 201, UW-Madison
Lecture 23 : Preflight 2 Density of substance in liquid phase is always lower than that in its solid phase. 1. Yes 2. No The density of liquid water is greater than that of ice. This is why fish survive at the bottom of the lake even when its surface is frozen. However, this is not true for all substances. 9/14/2018 Physics 201, UW-Madison
Pressure = Force per Unit Area Which will hurt more? 1) If you are pricked by a nail with a force equal to your weight 2) If your entire weight is supported by a bed of similar nails 3) Both will hurt the same 9/14/2018 Physics 201, UW-Madison
Pressure in a fluid Impulse to wall: Fxt = px = (Mvx) molecule Impulse to wall: Fxt = px = (Mvx) Fx = (Mvx)/ t Force is perpendicular to surface Force proportional to area of surface pressure (p) p = Force/area [N/m2] 1 N/m2 = 1 Pascal (Pa) 9/14/2018 Physics 201, UW-Madison
Pressure Atmospheric Pressure y Atmospheric Pressure Even when there is no breeze air molecules are continuously bombarding everything around - results in pressure normal atmospheric pressure = 1.01 x 105 Pa (14.7 lb/in2) 9/14/2018 Physics 201, UW-Madison
Lecture 23 : Preflight 3 Pressure on an object immersed in a liquid is felt only by its top surface. 1. Yes 2. No There is pressure all around! 9/14/2018 Physics 201, UW-Madison
Pressure is equal on all sides Net F = 0 Force same in all directions Pressure inside is perpendicular to surface at all points. Fluids at rest have no shear. 9/14/2018 Physics 201, UW-Madison
Variation of pressure with depth True for all shapes of containers 9/14/2018 Physics 201, UW-Madison
Forces on a Dam Two dams A and B are of identical height and length. A holds twice as much water behind it as B. How do the forces on the dams compare 1. Both exert the same pressure 2. Dam A exerts twice the pressure as Dam B 3. Dam A exerts four times the pressure as Dam B 9/14/2018 Physics 201, UW-Madison
Forces on a Dam 9/14/2018 Physics 201, UW-Madison
Barometer: atmospheric pressure p2=patm p1=0 p2 = p1 + gh patm = gh Measure h, determine patm example--Mercury = 13,600 kg/m3 patm = 1.05 x 105 Pa h(1 atm) = 0.757 m = 757 mm = 29.80” (for 1 atm) 9/14/2018 Physics 201, UW-Madison
Barometer Suppose you have a barometer with mercury and a barometer with water. How does the height hwater compare with the height hmercury? 1. hwater is much larger than hmercury 2. hwater is a little larger than hmercury 3. hwater is a little smaller than hmercury 4. hwater is much smaller than hmercury Pa h P=0 9/14/2018 Physics 201, UW-Madison
Lecture 23 : Preflight 6 Is it possible to stand on the roof of a five story (50 foot) tall house and drink, using a straw, from a glass on the ground? 1. No 2. Yes Pa h P=0 The pressure that the air pushes down on the liquid in the glass is not enough to push all of the liquid up the 50ft through the straw. Evacuate the straw by sucking How high will water rise? no more than h = Pa/g = 33.8” no matter how hard you suck! 9/14/2018 Physics 201, UW-Madison
Atmospheric pressure and free fall When a hole is made in the side of a container holding water, water flows out and follows a parabolic trajectory. If the container is dropped in free fall, the water flow 1. diminishes. 2. stops altogether. 3. goes out in a straight line. 4. curves upward. When the container is at rest with respect to Earth, there is a pressure on the walls of the container due to the water. The pressure depends on the depth, P = gh. When the container is in free fall, both the water and the container have an acceleration of zero, not g, in the container frame of reference. In this frame, P = 0 - no outward flow. 9/14/2018 Physics 201, UW-Madison