Chapter Fluid pressure and temperature

Pressure  What happens to your ears when you ride in an airplane?  What happens if a submarine goes too deep into the ocean?  What happens to your ears when you ride in an airplane?  What happens if a submarine goes too deep into the ocean?

What is Pressure?  Pressure is defined as the measure of how much force is applied over a given area  The SI unit of pressure is the pascal (PA), which is equal to N/m 2  10 5 Pa is equal to 1 atm  Pressure is defined as the measure of how much force is applied over a given area  The SI unit of pressure is the pascal (PA), which is equal to N/m 2  10 5 Pa is equal to 1 atm

Some Pressures Table 9-2 Some pressures LocationP(Pa) Center of the sun2 x Center of Earth4 x Bottom of the Pacific Ocean6 x 10 7 Atmosphere at sea level1.01 x 10 5 Atmosphere at 10 km above sea level2.8 x 10 4 Best vacuum in a laboratory1 x

Pressure applied to a fluid  When you inflate a balloon/tire etc, pressure increases  Pascal’s Principle  Pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and to the walls of a container  When you inflate a balloon/tire etc, pressure increases  Pascal’s Principle  Pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and to the walls of a container

Lets do a problem  In a hydraulic lift, a 620 N force is exerted on a 0.20 m 2 piston in order to support a weight that is placed on a 2.0 m 2 piston.  How much pressure is exerted on the narrow piston?  How much weight can the wide piston lift?  In a hydraulic lift, a 620 N force is exerted on a 0.20 m 2 piston in order to support a weight that is placed on a 2.0 m 2 piston.  How much pressure is exerted on the narrow piston?  How much weight can the wide piston lift?

Pressure varies with depth in a fluid  Water pressure increases with depth. WHY?  At a given depth, the water must support the weight of the water above it  The deeper you are, the more water there is to support  A submarine can only go so deep an withstand the increased pressure  Water pressure increases with depth. WHY?  At a given depth, the water must support the weight of the water above it  The deeper you are, the more water there is to support  A submarine can only go so deep an withstand the increased pressure

The example of a submarine  Lets take a small area on the hull of the submarine  The weight of the entire column of water above that area exerts a force on that area  Lets take a small area on the hull of the submarine  The weight of the entire column of water above that area exerts a force on that area

Fluid Pressure  Gauge Pressure  does not take the pressure of the atmosphere into consideration  Fluid Pressure as a function of depth  Absolute pressure = atmospheric pressure + (density x free-fall acceleration x depth)  Gauge Pressure  does not take the pressure of the atmosphere into consideration  Fluid Pressure as a function of depth  Absolute pressure = atmospheric pressure + (density x free-fall acceleration x depth)

Point to remember These equations are valid ONLY if the density is the same throughout the fluid

The Relationship between Fluid pressure and buoyant forces  Buoyant forces arise from the differences in fluid pressure between the top and bottom of an immersed object

Atmospheric Pressure  Pressure from the air above  The force it exerts on our body is N ( lb)  Why are we still alive??  Our body cavities are permeated with fluids and gases that are pushing outward with a pressure equal to that of the atmosphere -> Our bodies are in equilibrium  Pressure from the air above  The force it exerts on our body is N ( lb)  Why are we still alive??  Our body cavities are permeated with fluids and gases that are pushing outward with a pressure equal to that of the atmosphere -> Our bodies are in equilibrium

Atmospheric  A mercury barometer is commonly used to measure atmospheric pressure

Kinetic Theory of Gases  Gas contains particles that constantly collide with each other and surfaces  When they collide with surfaces, they transfer momentum  The rate of transfer is equal to the force exerted by the gas on the surface  Force per unit time is the gas pressure  Gas contains particles that constantly collide with each other and surfaces  When they collide with surfaces, they transfer momentum  The rate of transfer is equal to the force exerted by the gas on the surface  Force per unit time is the gas pressure

