Fluids Lecture Outline PDF

Chapter 10 Fluids © 2016 Pearson Education, Ltd.  10-1 Phases of Matter The three common phases of matter are solid, liquid, and gas. A solid has a definite shape and size. A liquid has a fixed volume but can b...

Chapter 10 Fluids © 2016 Pearson Education, Ltd.  10-1 Phases of Matter The three common phases of matter are solid, liquid, and gas. A solid has a definite shape and size. A liquid has a fixed volume but can be any shape. A gas can be any shape and also can be easily compressed. Liquids and gases both flow, and are called fluids. © 2016 Pearson Education, Ltd.  10-2 Density and Specific Gravity The density ρ of an object is its mass per unit volume: (10-1) The SI unit for density is kg/m3. Density is also sometimes given in g/cm3; to convert g/cm3 to kg/m3, multiply by 1000. Water at 4°C has a density of 1 g/cm3 = 1000 kg/m3. The specific gravity of a substance is the ratio of its density to that of water. © 2016 Pearson Education, Ltd.  Mass, given volume and density. What is the mass of a solid iron wrecking ball of radius 18 cm? A bottle has a mass of 35.00 g when empty and 98.44 g when filled with water. When filled with another fluid, the mass is 89.22 g. What is the specific gravity of this other fluid? © 2016 Pearson Education, Ltd.  10-3 Pressure in Fluids Pressure is defined as the force per unit area. Pressure is a scalar; the units of pressure in the SI system are pascals: 1 Pa = 1 N/m2 Pressure is the same in every direction in a fluid at a given depth; if it were not, the fluid would flow. Also for a fluid at rest, there is no component of force parallel to any solid surface once again, if there were the fluid would flow. © 2016 Pearson Education, Ltd.  10-3 Pressure in Fluids The pressure at a depth h below the surface of the liquid is due to the weight of the liquid above it. We can quickly calculate: (10-3a) This relation is valid for any liquid whose density does not change with depth. © 2016 Pearson Education, Ltd.  A 60-kg person’s two feet cover an area of (a) Determine the pressure exerted by the two feet on the ground. (b) If the person stands on one foot, what will be the pressure under that foot? The surface of the water in a storage tank is 30 m above a water faucet in the kitchen of a house. Calculate the difference in water pressure between the faucet and the surface of the water in the tank. © 2016 Pearson Education, Ltd.  10-4 Atmospheric Pressure and Gauge Pressure At sea level the atmospheric pressure is about 1.013 × 105 N/m2; this is called one atmosphere (atm). Another unit of pressure is the bar: 1 bar = 1.00 × 105 N/m2 Standard atmospheric pressure is just over 1 bar. This pressure does not crush us, as our cells maintain an internal pressure that balances it. © 2016 Pearson Education, Ltd.  10-4 Atmospheric Pressure and Gauge Pressure Most pressure gauges measure the pressure above the atmospheric pressure—this is called the gauge pressure. The absolute pressure is the sum of the atmospheric pressure and the gauge pressure. P = PA + PG © 2016 Pearson Education, Ltd.  10-5 Pascal’s Principle If an external pressure is applied to a confined fluid, the pressure at every point within the fluid increases by that amount. This principle is used, for example, in hydraulic lifts and hydraulic brakes. © 2016 Pearson Education, Ltd. © 2016 Pearson Education, Ltd.  10-6 Measurement of Pressure; Gauges and the Barometer There are a number of different types of pressure gauges. This one is an open- tube manometer. The pressure in the open end is atmospheric pressure; the pressure being measured will cause the fluid to rise until the pressures on both sides at the same height are equal. © 2016 Pearson Education, Ltd.  