A scalar is a quantity with a size, for example mass or length


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A scalar is a quantity with a size, for example mass or length

  • A scalar is a quantity with a size, for example mass or length

  • A vector has a size (magnitude) and a direction.



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

  • 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



Vectors can be broken down into 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



Acceleration is the change in Velocity during some small time interval. Notice that either speed or direction, or both, may change.

  • 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



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

  • 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.



Hydrologists will take 1/5th of Geol. jobs.

  • 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.





Hydrologists provide numbers to engineers and civil authorities. Clients ask, for example:

  • 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?



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.

  • 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 “



Water is flowing at a velocity of 30 meters per second from a spillway outlet. What is this speed in feet per second?

  • 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



The product of velocity and area is a flow rate

  • 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.



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?

  • 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?



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?

  • 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 (p) is the product of velocity and mass, p = mv

  • 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



Force is the change in momentum with respect to time.

  • 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



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

  • 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



Pressure is Force per unit Area



Density is the mass contained in a unit volume

  • 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



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.

  • 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



Mass Flow Rate is the product of the Density and the 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











Energy is the ability to do work, and work and energy have the same units

  • 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



Energy has

  • 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 Energy (KE) is the energy of motion

  • 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



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.

  • 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



An object falling under gravity loses Potential Energy and gains Kinetic Energy.

  • 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



We said earlier “Energy is Conserved”

  • 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 mV22 + mgh2 + P2v

  • If both places are at the same pressure (say both touch the atmosphere) the pressure terms are identical



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.

  • 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=1/2mV22 V2 = 2gh




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