1. Hydrology Basics We need to review fundamental information about physical properties and their units. We need to review fundamental information about physical properties and their units.

2. Scalars 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

3. Velocity 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

4. 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 Vectors can be added The brown vector plus the blue vector equals the green vector

5. 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/sec 2

6. SI Units: Kilogram, 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/sec 2 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

7. What’s in it for me? Hydrologists will take 1/5 th 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

8. Issaquah Creek Flood, WA http://www.issaquahpress.com/tag/howard-hanson-damhttp://www.issaquahpress.com/tag/howard-hanson-dam/

9. 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

10. Data 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

11. 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. Then calculate. (1) (2) 30 meters x 3.281 feet = 98.61 feet second meter second

12. Flow Rate Q = V. A Flow Rate Q = V. A The product of velocity and area is a flow rate V [meters/sec] x A [meters 2 ] = Flow Rate [m 3 /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.

13. 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?

14. 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 3 per hour? Let’s do this in two steps 3000 m 3 x 60 sec x 60 min = 10800000 m 3 /hour sec min hour 10800000 m 3 x (3.281 feet) 3 = 381454240. ft 3 /hr hour ( 1 meter) 3

15. 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 m 1 = m 2, one with initial speed v 1, the other at rest v 2 = 0, m 1 v 1 + m 2 v 2 = constant

16. Force Force is the change in momentum with respect to time. A normal speeds, Force is the product of Mass (kilograms) and Acceleration (meters/sec 2 ), So Force must have SI units of kg. m sec 2 1 kg. m is called a Newton (N) sec 2

17. Statics 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

18. Pressure Pressure is Force per unit Area So Pressure must have units of kg. m sec 2 m 2 1 kg. m is called a Pascal (Pa) sec 2 m 2

19. Density Density is the mass contained in a unit volume Thus density must have SI units kg/m 3 The symbol for density is  pronounced “rho” Very important  is not a p, it is an r It is NOT the same as pressure

20. Chaining Conversion Factors  Suppose you need the density of water in kg/m 3. You may recall that 1 cubic centimeter (cm 3 ) of water has a mass of 1 gram.  1 gram water x (100 cm) 3 x 1 kilogram = 1000 kg / m 3  (1 centimeter) 3 (1 meter) 3 1000 grams  water = 1000 kg / m 3 Don’t forget to cube the 100

21. Mass Flow Rate Mass Flow Rate is the product of the Density and the Flow Rate i.e. Mass Flow Rate =  AV elocity Thus the units are kg m 2 m = kg/sec m 3 sec

22. 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.  1 A 1 V 1 (mass inflow rate) =  2 A 2 V 2 ( 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

23. Conservation of Mass for a horizontal Nozzle Liquid water is incompressible, so the density does not change and  1 =  2. The density cancels out,  1 A 1 V 1 =  2 A 2 V 2 so A 1 V 1 =A 2 V 2 Notice If A 2 V 1 In a nozzle, A 2 < A 1.Thus, water exiting a nozzle has a higher velocity than at inflow The water exiting is called a JET Q 1 = A 1 V 1 A1A1 V 1 -> Q 2 = A 2 V 2 A 1 V 1 = A 2 V 2 A 2 V 2 ->  1 A 1 V 1 (mass inflow rate) =  2 A 2 V 2 ( mass outflow rate) Consider liquid water flowing in a horizontal pipe where the cross-sectional area changes.

24. 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.

25. Example Problem Q 1 = A 1 V 1 A1A1 V 1 -> Q 2 = A 2 V 2 A 1 V 1 = A 2 V 2 A 2 V 2 -> Water enters the inflow of a horizontal nozzle at a velocity of V 1 = 10 m/sec, through an area of A 1 = 100 m 2 The exit area is A 2 = 10 m 2. Calculate the exit velocity V 2. Solve the equation for V 2, plug in the numbers and state the answer and units. V2 = A1/A2 x V1 = 100/10 x 10m/sec = 100m/sec The Equation

26. 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 Distance has SI units of meters 1 kg. m 2 is called a N. m or Joule (J) sec 2 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 volume An isolated system, as contrasted with an open system, is a physical system that does not interact with its surroundings.

27. Pressure Energy is Pressure x volume Energy has units kg. m 2 sec 2 So pressure energy must have the same units, and Pressure alone is kg. m sec 2 m 2 So if we multiply Pressure by a unit volume m3 we get units of energy

28. Kinetic Energy Kinetic Energy (KE) is the energy of motion KE = 1/2 mass. Velocity 2 = 1/2 mV 2 SI units for KE are 1/2. kg. m. m sec 2 Note 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

29. 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 sec 2 Note that the first two units make a Newton (force) and the remaining unit is meters, so the units of PE are indeed Energy Note also, these are the same units as for KE

30. 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 because it stops A pendulum in a vacuum has kinetic energy KE = 1/2 mass. V 2 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.

31. Conservation 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 mV 1 2 + mgh 1 + P 1 v = 1/2 mV 2 2 + mgh 2 + P 2 v If both places are at the same pressure (say both touch the atmosphere) the pressure terms are identical

32. Example Problem A tank has an opening h = 1 m below the water level. The opening has area A 2 = 0.003 m 2, small compared to the tank with area A 1 = 3 m 2. Therefore assume V 1 ~ 0. Calculate V 2.  Method: only PE at 1, KE at 2 mgh 1 =1/2mV 2 2 V 2 = 2gh 1/2 mV 1 2 + mgh 1 = 1/2 mV 2 2 + mgh 2