This is a mercury barometer, developed by Torricelli to measure atmospheric pressure. The height of the column of mercury is such that the pressure in the tube at the surface level is 1 atm. Therefore, pressure is often quoted in millimeters (or inches) of mercury. © 2016 Pearson Education, Ltd. © 2016 Pearson Education, Ltd. © 2016 Pearson Education, Ltd.  10-7 Buoyancy and Archimedes’ Principle This is an object submerged in a fluid. There is a net force on the object because the pressures at the top and bottom of it are different. The buoyant force is found to be the upward force on the same volume of water: © 2016 Pearson Education, Ltd.  10-7 Buoyancy and Archimedes’ Principle The net force on the object is then the difference between the buoyant force and the gravitational force. © 2016 Pearson Education, Ltd.  10-7 Buoyancy and Archimedes’ Principle If the object’s density is less than that of water, there will be an upward net force on it, and it will rise until it is partially out of the water. © 2016 Pearson Education, Ltd.  A 70-kg ancient statue lies at the bottom of the sea. Its volume is 30000 cm3 How much force is needed to lift it (without acceleration)? © 2016 Pearson Education, Ltd.  When a crown of mass 14.7 kg is submerged in water, an accurate scale reads only 13.4 kg. Is the crown made of gold? © 2016 Pearson Education, Ltd.  10-7 Buoyancy and Archimedes’ Principle For a floating object, the fraction that is submerged is given by the ratio of the object’s density to that of the fluid. © 2016 Pearson Education, Ltd. © 2016 Pearson Education, Ltd.  What volume V of helium is needed if a balloon is to lift a load of 180 kg (including the weight of the empty balloon)? © 2016 Pearson Education, Ltd.  10-8 Fluids in Motion; Flow Rate and the Equation of Continuity If the flow of a fluid is smooth, it is called streamline or laminar flow (a). Above a certain speed, the flow becomes turbulent (b). Turbulent flow has eddies; the viscosity of the fluid is much greater when eddies are present. © 2016 Pearson Education, Ltd.  10-8 Fluids in Motion; Flow Rate and the Equation of Continuity We will deal with laminar flow. The mass flow rate is the mass that passes a given point per unit time. The flow rates at any two points must be equal, as long as no fluid is being added or taken away. This gives us the equation of continuity: (10-4a) © 2016 Pearson Education, Ltd.  10-8 Fluids in Motion; Flow Rate and the Equation of Continuity If the density doesn’t change—typical for liquids—this simplifies to A1v1 = A2v2. Where the pipe is wider, the flow is slower. © 2016 Pearson Education, Ltd. © 2016 Pearson Education, Ltd.  10-9 Bernoulli’s Equation A fluid can also change its height. By looking at the work done as it moves, we find: (10-5) This is Bernoulli’s equation. One thing it tells us is that as the speed goes up, the pressure goes down. © 2016 Pearson Education, Ltd. © 2016 Pearson Education, Ltd.  10-10 Applications of Bernoulli’s Principle: Torricelli, Airplanes, Baseballs, Blood Flow Using Bernoulli’s principle, we find that the speed of fluid coming from a spigot on an open tank is: (10-6) This is called Torricelli’s theorem. © 2016 Pearson Education, Ltd.  10-10 Applications of Bernoulli’s Principle: Torricelli, Airplanes, Baseballs, Blood Flow Lift on an airplane wing is due to the different air speeds and pressures on the two surfaces of the wing. © 2016 Pearson Education, Ltd.  10-10 Applications of Bernoulli’s Principle: Torricelli, Airplanes, Baseballs, Blood Flow A venturi meter can be used to measure fluid flow by measuring pressure differences. © 2016 Pearson Education, Ltd.  10-12 Flow in Tubes; Poiseuille’s Equation, Blood Flow The rate of flow in a fluid in a round tube depends on the viscosity of the fluid, the pressure difference, and the dimensions of the tube. The volume flow rate is proportional to the pressure difference, inversely proportional to the length of the tube and to the pressure difference, and proportional to the fourth power of the radius of the tube. © 2016 Pearson Education, Ltd. © 2016 Pearson Education, Ltd. © 2016 Pearson Education, Ltd. © 2016 Pearson Education, Ltd. © 2016 Pearson Education, Ltd. © 2016 Pearson Education, Ltd.