PHY132 lecture 15 fluid mechanics - Cal ... - Cal Poly Pomonaesalik/phy132/PHY132_lecture_15_fluid... · Fluid Mechanics • Fluid Statics ... The system is in static equilibrium

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Chapter 15. Fluids and Elasticity In this chapter we study macroscopic systems: systems with many particles, such as the water the kayaker is paddling through. We will introduce the concepts of density, pressure, fluid statics, fluid dynamics, and the elasticity of solids. Chapter Goal: To understand macroscopic systems that flow or deform.


Topics: •  Fluids •  Pressure •  Measuring and Using Pressure •  Buoyancy •  Fluid Dynamics •  Elasticity

Chapter 15. Fluids and Elasticity


What is a fluid?

•  A substance that flows! •  A fluid is a collection of molecules that are

randomly arranged and held together by weak cohesive forces and by forces exerted by the walls of a container. Both liquids and gases are fluids.


Fluid Mechanics

•  Fluid Statics •  Fluid Dynamics

•  Some applications: How ships float? How airplanes keep aloft?

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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Density

The ratio of an object’s or material’s mass to its volume is called the mass density, or sometimes simply “the density.”

The SI units of mass density are kg/m3.



Pressure A fluid in a container presses with an outward force against the walls of that container. The pressure is defined as the ratio of the force to the area on which the force is exerted.

The SI units of pressure are N/m2, also defined as the pascal, where 1 pascal = 1 Pa = 1 N/m2.


Touch sensitive artificial skin?

•  http://www.nature.com/news/2010/100912/full/news.2010.463.html


Atmospheric Pressure The global average sea-level pressure is 101,300 Pa. Consequently we define the standard atmosphere as

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Atmospheric Pressure Can Demo


Air pressure on Index Card holds water Demo


Pressure in Liquids

The pressure at depth d in a liquid is

where ρ is the liquid’s density, and p0 is the pressure at the surface of the liquid. Because the fluid is at rest, the pressure is called the hydrostatic pressure. The fact that g appears in the equation reminds us that there is a gravitational contribution to the pressure.


Pascal’s Three Hole Can Demo


CT Mazur 140

When a hole is made in the side of a container holding water, water flows out and follows a parabolic trajectory. If the container is dropped in free fall, the water flow

1.  diminishes. 2.  stops altogether. 3.  goes out in a straight line. 4.  curves upward.


CT Mazur 139

Imagine holding two identical bricks underwater. Brick A is just beneath the surface of the water, while brick B is at a greater depth. The force needed to hold brick B in place is

1.  larger 2.  the same as 3.  Smaller than the force required to hold brick A in place.

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Equilibrium Tubes Demo


15.13 What is the longest vertical soda straw you can possibly drink from?

A) 50 cm B) 3 m C) 10 m D) 100 m E) There is no limit


Gauge Pressure Many pressure gauges, such as tire gauges and the gauges on air tanks, measure not the actual or absolute pressure p but what is called gauge pressure pg.

where 1 atm = 101.3 kPa.


Pascal’s principle

•  a change in the pressure applied to a fluid is transmitted undiminished to every point of the fluid and to the walls of the container.


CT Mazur 141


Hydraulics Consider a hydraulic lift, such as the one that lifts your car at the repair shop. The system is in static equilibrium if

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Buoyant Force


Archimedes Principle

the magnitude of the buoyant force always equals the weight of the fluid displaced by the object.


Tactics: Finding whether an object floats or sinks






Float or Sink?

The volume of fluid displaced by a floating object of uniform density is

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CT Mazur 143


CT Mazur 144


CT Mazur 146


CT Mazur 148


How ships float in a stable way?

•  Ideally, the center of buoyancy needs to be above the center of mass. Otherwise, the ship might capsize easily.


Fluid Dynamics Assumptions

1- the fluid is nonviscous: internal friction is neglected.

2- the flow is steady (laminar)- the velocity at each point remains constant (not turbulent, irregular,

3- the fluid is incompressible- density is constant 4- the flow is irrotational- angular momentum is

zero about any point

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CT Mazur 152


CT Mazur 153


Fluid Dynamics Comparing two points in a flow tube of cross section A1 and A2, we may use the equation of continuity

where v1 and v2 are the fluid speeds at the two points. The flow is faster in narrower parts of a flow tube, slower in wider parts. This is because the volume flow rate Q, in m3/s, is constant.


Bernoulli’s Equation


The energy equation for fluid in a flow tube is

An alternative form of Bernoulli’s equation is

Bernoulli’s Equation


CT Mazur 156

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Bernoulli’s atomizer


Ping pong Ball and Funnel Demo


Elasticity


Elasticity F/A is proportional to ΔL/L. We can write the proportionality as

•  The proportionality constant Y is called Young’s modulus. •  The quantity F/A is called the tensile stress. •  The quantity ΔL/L, the fractional increase in length, is called strain. With these definitions, we can write


EXAMPLE 15.13 Stretching a wire

QUESTIONS:

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Volume Stress and the Bulk Modulus


Volume Stress and the Bulk Modulus

•  A volume stress applied to an object compresses its volume slightly. •  The volume strain is defined as ΔV/V, and is negative when the volume decreases. •  Volume stress is the same as the pressure.

where B is called the bulk modulus. The negative sign in the equation ensures that the pressure is a positive number.

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PHY132 lecture 15 fluid mechanics - Cal ... - Cal Poly Pomonaesalik/phy132/PHY132_lecture_15_fluid... · Fluid Mechanics • Fluid Statics ... The system is in static equilibrium