basics we need to review fundamental information about physical properties and their units. we need...
TRANSCRIPT
![Page 1: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/1.jpg)
BasicsBasics
• We need to review fundamental We need to review fundamental information about physical properties information about physical properties and their units.and their units.
![Page 2: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/2.jpg)
Scalars and VectorsScalars and Vectors• A scalar is a quantity with a size, for
example mass or length
• A vector has a size (magnitude) and a direction.
http://www.engineeringtoolbox.com/average-velocity-d_1392.html
![Page 3: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/3.jpg)
VelocityVelocity• Velocity is the rate and direction of
change in position of an object.
• For example, at the beginning of the Winter Break, our car had an average speed of 61.39 miles per hour, and a direction, South. The combination of these two properties, speed and direction, forms the vector quantity Velocity
http://www.engineeringtoolbox.com/average-velocity-d_1392.html
![Page 4: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/4.jpg)
Vector ComponentsVector Components• Vectors can be broken down into components
• For example in two dimensions, we can define two mutually perpendicular axes in convenient directions, and then calculate the magnitude in each direction
• Vectors can be added
• The brown vector plus
the blue vector equals
the green vector
![Page 5: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/5.jpg)
Trig & GeometryTrig & Geometry• cos = adj / hyp = abs /hyp• sine = opp / hyp = ord / hyp• tan = ord / abs• Usually angle known, solve • eqn. to find size of an unknown
The sum of angles inside a triangle = 180o
![Page 6: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/6.jpg)
Vectors 2: Acceleration.Vectors 2: Acceleration.• Acceleration is the change in Velocity during
some small time interval. Notice that either speed or direction, or both, may change.
• For example, falling objects are accelerated by gravitational attraction, g. In English units, the speed of falling objects increases by about
g = 32.2 feet/second every second, written g = 32.2 ft/sec2
![Page 7: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/7.jpg)
SI Units: SI Units: Kilogram, meter, secondKilogram, meter, second
• Most scientists and engineers try to avoid English units, preferring instead SI units. For example, in SI units, the speed of falling objects increases by about 9.81 meters/second every second, written
g = 9.81 m/sec2
• Unfortunately, in Hydrology our clients are mostly civilians, who expect answers in English units. We must learn to use both.
http://en.wikipedia.org/wiki/International_System_of_Units
Système international d'unités pron dooneetay
![Page 8: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/8.jpg)
Data and Conversion FactorsData and Conversion Factors• In your work as a hydrologist, you will be
scrounging for data from many sources. It won’t always be in the units you want. We convert from one unit to another by using conversion factors.
• Conversion Factors involve multiplication by one, nothing changes
• 1 foot = 12 inches so 1 foot = 1 12 “
http://waterdata.usgs.gov/nj/nwis/current/?type=flow
http://climate.rutgers.edu/njwxnet/dataviewer-netpt.php?yr=2010&mo=12&dy=1&qc=&hr=10&element_id%5B%5D=24&states=NJ&newdc=1
![Page 9: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/9.jpg)
ExampleExample
• Water is flowing at a velocity of 30 meters per second through a canyon. What is this speed in feet per second?
• Steps: (1) write down the value you have, then (2) select a conversion factor and write it as a fraction so the unit you want to get rid of is on the opposite side, and cancel. Then calculate.
• (1) (2)• 30 meters x 3.281 feet = 98.61 feet
second meter second
![Page 10: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/10.jpg)
Flow Rate Q = V Flow Rate Q = V .. A A
• The product of velocity and area is a flow rate
• V [meters/sec] x A [meters2] = Flow Rate [m3/sec]
• Notice that flow rates have units of Volume/ second
• It is very important that you learn to recognize which units are correct for each measurement or property.
![Page 11: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/11.jpg)
Example ProblemExample Problem
• Water is flowing at a velocity of 30 meters per second though a sea arch that has a diameter of 10 meters. What is the flow rate?
A = x 52 = 78.54m2
Q = VA = 30 m/s x 78.54 m2
Q = 2356.2 m3/s
Radius r = D/2 = 5 m
![Page 12: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/12.jpg)
Chaining Conversion FactorsChaining Conversion Factors• Water is flowing at a rate of 3000 meters cubed per
second from a spillway outlet. What is this flow rate in feet3 per hour?
•
• 3000 m3 x 60 sec x 60 min = 10800000 m3/hour
sec min hour
10800000 m3 x (3.281 feet)3 = 381454240. ft3/hr
hour ( 1 meter) 3
![Page 13: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/13.jpg)
Momentum (plural: momenta)Momentum (plural: momenta)• Momentum (p) is the product of velocity and mass, p =
mv• In a collision between two particles, for example, the total
momentum is conserved.
• Ex: two particles collide and m1 = m2, one with initial speed v1 ,
the other at rest v2 = 0,
• m1v1 + m2v2 = constant
![Page 14: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/14.jpg)
ForceForce• Force is the change in momentum with respect to time.
• A normal speeds, Force is the product of Mass (kilograms) and Acceleration (meters/sec2), so Force F = ma
• So Force must have SI units of kg . m
sec2
• 1 kg . m is called a Newton (N)
sec2
An example of Force is weight, F = mg
![Page 15: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/15.jpg)
Statics and DynamicsStatics and Dynamics
• If all forces and torques are balanced, an object doesn’t move, and is said to be static. We will use force balances shortly.
