Fluids and Pressure Introduction Section 0 Lecture 1 Slide 1 Lecture 20 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 20 Fluids and Pressure

Introduction Section 0 Lecture 1 Slide 2 Lecture 20 Slide 2 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet *Homework Handout

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 3 Lecture 20 Slide 3 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 20 Fluids and Pressure Introduction

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 4 Lecture 20 Slide 4 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Dennison’s Laws of Fluids When push comes to shove, fluids are just like other stuff. Pascal’s Principle: Pressure extends uniformly in all directions in a fluid. Boyle’s Law: Work on a fluid equals PΔV Bernoulli’s Principle: Conservation of energy for fluids

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 5 Lecture 20 Slide 5 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 20 Fluids and Pressure Hydraulics: A Simple Machine with Fluids

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 6 Lecture 20 Slide 6 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 How does a hydraulic jack work? A force applied to a piston with a small area can produce a large increase in pressure in the fluid because of the small area of the piston. This increase in pressure is transmitted through the fluid to the piston with the larger area (Pascal’s Principle). The force exerted on the larger piston is proportional to the area of the piston: F = PA. Applying the same pressure to the larger area of the second piston results in a larger force on the second piston. But this comes at a price. Conservation of energy says work in must equal work out that is ΔW=F Δd = (P A) Δd = P ΔV, so Δd 1 > Δd 2 Another way to think of this is conservation of stuff: V in = V out

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 7 Lecture 20 Slide 7 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 A force of 10 N is applied to a circular piston with an area of 2 cm 2 in a hydraulic jack. The output piston for the jack has an area of 100 cm 2. What is the pressure in the fluid? a)0.002 Pa b)5 Pa c)10 Pa d)50 kPa F 1 = 10 N A 1 = 2 cm 2 = m 2 P = F 1 / A 1 = 10 N / m 2 = 50,000 N/m 2 = 50 kPa

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 8 Lecture 20 Slide 8 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 What is the force exerted on the output piston by the fluid? a)50 N b)500 N c)5,000 N d)50,000 N P = 50 kPa A 2 = 100 cm 2 = 0.01 m 2 F 1 = PA 1 = (50,000 N/m 2 )(0.01 m 2 )= 500 N The mechanical advantage is 500 N / 10 N = 50.

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 9 Lecture 20 Slide 9 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Hydraulic Devices

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 10 Lecture 20 Slide 10 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Hydraulic Brakes

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 11 Lecture 20 Slide 11 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 20 Fluids and Pressure Barometers and Atmospheric Pressure

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 12 Lecture 20 Slide 12 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Atmospheric Pressure and the Behavior of Gases Living on the surface of the earth, we are at the bottom of a sea of air. This sea of air is thinner at higher altitudes. It is also thinner during certain weather conditions. We describe this property by atmospheric pressure: the pressure of the layer of air that surrounds the earth. –At sea level, the atmospheric pressure is 100 kPa, or 14.7 pounds per square inch, but it decreases with altitude.

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 13 Lecture 20 Slide 13 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Torricelli invented the barometer, a device for measuring atmospheric pressure, in an attempt to explain why water pumps could pump water to a height of only 32 feet. He filled a tube with mercury and inverted it into an open container of mercury. Mercury worked well because it is much denser than water. –Density is the mass of an object divided by its volume. Air pressure acting on the mercury in the dish supported a column of mercury, of height proportional to the atmospheric pressure. The Barometer

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 14 Lecture 20 Slide 14 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Otto von Guericke performed a famous experiment to demonstrate the effects of air pressure. He designed two bronze hemispheres that could be smoothly joined together at their rims. He pumped the air out of the sphere formed from the two hemispheres. Two eight-horse teams were unable to pull the hemispheres apart. Making Physics Pay Big Bucks

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 15 Lecture 20 Slide 15 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 In other experiments on variations in atmospheric pressure, Pascal sent his brother-in-law to the top of a mountain with a barometer and a partially inflated balloon. The balloon expanded as the climbers gained elevation. This was evidence of a decrease in the external atmospheric pressure.

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 16 Lecture 20 Slide 16 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Boyle’s Law Variations in the volume and density of a gas that accompanies changes in pressure were studied by Boyle and Mariotte. The density of a column of air decreases as altitude increases because air expands as pressure decreases.

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 17 Lecture 20 Slide 17 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Application of Avagadro’s NUmber

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 18 Lecture 20 Slide 18 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Application of Avagadro’s NUmber

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 19 Lecture 20 Slide 19 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Boyle’s Law Boyle discovered that the volume of a gas is inversely proportional to the pressure. Boyle’s Law: PV = constant If the pressure increases, the volume decreases. The density of a column of air decreases as altitude increases because air expands as pressure decreases. P 1 V 1 = P 2 V 2

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 20 Lecture 20 Slide 20 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 A fixed quantity of gas is held in a cylinder capped at one end by a movable piston. The pressure of the gas is initially 1 atmosphere (101 kPa) and the volume is initially 0.3 m 3. What is the final volume of the gas if the pressure is increased to 3 atmospheres at constant temperature? a)0.1 m 3 b)0.3 m 3 c)1 m 3 d)3 m 3 P 1 = 1 atm P 2 = 3 atm V 1 = 0.3 m 3 V 2 = ? V 2 = P 1 V 1 / P 2 = (1 atm)(0.3 m 3 ) / 3 atm = 0.1 m 3

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 21 Lecture 20 Slide 21 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Range of Pressures

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 22 Lecture 20 Slide 22 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Barometers

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 23 Lecture 20 Slide 23 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Pressure Gauges

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 24 Lecture 20 Slide 24 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Capacitance Manometer

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 25 Lecture 20 Slide 25 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Convection Pressure Gauges

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 26 Lecture 20 Slide 26 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 27 Lecture 20 Slide 27 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 20 Fluids and Pressure Archimedes's Principle: Buoyant Forces

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 28 Lecture 20 Slide 28 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Archimedes’ Principle The average density of an object compared to a fluid determines whether the object will sink or float in that liquid. The upward force that pushes objects back toward the surface in liquids is called the buoyant force. Archimedes’ Principle: The buoyant force acting on an object fully or partially submerged in a fluid is equal to the weight of the fluid displaced by the object.

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 29 Lecture 20 Slide 29 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 30 Lecture 20 Slide 30 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Archimedes’ Principle For example, consider a block submerged in water, suspended from a string. –The pressure of the water pushes on the block from all sides. –Because the pressure increases with depth, the pressure at the bottom of the block is greater than at the top. –There is a larger force ( F = PA ) pushing up at the bottom than there is pushing down at the top. –The difference between these two forces is the buoyant force. The buoyant force is proportional to both the height and the cross-sectional area of the block, and thus to its volume. The volume of the fluid displaced is directly related to the weight of the fluid displaced.

Fluids and Pressure Introduction Section 0 Lecture 1 Slide 31 Lecture 20 Slide 31 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology Next Lab/Demo: Rotational Motion Fluids Thursday 1:30-2:45 ESLC 46 Ch 8 and 9 Next Class: Wednesday 10:30-11:20 BUS 318 room Review Ch 9