chapter 14: fluids - university of florida€¦ · fluids take the form of their container. when...
TRANSCRIPT
![Page 1: Chapter 14: Fluids - University of Florida€¦ · Fluids take the form of their container. When shear stress is applied they flow. Fluids can only exert a force perpendicular to](https://reader034.vdocuments.net/reader034/viewer/2022042120/5e999089ab328161282166a1/html5/thumbnails/1.jpg)
Chapter 14: FluidsLecture 3011/9/2009
![Page 2: Chapter 14: Fluids - University of Florida€¦ · Fluids take the form of their container. When shear stress is applied they flow. Fluids can only exert a force perpendicular to](https://reader034.vdocuments.net/reader034/viewer/2022042120/5e999089ab328161282166a1/html5/thumbnails/2.jpg)
FluidsGoals for this Lecture:
Study the behavior of fluids.
Static fluids:Pressure exerted by a static fluidMethods of measuring pressurePascal’s principleArchimedes’ principle, buoyancy
Real versus ideal Fluids in motion:Fluids Equation of continuityBernoulli’s equation
![Page 3: Chapter 14: Fluids - University of Florida€¦ · Fluids take the form of their container. When shear stress is applied they flow. Fluids can only exert a force perpendicular to](https://reader034.vdocuments.net/reader034/viewer/2022042120/5e999089ab328161282166a1/html5/thumbnails/3.jpg)
What is a Fluid?A substance that can flow
Gases (easy to compress)
Liquids (difficult to compress)
Solids ? (gel = toothpaste, glass)?
Basic properties:Fluids take the form of their container.
When shear stress is applied they flow.
Fluids can only exert a force perpendicular to their surface
The molecules in fluids are in constant random motion (Brownian motion).
The field of physics that describes the fluid motion is called “Fluid Mechanics”
![Page 4: Chapter 14: Fluids - University of Florida€¦ · Fluids take the form of their container. When shear stress is applied they flow. Fluids can only exert a force perpendicular to](https://reader034.vdocuments.net/reader034/viewer/2022042120/5e999089ab328161282166a1/html5/thumbnails/4.jpg)
Fluid Properties: DensityDensity (sometimes referred to as “mass density”) is the mass of a given material per unit volume.
Unit: ! = !m/!V = [kg]/[m3]
The density can be different at each point of the fluid.
An object is uniform (or homogenous) if the density is constant at any point of the body: ! = !m/!V⇒ mtot/Vtot
A fluid is incompressible if the density does not change as a result of an applied pressure.
! = !m/!V
![Page 5: Chapter 14: Fluids - University of Florida€¦ · Fluids take the form of their container. When shear stress is applied they flow. Fluids can only exert a force perpendicular to](https://reader034.vdocuments.net/reader034/viewer/2022042120/5e999089ab328161282166a1/html5/thumbnails/5.jpg)
Examples of Fluid Densities
Fluid Density [kg/m3]
Interstellar space 10-20
Laboratory vacuum 10-17
Air (1 atm 20° C) 1.21
Ice 917
Water 998
Seawater 1024
Earth 5500
Neutron star 10+18
Average person
![Page 6: Chapter 14: Fluids - University of Florida€¦ · Fluids take the form of their container. When shear stress is applied they flow. Fluids can only exert a force perpendicular to](https://reader034.vdocuments.net/reader034/viewer/2022042120/5e999089ab328161282166a1/html5/thumbnails/6.jpg)
Fluid Properties: PressurePressure is defined as force (perpendicular to a given surface) per unit area
Pressure is not just what a quarterback feels when Carlos Dunlap is closing in on him
Unit: p = !F/!A = [N]/[m2] ! [Pa] (Pa = Pascal)
Other popular units: 1 atm = 1 bar = 1.01x105 Pa = 760 torr = 14.7 lb/in2
Pressure is a scalar: it has the the same value in all directions!
