Advanced Physics Chapter 10 Fluids

Chapter 10 Fluids 10.1 Phases of Matter 10.2 Density and Specific Gravity 10.3 Pressure in Fluids 10.4 Atmospheric and Gauge Pressure 10.5 Pascal's Principle 10.6 Measurement of Pressure 10.7 Buoyancy and Archimedes’ Principle 10.8 Fluids in Motion 10.9 Bernoulli’s Principle Applications of Bernoulli’s Principle Viscosity Flow in Tubes Surface Tension and Capillarity Pumps; the Heart and Blood Pressure

10.1 Phases of Matter Four phases of matter (each with different properties) Solid Liquid Gas Plasma Fluids are anything that can flow so they are ?

10.2 Density and Specific Gravity Density- how compact an object is Ratio of mass to volume  = m/V Many units for density Specific Gravity- ratio of the density of a substance to the density of a standard substance (usually water) No units (Why?)

10.3 Pressure in Fluids Pressure—a force applied per unit area P = F/A Units Pascal (N/m 2 )

10.3 Pressure in Fluids Important properties of fluids at rest: Fluids exert a pressure in all directions The force always acts perpendicular to the surface it is in contact with The pressure at equal depths within the fluid is the same

10.3 Pressure in Fluids Pressure variation with depth P = F/A =  gh Change in pressure with change in depth  P =  g  h

10.4 Atmospheric and Gauge Pressure Atmospheric Pressure (P A )—the pressure of the Earth's atmosphere at sea level 1atm = 101.3kPa = 14.7 lbs/in 2 = 760 mmHg

10.4 Atmospheric and Gauge Pressure Gauge Pressure (P G )— the pressure measured on a pressure gauge Measures the pressure over and above atmospheric pressure P = P A + P G P = Absolute pressure

10.5 Pascal's Principle Pascal's Principle states that pressure applied to a confined fluid increases the pressure throughout by the same amount Example: hydraulic lift

10.5 Pascal's Principle Pascal's Principle Example: hydraulic lift P in = P out F out /A out = F in /A in F out /F in = A out /A in F in F out

10.6 Measurement of Pressure Manometer—tubular device used for measuring pressure To measure pressure with a manometer remember the quote “Nothing sucks in Science, it just blows”

10.6 Measurement of Pressure Manometer—tubular device used for measuring pressure Types: Open-tube manometer Closed-tube manometer (barometer)

10.6 Measurement of Pressure Open-tube manometer both ends of tube are open; one is connected to the container of gas and the other is open to the atmosphere GAS

10.6 Measurement of Pressure Open-tube manometer P = P o +  gh Where: P = pressure of gas P o = atmospheric pressure  gh = pressure of fluid displaced GAS

10.6 Measurement of Pressure Closed-tube manometer one end of tube is open; one is connected to the container of gas is open and the other is sealed GAS

10.6 Measurement of Pressure Closed-tube manometer P = P o +  gh But since it is closed P o = 0 so….. P =  gh GAS

10.6 Measurement of Pressure Barometer-closed-tube manometer inverted in a cup of mercury used to measure atmospheric pressure P =  gh Where  is the density of mercury (13.6 x 10 3 kg/m 2 )

10.7 Buoyancy and Archimedes’ Principle Objects submerged in a fluid appear to weigh less than they do outside the fluid Many objects will float in a fluid These are two examples of buoyancy

10.7 Buoyancy and Archimedes’ Principle Buoyant force—the upward force exerted on an object in a fluid. It occurs because the pressure in a fluid increases with depth

10.7 Buoyancy and Archimedes’ Principle Buoyant force (F B ) The net force due to the force of the fluid down (F 1 ) and up (F 2 ) F B = F 2 – F 1 Since F = PA =  F ghA F B =  F gA(h 2 —h 1 ) F B =  F gAh =  F gV F1F1 F2F2 h1h1 h2h2 h=h 2 -h 1

10.7 Buoyancy and Archimedes’ Principle Archimedes’ Principle The buoyant force on a body immersed in a fluid is equal to the weight of the fluid displaced by that object F B =  F gV = m F g To be in equilibrium the weight of object must be the same as the weight of fluid displaced so that it is equal and opposite F B FBFB Wt = mg

10.7 Buoyancy and Archimedes’ Principle Archimedes’ Principle So when an object is weighed in water its apparent weight (in fluid, w’) is equal to its actual weight (w) minus its buoyant force (F B ) w’ = w – F B w/(w—w’) =  o /  F FBFB Wt = mg

10.7 Buoyancy and Archimedes’ Principle Archimedes’ Principle Also relates to objects floating in fluid Object floats in a fluid if its density is less than the density of the fluid The amount submerged can be calculated by V displ /V o =  o /  F F B =  F V displ g W= mg=  o V o g

Homework? Read Ch due Monday Problems on page 281: 1, 3, 5, 9, 11, 17, 22, 23, 25, 29, 31, 33 will go over some on Monday….

