Advanced Physics Chapter 10 Fluids

Chapter 10 Fluids 10.1 Density and Specific Gravity 10.1 Density and Specific Gravity 10.2 Pressure in Fluids 10.3 Atmospheric and Gauge Pressure 10.4 Pascal's Principle 10.5 Measurement of Pressure 10.6 Buoyancy and Archimedes’ Principle 10.7 Fluids in Motion 10.8 Bernoulli’s Principle 10.9 Applications of Bernoulli’s Principle 10.10 Viscosity 10.11 Flow in Tubes 10.12 Surface Tension and Capillarity 10.13 Pumps; the Heart and Blood Pressure

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

10.1 Density and Specific Gravity 10.1 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?)

10.2 Pressure in Fluids P = F/A Pressure—a force applied per unit area 10.2 Pressure in Fluids Pressure—a force applied per unit area P = F/A Units Pascal (N/m2)

10.2 Pressure in Fluids Important properties of fluids at rest: 10.2 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

10.2 Pressure in Fluids P = F/A = gh P = gh 10.2 Pressure in Fluids Pressure variation with depth P = F/A = gh Change in pressure with change in depth P = gh

10.3 Atmospheric and Gauge Pressure 10.3 Atmospheric and Gauge Pressure Atmospheric Pressure (PA)—the pressure of the Earth's atmosphere at sea level 1atm = 101.3kPa = 14.7 lbs/in2 = 760 mmHg

10.3 Atmospheric and Gauge Pressure Gauge Pressure (PG)—the pressure measured on a pressure gauge Measures the pressure over and above atmospheric pressure P = PA + PG P = Absolute pressure

10.4 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

10.4 Pascal's Principle Pin = Pout Fout/Aout = Fin/Ain Example: hydraulic lift Pin = Pout Fout/Aout = Fin/Ain Fout/Fin = Aout/Ain Fin

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

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

10.5 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

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

10.5 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

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

10.5 Measurement of Pressure 10.5 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 103 kg/m2)

10.6 Buoyancy and Archimedes’ Principle 10.6 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

10.6 Buoyancy and Archimedes’ Principle 10.6 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

10.6 Buoyancy and Archimedes’ Principle 10.6 Buoyancy and Archimedes’ Principle Buoyant force (FB) The net force due to the force of the fluid down (F1) and up (F2) FB = F2 – F1 Since F = PA =FghA FB = FgA(h2—h1) FB = FgAh = FgV F1 h1 h2 h=h2-h1 F2

10.6 Buoyancy and Archimedes’ Principle 10.6 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 FB = FgV = mFg 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 FB FB Wt = mg

10.6 Buoyancy and Archimedes’ Principle 10.6 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 (FB) w’ = w – FB w/(w—w’) = o/ F FB Wt = mg

10.6 Buoyancy and Archimedes’ Principle 10.6 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 Vdispl/Vo = o/ F FB = FVdisplg W= mg=oVog

10.7 Fluids in Motion Fluid Dynamics (Hydrodynamics) 10.7 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

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

10.7 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 l2 v1 v2 A2 A1

10.7 Fluids in Motion Mass Flow rate 10.7 Fluids in Motion Mass Flow rate The volume of fluid passing through area A1 in time t is just A1 l1 where l1 is the distance the fluid moves in time t. Since the velocity of fluid passing A1 is v = l1/ t, the mass flow rate m1/ t through area A1 is m1/ t = 1A1v1 l1 l2 v1 v2 A2 A1

10.7 Fluids in Motion Mass Flow rate m1/ t = 1A1v1 10.7 Fluids in Motion Mass Flow rate m1/ t = 1A1v1 Since what flow through A1 must also flow through A2 then m1/ t = m2/ t So 1A1v1 = 2A2v2 l1 l2 v1 v2 A2 A1

10.7 Fluids in Motion Mass Flow rate 1A1v1 = 2A2v2 10.7 Fluids in Motion Mass Flow rate 1A1v1 = 2A2v2 Since for most fluids density doesn’t change (too much) with an increase in depth so it can be cancelled out. Equation of continuity A1v1 = A2v2 [Av] represents the volume rate of flow V/t of the fluid l1 l2 v1 v2 A2 A1

10.7 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 l2 v1 v2 A2 A1

10.8 Bernoulli’s Principle 10.8 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 A2 then it would back up fluid in A1 so its slow down from A1to A2 but it actually speeds up. l1 l2 v1 P1 v2 P2 A2 A1

10.8 Bernoulli’s Principle 10.8 Bernoulli’s Principle Bernoulli’s Equation (derivation in Book) P1 + 1/2v12 + gy1 = P2 + 1/2v22 + gy2 Or P + 1/2v2 + gy = constant This is based on the work needed to move the fluid from Part 1 to Part 2 of the tube. l2 V2 P2 A2 l1 V1 P1 A1 y2 y1

10.9 Applications of Bernoulli’s Principle 10.9 Applications of Bernoulli’s Principle Special cases of Bernoulli’s Equation: Liquid flowing out of an open container with a spigot at the bottom Since both P’s are atmospheric pressure and v2 is almost zero 1/2v12 + gy1 = gy2 v1 = (2g(y2 – y1))1/2 V2 = 0 Y2 – y1 v1

10.9 Applications of Bernoulli’s Principle 10.9 Applications of Bernoulli’s Principle Special cases of Bernoulli’s Equation: Liquid flowing but there is no appreciable change in height P1 + 1/2v12 = P2 + 1/2v22 Example: your Physics toy

Read and Write Worksheet Read and Write Worksheet Read Sections 10.10 –10.13 Answer the questions written on ½ sheet of paper