p = !F/!A
Blaise Pascal
![Page 7: Chapter 14: Fluids - University of Florida€¦ · Fluids take the form of their container. When shear stress is applied they flow. Fluids can only exert a force perpendicular to](https://reader034.vdocuments.net/reader034/viewer/2022042120/5e999089ab328161282166a1/html5/thumbnails/7.jpg)
Origin of PressureWhy is pressure defined as force per unit area? Look at the microscopic picture:
There are many atoms bouncing off a surface in a given amount of time. Each one exerts a tiny bit of force on the surface
If the surface area is doubled, the number of collisions doubles
This is also why the pressureat a given point in the fluid is the same in all directions, i.e. a scalar,not a vector
![Page 8: Chapter 14: Fluids - University of Florida€¦ · Fluids take the form of their container. When shear stress is applied they flow. Fluids can only exert a force perpendicular to](https://reader034.vdocuments.net/reader034/viewer/2022042120/5e999089ab328161282166a1/html5/thumbnails/8.jpg)
Examples of Fluid Pressures
Location Pressure [Pa]
Sea level atm. pressure 1.013x10+5 = (29.92 in Hg)
Low pressure storm system 0.999x10+5 = (29.5 in Hg)
Hurricane 0.982x10+5 = (29 in Hg)
Bottom of the ocean 1x10+8
Center of the Earth 4x10+11
Center of the Sun 2x10+16
![Page 9: Chapter 14: Fluids - University of Florida€¦ · Fluids take the form of their container. When shear stress is applied they flow. Fluids can only exert a force perpendicular to](https://reader034.vdocuments.net/reader034/viewer/2022042120/5e999089ab328161282166a1/html5/thumbnails/9.jpg)
Pressure in Fluids at RestConsider a fluid with density ! in static equilibrium (i.e. not accelerating)
The portion of the fluid that is outlined as several forces acting on it
Downward force from gravity: Fg
Downward force from the pressure of the fluid above it: F1
Upward force from the pressure of the fluid below it: F2
The fluid is not accelerating so Fnet = 0
![Page 10: Chapter 14: Fluids - University of Florida€¦ · Fluids take the form of their container. When shear stress is applied they flow. Fluids can only exert a force perpendicular to](https://reader034.vdocuments.net/reader034/viewer/2022042120/5e999089ab328161282166a1/html5/thumbnails/10.jpg)
The fluid is not accelerating so Fnet = 0
-Fg - F1 + F2 = 0
F2 - F1 = mg
Recall that pressure is force per unit area: p = F/A ⇒ F = pA
Newton’s law on this portion of fuid gives us:
F2 - F1 = mg ⇒ p2A - p1A = mg
but, m = !V = !(hA) = !A(y1-y2)
p2A - p1A = !A(y1-y2) ⇒ p2 - p1 = !(y1-y2)g
Let the pressure at the surface (y=0) be p0
p = p0 + !gh (h = depth below the surface)
Pressure in Fluids at Rest
Area = A
F1
F2
![Page 11: Chapter 14: Fluids - University of Florida€¦ · Fluids take the form of their container. When shear stress is applied they flow. Fluids can only exert a force perpendicular to](https://reader034.vdocuments.net/reader034/viewer/2022042120/5e999089ab328161282166a1/html5/thumbnails/11.jpg)
Let the pressure at the surface (y=0) be p0
p is the absolute pressure and is given by: p = p0 + !gh (h = depth below the surface)
p - p0 is known as the “gauge pressure” and is given by pg = !gh
Pressure in Fluids at Rest
Area = A
F1
F2
![Page 12: Chapter 14: Fluids - University of Florida€¦ · Fluids take the form of their container. When shear stress is applied they flow. Fluids can only exert a force perpendicular to](https://reader034.vdocuments.net/reader034/viewer/2022042120/5e999089ab328161282166a1/html5/thumbnails/12.jpg)
You want to lift a 10 kg bowling ball with a vacuum cleaner hose attachment with a 1” radius. If the (less than excellent) vacuum cleaner can only provide a vacuum pressure of 50 kPa, would you be able to lift the ball?
Vacuum Pickup
![Page 13: Chapter 14: Fluids - University of Florida€¦ · Fluids take the form of their container. When shear stress is applied they flow. Fluids can only exert a force perpendicular to](https://reader034.vdocuments.net/reader034/viewer/2022042120/5e999089ab328161282166a1/html5/thumbnails/13.jpg)
Consider the forces on the ballFnet = F2 - F1 -Fg = pair A - pvac A - mg " 0 = A(pair - pvac) - mg " 0 ?A = #r2 = #(1 in)2 = #(0.0254 m)2 = 2x10-3 m2 pvac = 50 kPa, pair = 101.3 kPaA(pair - pvac) = (2x10-3 m2)(51.3 kPa) = 104 N
mg = (10 kg)(9.81 m/s2) = 98.1 N
⇒ A(pair - pvac) - mg " 0 ;)
Vacuum Pickup
Fg = mg
F1 = pvacA
F2 = pairA