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Chapter 9
Solids and Fluids
1. Introduction
2. Fluids at Rest
3. Fluid Motion
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States of Matter
� Solid
� Liquid
� Gas
� Plasma
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Density and Specific Gravity
� What is Density?
� How do I calculate it?
� What are its SI units?
� What is Specific Gravity?
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Pressure
� What is pressure?
� How do I calculate it?
� What are its SI units?
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Measuring Pressure
� The spring is calibrated by a known force
� The force the fluid exerts on the piston is then measured
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Density - Example
1. A water bed is 2.0 m wide and 30.0 cm deep. Find its weight and the pressure that the bed exerts on the floor.
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Pressure and Depth
� How do I find pressure at different depths?
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Pascal’s Principle
� What is Pascal’s Principle?
� How do I use this principle?
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Absolute vs. Gauge Pressure
� What’s the difference?
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Pressure Measurements:Manometer
� How does it work?
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Blood Pressure
� Blood pressure is measured with a special type of manometer called a sphygmomano-meter
� Pressure is measured in mm of mercury
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Pressure Measurements: Barometer
� Invented by Torricelli (1608 –1647)
� What does it measure?
� How does it work?
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Pressure Values in Various Units
� One atmosphere of pressure is defined as the pressure equivalent to a column of mercury exactly 0.76 m tall at 0o C where g = 9.806 65 m/s2
� One atmosphere (1 atm) =� 76.0 cm of mercury
� 1.013 x 105 Pa
� 14.7 lb/in2
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Pascal’s Principle - Example
1. In a car lift used in a service station, compressed air exerts a force on a small piston of circular cross section having a radius of 5.00 cm. This pressure is transmitted by an incompressible liquid to a second piston of radius 15.0 cm. (a) what force must the compressed air exert in order to lift a car weighing 13,300 N? (b) What air pressure will produce this force? (c) Show that the input energy transfer is equal in magnitude to the output energy transfer.
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Archimedes
� 287 – 212 BC
� Greek mathematician, physicist, and engineer
� Buoyant force
� Inventor
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Archimedes' Principle
� Any object completely or partially submerged in a fluid is buoyed up by a force whose magnitude is equal to the weight of the fluid displaced by the object.
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Buoyant Force
� What is a buoyant force?
� How does it occur?
� How do I calculate it?
� What doesn’t affect it?
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Totally Submerged Object
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Archimedes’ Principle:Floating Object
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Archimedes’ Principle -Example1. A bargain hunter
purchases a “gold”crown at a flea market. After she gets home, she hangs it from a scale and finds its weight to be 7.84 N. She then weighs the crown while it is immersed in water of density 1,000 kg/m3, and now the scale reads 6.86 N. Is the crown made of pure gold?
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Fluids in Motion:Streamline Flow
� What is a fluid?
� What is Streamline flow?
� What is viscosity?
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Characteristics of an Ideal Fluid
� The fluid is nonviscous� There is no internal friction between adjacent layers
� The fluid is incompressible� Its density is constant
� The fluid motion is steady� Its velocity, density, and pressure do not change in time
� The fluid moves without turbulence� No eddy currents are present
� The elements have zero angular velocity about its center
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Equation of Continuity
� What is Continuity equation?
� What is flow rate?
� It’s relation to conservation of Mass
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Daniel Bernoulli
� 1700 – 1782
� Swiss physicist and mathematician
� Wrote Hydrodynamica
� Also did work that was the beginning of the kinetic theory of gases
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Bernoulli’s Equation
� Relates pressure to fluid speed and elevation
� Bernoulli’s equation is a consequence of Conservation of Energy applied to an ideal fluid
� Assumes the fluid is incompressible and nonviscous, and flows in a nonturbulent, steady-state manner
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Bernoulli’s Equation
� What is it?
� Conservation of Energy
� When can it be used?
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Application – Airplane Wing
� The air speed above the wing is greater than the speed below
� The air pressure above the wing is less than the air pressure below
� There is a net upward force� Called lift
� Other factors are also involved
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Application – Airplane Wing
1. When a person inhales, air moves down the bronchus (windpipe) at 15 cm/s. The average flow speed of the air doubles through a constriction in the bronchus. Assuming incompressible flow, determine the pressure drop in the constriction.
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Surface Tension
� What is surface Tension?
� How do I find it?
� What are its units?
� What is contact angle?
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Surface Tension - Example
1.
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Viscosity
� What is Viscosity
� How do I find it?
� What are the units?
� What is Poiseuille’sLaw?
� What is Reynolds number?
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Motion through a viscous medium
� What is terminal velocity?
� Motion in Air
F
R
R
W
v
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Terminal Velocity
� The Speed vs. Time Graph for Terminal Velocity
� v = zero, a is g = 9.8 m/s2.
� As a tends to zero. V increases.
� At a=0, v is maximum and this is terminal velocity vt.
� What is the distance traveled by the object in each time interval with terminal velocity?
Terminal Velocity Vt
Time
Vel
oci
ty
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Application - Centrifuge
� High angular speeds give the particles a large radial acceleration
� Much greater than g