10.8 Fluids in Motion Fluid Dynamics (Hydrodynamics) The study of fluids in motion Two types of fluid flow: Streamline (laminar) flow--particles follow a smooth path Turbulent flow—small eddies (whirlpool-like circles) form

10.8 Fluids in Motion Turbulent flow causes an effect called viscosity due to the internal friction of the fluid particles

10.8 Fluids in Motion Lets study the laminar flow of a liquid through an enclosed tube or pipe Mass Flow rate is the mass of fluid (  m) that passes a given point per unit time (  t) l1l1 l2l2 A1A1 A2A2 v1v1 v2v2

10.8 Fluids in Motion Mass Flow rate The volume of fluid passing through area A 1 in time  t is just A 1  l 1 where  l 1 is the distance the fluid moves in time  t. Since the velocity of fluid passing A 1 is v =  l 1 /  t, the mass flow rate  m 1 /  t through area A 1 is  m 1 /  t =  1 A 1 v 1 l1l1 l2l2 A1A1 A2A2 v1v1 v2v2

10.8 Fluids in Motion Mass Flow rate  m 1 /  t =  1 A 1 v 1 Since what flow through A 1 must also flow through A 2 then  m 1 /  t =  m 2 /  t So  1 A 1 v 1 =  2 A 2 v 2 l1l1 l2l2 A1A1 A2A2 v1v1 v2v2

10.8 Fluids in Motion Mass Flow rate  1 A 1 v 1 =  2 A 2 v 2 Since for most fluids density doesn’t change (too much) with an increase in depth so it can be cancelled out. Equation of continuity A 1 v 1 = A 2 v 2 [Av] represents the volume rate of flow  V/  t of the fluid l1l1 l2l2 A1A1 A2A2 v1v1 v2v2

10.8 Fluids in Motion Since the volume rate of flow  V/  t of the fluid is the same in all parts of the pipe the velocity through smaller diameter sections must be greater than through larger diameter sections l1l1 l2l2 A1A1 A2A2 v1v1 v2v2

10.9 Bernoulli’s Principle Bernoulli’s Principle— where the velocity of a fluid is high, the pressure is low and where the velocity is low the pressure is high. This makes sense; if the pressure was larger at A 2 then it would back up fluid in A 1 so its slow down from A 1 to A 2 but it actually speeds up. l1l1 l2l2 A1A1 A2A2 v1v1 v2v2 P1P1 P2P2

10.9 Bernoulli’s Principle Bernoulli’s Equation (derivation in Book) P 1 + 1/2  v  gy 1 = P 2 + 1/2  v  gy 2 Or P + 1/2  v 2 +  gy = constant This is based on the work needed to move the fluid from Part 1 to Part 2 of the tube. y1y1 y2y2 l1l1 l2l2 A1A1 A2A2 V1P1V1P1 V2P2V2P2

10.10 Applications of Bernoulli’s Principle Special cases of Bernoulli’s Equation: Liquid flowing out of an open container with a spigot at the bottom Torricelli’s theorem Since both P’s are atmospheric pressure and v 2 is almost zero 1/2  v  gy 1 =  gy 2 v 1 = (2g(y 2 – y 1 )) 1/2 V 2 = 0 v1v1 Y 2 – y 1

10.10 Applications of Bernoulli’s Principle Special cases of Bernoulli’s Equation: Liquid flowing but there is no appreciable change in height P 1 + 1/2  v 1 2 = P 2 + 1/2  v 2 2

10.10 Applications of Bernoulli’s Principle Airplane wings and dynamic lift Airplanes experience a “lift” force due to the shape of their wings Air get to top and bottom at same time Air must move faster on top so lower pressure than bottom Net upward force

10.10 Applications of Bernoulli’s Principle

Airplane wings and dynamic lift What about the shape of a spoiler?

10.10 Applications of Bernoulli’s Principle Sailboats Due to shape of sail Needs a keel of it would fall over

10.10 Applications of Bernoulli’s Principle Baseballs throwing a curve

10.10 Applications of Bernoulli’s Principle Venturi tube A tube that is constructed in the middle to speed up the flow of air

10.10 Applications of Bernoulli’s Principle Venturi tube When a tube is placed in the center fluid is drawn up it (why?)

10.10 Applications of Bernoulli’s Principle Chimneys

10.10 Applications of Bernoulli’s Principle Air brush or paint gun