• Torque is force at some distance
• Demo Torques, ruler, See-sawF=2
F=1
-1 0 +2
F=3
Both forces and torques balanced
![Page 16: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/16.jpg)
PressurePressure
• Pressure is Force per unit Area
• So Pressure must have units of kg . m
sec2 m2
• 1 kg . m is called a Pascal (Pa)
sec2 m2
![Page 17: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/17.jpg)
DensityDensity• Density is the mass contained in a unit volume
• Thus density must have SI units kg/m3
• The symbol for density is pronounced “rho”
• Very important is not a p, it is an r• It is NOT the same as pressure
![Page 18: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/18.jpg)
Chaining Conversion FactorsChaining Conversion Factors
Suppose you need the density of water in kg/m3. You may recall that 1 cubic centimeter (cm3) of water has a mass of 1 gram.
1 gram water x (100 cm)3 x 1 kilogram = 1000 kg / m3
(centimeter)3 (1 meter)3 1000 grams
water = 1000 kg / m3
Don’t forget to cube the 100
![Page 19: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/19.jpg)
Mass Flow RateMass Flow Rate
• Mass Flow Rate is the product of the Density and the Flow Rate
• i.e. Mass Flow Rate = AVelocity
• Thus the units are kg m2 m = kg/sec
m3 sec
![Page 20: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/20.jpg)
Conservation of Mass – No Storage
Conservation of Mass : In a confined system “running full” and filled with an incompressible fluid, all of the mass that enters the
system must also exit the system at the same time.
1A1V1(mass inflow rate) = 2A2V2( mass outflow rate)
What goes in, must come out.
Notice all of the conditions/assumptions confined (pipe), running full (no compressible air), horizontal (no Pressure differences) incompressible fluid.
![Page 21: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/21.jpg)
EnergyEnergy• Energy is the ability to do work, and work and
energy have the same units• Work is the product of Force times distance, • W = Fd
• 1 kg . m2 is called a N.m or Joule (J)
sec2
• Energy in an isolated system is conserved • KE + PE + Pv + Heat = constant
N.m is pronounced Newton meter, Joule sounds like Jewel. KE is Kinetic Energy, PE is Potential Energy, P-v is Pressure energy, v is unit volumeAn isolated system, as contrasted with an open system, is a physical system that does not interact with its surroundings.
![Page 22: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/22.jpg)
Kinetic EnergyKinetic Energy
• Kinetic Energy (KE) is the energy of motion
• KE = 1/2 mass . Velocity 2 = 1/2 mV2
• SI units for KE are 1/2 . kg . m . m• sec2Note the use of m both for meters and for mass. The context will tell you which.
That’s the reason we study units.Note that the first two units make a Newton (force) and the remaining unit is meters, so the units of KE are indeed Energys
![Page 23: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/23.jpg)
Potential EnergyPotential Energy
• Potential energy (PE) is the energy possible if an object is released within an acceleration field, for example above a solid surface in a gravitational field.
• The PE of an object at height h is
PE = mgh Units are kg . m . m
sec2
Note that the first two units make a Newton (force) and the remaining unit is meters, so the units of PE are indeed EnergyNote also, these are the same units as for KE
![Page 24: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/24.jpg)
KE and PE exchangeKE and PE exchange• An object falling under gravity loses
Potential Energy and gains Kinetic Energy.• A pendulum in a vacuum has potential
energy PE = mgh at the highest points, and no kinetic energy because it stops
• A pendulum in a vacuum has kinetic energy KE = 1/2 mass.V2 at the lowest point h = 0, and no potential energy.
• The two energy extremes are equal
Stops v=0 at high point, fastest but h = 0 at low point.Without friction, the kinetic energy at the lowest spot (1) equals the potential energy at the highest spot, and the pendulum will run forever.
![Page 25: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/25.jpg)
Conservation of EnergyConservation of Energy• We said earlier “Energy is Conserved” • This means
KE + PE + Pv + Heat = constant • For simple systems involving liquid water without
friction heat, at two places 1 and 2
1/2 mV12 + mgh1 + P1v = 1/2 mV2
2 + mgh2 + P2v
If both places are at the same pressure (say both touch the atmosphere) the pressure terms are identical
• 1/2 mV12 + mgh1 + P1v = 1/2 mV2
2 + mgh2 + P2v
![Page 26: Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties](https://reader036.vdocument.in/reader036/viewer/2022081519/56649e155503460f94aff10f/html5/thumbnails/26.jpg)
Example ProblemExample Problem• A Watchung Lava flow dammed a
proglacial lake, Lake Passaic, south of the melting Wisconsinan glacier. A leaky area had an opening h = 100 m below the water level. The opening had an area A2 = 10 m2 , small compared to the lake surface with area A1 = 3,000,000 m2. Therefore
assume V1 ~ 0.
• Calculate V2. note m1 = m2
Method: only PE at 1, KE at 2 mgh1=1/2mV2
2 V2 = 2gh
1/2mV12 + mgh1 = 1/2mV2
2 + mgh2
44.29m/sec