Chapter 11 Fluids

States of matter Solid Liquid Gas Plasma

Fluids Fluids – substances that can flow (gases, liquids) Fluids conform with the boundaries of any container in which they are placed Fluids lack orderly long-range arrangement of atoms and molecules they consist of Fluids can be compressible and incompressible

Liquids Have a definite volume, but no definite shape Exist at a higher temperature than solids The molecules “wander” through the liquid in a random fashion The intermolecular forces are not strong enough to keep the molecules in a fixed position

Gases Have neither definite volume nor definite shape Molecules are in constant random motion The molecules exert only weak forces on each other Average distance between molecules is large compared to the size of the molecules

Plasmas Matter heated to a very high temperature Many of the electrons are freed from the nucleus Result is a collection of free, electrically charged ions Plasmas exist inside stars

Density and pressure Density SI unit of density: kg/m3 Pressure Blaise Pascal (1623 - 1662) Density and pressure Density SI unit of density: kg/m3 Pressure SI unit of pressure: N/m2 = Pa (pascal) Pressure is a scalar – at a given point in a fluid the measured force is the same in all directions For a uniform force on a flat area

Atmospheric pressure Atmospheric pressure: P0 = 1.00 atm = 1.013 x 105 Pa Specific gravity of a substance is the ratio of its density to the density of water at 4° C (1000 kg/m3) Specific gravity is a unitless ratio

Fluids at rest For a fluid at rest (static equilibrium) the pressure is called hydrostatic For a horizontal-base cylindrical water sample in a container

Fluids at rest The hydrostatic pressure at a point in a fluid depends on the depth of that point but not on any horizontal dimension of the fluid or its container Difference between an absolute pressure and an atmospheric pressure is called the gauge pressure

Measuring pressure Mercury barometer Open-tube manometer

Chapter 11 Problem 29 A 1.00-m-tall container is filled to the brim, partway with mercury and the rest of the way with water. The container is open to the atmosphere. What must be the depth of the mercury so that the absolute pressure on the bottom of the container is twice the atmospheric pressure?

Pascal’s principle Pascal’s principle: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container Hydraulic lever With a hydraulic lever, a given force applied over a given distance can be transformed to a greater force applied over a smaller distance

Archimedes’ principle of Syracuse (287-212 BCE) Archimedes’ principle Buoyant force: For imaginary void in a fluid p at the bottom > p at the top Archimedes’ principle: when a body is submerged in a fluid, a buoyant force from the surrounding fluid acts on the body. The force is directed upward and has a magnitude equal to the weight of the fluid that has been displaced by the body

Archimedes’ principle Sinking: Floating: Apparent weight: If the object is floating at the surface of a fluid, the magnitude of the buoyant force (equal to the weight of the fluid displaced by the body) is equal to the magnitude of the gravitational force on the body

Chapter 11 Problem 53 One kilogram of glass (ρ = 2.60 × 103 kg/m3) is shaped into a hollow spherical shell that just barely floats in water. What are the inner and outer radii of the shell? Do not assume that the shell is thin.

Motion of ideal fluids Flow of an ideal fluid: Steady (laminar) – the velocity of the moving fluid at any fixed point does not change with time (either in magnitude or direction) Incompressible – density is constant and uniform Nonviscous – the fluid experiences no drag force Irrotational – in this flow the test body will not rotate about its center of mass

Equation of continuity Equation of continuity For a steady flow of an ideal fluid through a tube with varying cross-section Equation of continuity

Bernoulli’s equation For a steady flow of an ideal fluid: Daniel Bernoulli (1700 - 1782) Bernoulli’s equation For a steady flow of an ideal fluid: Kinetic energy Gravitational potential energy Internal (“pressure”) energy

Bernoulli’s equation Total energy

Chapter 11 Problem 72 An airplane has an effective wing surface area of 16 m2 that is generating the lift force. In level flight the air speed over the top of the wings is 62.0 m/s, while the air speed beneath the wings is 54.0 m/s. What is the weight of the plane?

Viscous fluid flow Viscosity: friction between the layers of a fluid Layers in a viscous fluid have different velocities The velocity is greatest at the center Cohesive forces between the fluid and the walls slow down the fluid on the outside

Questions?