Hydrology BasicsHydrology Basics

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

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

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

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

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

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

What’s in it for me?What’s in it for me?• Hydrologists will take 1/5th of Geol. 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 petroleum geologist makes a mistake, the bottom line suffers. When a hydrologist makes a mistake, people suffer.

http://www.bls.gov/oco/ocos312.htm

Issaquah Creek Flood, WAIssaquah Creek Flood, WAhttp://www.issaquahpress.com/tag/howard-hanson-dam/

What does a Hydrologist do?What does a Hydrologist do?• Hydrologists provide numbers to

engineers and civil authorities. Clients 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

Dupont and Pompton Lakes, Syncon Resins and Passaic River

Trenton, Bound Brook, Rahway, Pompton, Wayne, Paterson after Hurricane Irene

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

ExampleExample

• 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. Then calculate.

• (1) (2)• 30 meters x 3.281 feet = 98.61 feet

second meter second

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.

Example ProblemExample 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?

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?

• Let’s do this in two steps

• 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

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, if there

is no friction 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

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 must have SI units of kg . m

sec2

• 1 kg . m is called a Newton (N)

sec2

Statics and DynamicsStatics and Dynamics

• If all forces and Torques are balanced, an object doesn’t move, and is said to be static

• Discussion Torques, See-saw

• Reference frames

• Discussion Dynamics

F=2

F=1

-1 0 +2

F=3

Dynamics is the study of moving objects. Fluid Dynamics is the study of fluid flow.

The forces are balanced in the y direction. 2 + 1 force units (say, pounds) down are balanced by three pounds directed up.The torques are also balanced around the pivot: 1 pounds is 2 feet to the right of the pivot (= 2 foot-pounds) and 2 pounds one foot to the left = -2 foot - pounds

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

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

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

(1 centimeter)3 (1 meter)3 1000 grams

water = 1000 kg / m3

Don’t forget to cube the 100

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

Conservation of Mass – No Storage

Conservation of Mass : In a confined system “running full” and filled with an incompressible fluid, the same amount of 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.

A pipe full of water

Conservation of Mass for a horizontal Nozzle

Liquid water is incompressible, so the density does not change

and 1= 2. The density cancels

out, 1A1V1 = 2A2V2

so A1V1 =A2V2

Notice If A2 < A1 then V2 > V1

In a nozzle, A2 < A1 .Thus, water exiting a nozzle has a higher

velocity than at inflow

The water exiting is called a JETQ1 = A1V1

A1

V1 ->

Q2 = A2V2

A1V1 = A2V2

A2 V2 ->

1A1V1(mass inflow rate) = 2A2V2( mass outflow rate)

Consider liquid water flowing in a horizontal pipe where the cross-sectional area changes.

Spillway Outlet. Here is Hoover Dam, a hydroelectric plant that provides tremendous amounts of electricity to the west. Notice the jets of water at the outlets. These are produced by horizontal nozzles. The water must be going fast enough to reach the center of the river where it strikes an opposing jet. The opposing momenta nearly cancel, slowing both flows. This is easier on the life in the river.

Example Problem

Q1 = A1V1

A1

V1 ->

Q2 = A2V2

A1V1 = A2V2

A2 V2 ->

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.

Solve the equation for V2, plug in the numbers and state the answer and units.V2 = A1/A2 x V1 = 100/10 x 10m/sec = 100m/sec

The Equation

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 Distance has SI units of meters

• 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, Pv 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.

Pressure Energy is Pressure Energy is Pressure x volumePressure x volume

• Energy has

units kg . m2

sec2

So pressure energy must have the same units, and Pressure alone is kg . m

sec2 m2

So if we multiply Pressure by a unit volume m3 we get units of energy

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 Energy

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

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 equalStops 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.

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

Example ProblemExample 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: only PE at 1, KE at 2 mgh1=1/2mV2

2 V2 = 2gh

1/2mV12 + mgh1 = 1/2mV2

2 + mgh2