Lets do a Problem  Find the atmospheric pressure at an altitude of 1.0 x 103 m if the air density is constant. Assume that the air density is uniformly 1.29 kg/m 3 and P0=1.01 x 10 5 Pa

Temperature in a gas  Temperature is the a measure of the average kinetic energy of the particles in a substance  The higher the temperature, the faster the particles move  The faster the particles move, the higher the rate of collisions against a given surface  This results in increased pressure  Temperature is the a measure of the average kinetic energy of the particles in a substance  The higher the temperature, the faster the particles move  The faster the particles move, the higher the rate of collisions against a given surface  This results in increased pressure

HW Assignment  Page 330: Practice 9C, page 331: Section Review

Chapter Fluids in Motion

Fluid Flow  Fluid in motion can be characterized in two ways:  Laminar: Every particle passes a particular point along the same smooth path (streamline) traveled by the particles that passed that point earlier  Turbulent: Abrupt changes in velocity  Eddy currents: Irregular motion of the fluid  Fluid in motion can be characterized in two ways:  Laminar: Every particle passes a particular point along the same smooth path (streamline) traveled by the particles that passed that point earlier  Turbulent: Abrupt changes in velocity  Eddy currents: Irregular motion of the fluid

Ideal Fluid  A fluid that has no internal friction or viscosity and is incompressible  Viscosity: The amount of internal friction within a fluid  Viscous fluids loose kinetic energy because it is transformed into internal energy because of internal friction.  A fluid that has no internal friction or viscosity and is incompressible  Viscosity: The amount of internal friction within a fluid  Viscous fluids loose kinetic energy because it is transformed into internal energy because of internal friction.

Ideal Fluid  Characterized by Steady flow  Velocity, density and pressure are constant at each point in the fluid  Nonturbulent  There is no such thing as a perfectly ideal fluid, but the concept does allow us to understand fluid flow better  In this class, we will assume that fluids are ideal fluids unless otherwise stated  Characterized by Steady flow  Velocity, density and pressure are constant at each point in the fluid  Nonturbulent  There is no such thing as a perfectly ideal fluid, but the concept does allow us to understand fluid flow better  In this class, we will assume that fluids are ideal fluids unless otherwise stated

Principles of Fluid Flow  If a fluid is flowing through a pipe, the mass flowing into the pipe is equal to the mass flowing out of the pipe

Pressure and Speed of Flow  In the Pipe shown to the right, water will move faster through the narrow part  There will be an acceleration  This acceleration is due to an unbalanced force  The water pressure will be lower, where the velocity is higher  In the Pipe shown to the right, water will move faster through the narrow part  There will be an acceleration  This acceleration is due to an unbalanced force  The water pressure will be lower, where the velocity is higher

Bernoulli’s Principle  The pressure in a fluid decreases as the fluid’s velocity increases

Bernoulli’s Equation  Pressure is moving through a pipe with varying cross- section and elevation  Velocity changes, so kinetic energy changes  This can be compensated for by a change in gravitational potential energy or pressure  Pressure is moving through a pipe with varying cross- section and elevation  Velocity changes, so kinetic energy changes  This can be compensated for by a change in gravitational potential energy or pressure

Bernoulli’s Equation

Bernoulli’s Principle: A Special Case  In a horizontal pipe

The Ideal Gas Law  k B is a constant called the Boltzmann’s constant and has been experimentally determined to be 1.38 x J/K

Ideal Gas Law Cont’d  If the number of particles is constant then:  Alternate Form:  m=mass of each particle, M=N x m Total Mass of the gas  If the number of particles is constant then:  Alternate Form:  m=mass of each particle, M=N x m Total Mass of the gas

Real Gas  An ideal gas can be described by the ideal gas law  Real gases depart from ideal gas behavior at high pressures and low temperatures.  An ideal gas can be described by the ideal gas law  Real gases depart from ideal gas behavior at high pressures and low temperatures.