Hydrology Basics

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Hydrology Basics

• We need to review fundamental information about
  physical properties and their units.

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Vectors 1 Velocity
http//www.engineeringtoolbox.com/average-velocity
-d_1392.html

• A scalar is a quantity with a size, for example
  mass or length
• A vector has a size (magnitude) and a direction.
  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, is called Velocity

velocity is the rate and direction of change in
position of an object.
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Vector 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

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Example Vector Components

• A folded sandstone layer is exposed along the
  coast of Lake Michigan. In some places it is
  vertical, on others gently dipping. Which surface
  is struck by a greater wave force?

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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

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SI Units

• 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
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Whats in it for me?

• Hydrologists will take 1/5th of GS jobs.
• Petroleum Geologists make more money, 127K vs.
  80K, but have much less job security during
  economic downturns.
• Hydrologists have much greater responsibility.
• When a geologist makes a mistake, the bottom line
  suffers. When a hydrologist makes a mistake,
  people suffer.

http//www.bls.gov/oco/ocos312.htm
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Issaquah Creek Flood, WA
http//www.issaquahpress.com/tag/howard-hanson-dam
/
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What does a Hydrologist do?

• Hydrologists provide numbers to engineers and
  civil authorities. They ask, for example
• When will the crest of the flood arrive, and how
  high will it be?
• When will the contaminant plume arrive at our
  municipal water supply?

http//www.weitzlux.com/dupont-plume_1961330.html
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Data and Conversion Factors

• In your work as a hydrologist, you will be
  scrounging for data from many sources. It wont
  always be in the units you want. To 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/?typefl
ow
http//climate.rutgers.edu/njwxnet/dataviewer-netp
t.php?yr2010mo12dy1qchr10element_id5B5
D24statesNJnewdc1
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Example

• Water is flowing at a velocity of 30 meters per
  second from a spillway outlet. 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.
• (1) (2)
• 30 meters x 3.281 feet 98.61 feet
• second meter second

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Flow Rate

• The product of velocity and area is a flow rate
• Vel m/sec x Area meters2 Flow Rate
  m3/sec
• Notice that flow rates have units of Volume/
  second
• Discussion recognizing units

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Example Problem

• Water is flowing at a velocity of 30 meters per
  second from a spillway outlet that has a diameter
  of 10 meters. What is the flow rate?

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Chaining Conversion Factors

• Water is flowing at a rate of 3000 meters cubed
  per second from a spillway outlet. What is this
  flow rate in feet per hour?
• 3000 m3 x 60 sec x 60 min
• sec min hour

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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

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Force

• 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

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Statics and Dynamics

• If all forces and Torques are balanced, an object
  doesnt move, and is said to be static
• Discussion Torques, See-saw
• Reference frames
• Discussion Dynamics

F2
F1
-1 0 2
F3
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Pressure

• 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

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Density

• Density is the mass contained in a unit volume
• Thus density must have units kg/m3
• The symbol for density is r

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Chaining Conversion Factors

• Suppose you need the density of water in kg/m3.
  You find 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
• r water 1000 kg / m3

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Mass Flow Rate

• Mass Flow Rate is the product of the Density and
  the Flow Rate
• i.e. Mass Flow Rate rAV
• Thus the units are kg m2 m kg/sec
• m3 sec

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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.
r1A1V1(mass inflow rate) r2A2V2( mass outflow
rate)
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Conservation of Mass for a horizontal Nozzle
Consider liquid water flowing in a horizontal
pipe where the cross-sectional area changes.
r1A1V1(mass inflow rate) r2A2V2( mass outflow
rate)
Liquid water is incompressible, so the density
does not change and r1 r2. The density cancels
out, r1A1V1 r2A2V2 so A1V1
A2V2 Notice If A2 lt A1 then V2 gt V1 In a
nozzle, A2 lt A1 .Thus, water exiting a nozzle has
a higher velocity than at inflow The water is
called a JET
V1 -gt
A1
A2 V2 -gt
Q2 A2V2
A1V1 A2V2
Q1 A1V1
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Example Problem
Water enters the inflow of a horizontal nozzle at
a velocity of V1 10 m/sec, through an area of
A1 100 m2 The exit area is A2 10 m2.
Calculate the exit velocity V2.
V1 -gt
A1
A2 V2 -gt
Q2 A2V2
Q1 A1V1
A1V1 A2V2
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Energy

• 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 is conserved
• KE PE P/v Heat constant

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Kinetic 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
• 
  sec2

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Potential 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

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KE 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.
• 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

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Conservation of Energy

• We said earlier Energy is Conserved
• This means
• KE PE P/v Heat constant
• For simple systems involving liquid water without
  friction heat, at two places 1 and 2
• 1/2 mV12 mgh1 P1/v 1/2 mV22 mgh2
  P2/v
• If both places are at the same pressure (say both
  touch the atmosphere) the pressure terms are
  identical
• 1/2 mV12 mgh1 P1/v 1/2 mV22 mgh2 P2/v

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Example Problem

• A tank has an opening h 1 m below the water
  level. The opening has area A2 0.003 m2 , small
  compared to the tank with area A1 3 m2.
  Therefore assume V1 0.
• Calculate V2.
• Method Assume no friction, then
  mgh11/2mV22 V2 2gh

1/2mV12 mgh1 1/2mV22 mgh2