Units and Conversions - Sahraweb.sahra.arizona.edu/.../lesson2b/Hwr203Units.pdf · Arizona Water Issues New Units? - Volume Acre-foot The volume of water necessary to cover one acre

Units and Conversions

Common Core

Arizona Water Issues © 2012 - The University or Arizona - HWR203 1

Arizona Water Issues

Why do we care about the units?I bet the guys at NASA care!

Ill-fated Mars ObserverOne team of researchersUsed metric, the otherEnglish units - resulting miscalculations caused the probe to burn up in Mars atmosphere

2© 2012 - The University or Arizona - HWR203


Numbers/units are important to:

1. Appreciate water quantities – don’t tune #’s out!

2. Compare and understand usage amounts(agricultural, domestic, industrial; balances)

3. Estimate relative magnitudes of water resources(areas, volumes, flows)

4. Understand semi-technical topics and literature


Powers of Ten


109 = billion (B) giga-

106 = million (M) mega-

103 = thousand (k) kilo-

… … …

10-2 = (c) centi-

10-3 = (m) milli-

10-6 = (μ) micro-

10-9 = (n) nano-

Its perfectly acceptable (and often more common) to express your answers using common powers of 10 abbreviations

15.6 Maf = 15,600,00 af2.3 mg/L = .0023 g/L

Scientific Notation & Sig.Figs.


Significant Figures – related to a number’s precision.

Important here mostly to avoid insignificant digits.

Writing in scientific notation removes ambiguity related to leading or trailing zeroes.

Unless directed otherwise, express your answers to 3 sig.figs.

Sci. Notation format: x.xx * 10exp

Examples


Sci. Notation format: x.xx * 10exp

http://antoine.frostburg.edu/chem/senese/101/measurement/sigfig-quiz.shtml

If your calculator says:

You should write it as: Shift decimal:

0.0002358 2.36 * 10-4 4 places to right

45,249.632 4.52 * 104 4 places to left

You try it:0.01234234,567

89.501 million meters34.501 millimeters

Common Units – Relative sizes

Relative Lengthsmmcminftydmkmmimi

Equivalents10 mm = 1 cm2.54 cm = 1 in

12 in = 1 ft3 ft = 1 yd

39.4 in ~ 1 m100 cm = 1 m

1000 m = 1 km1.609 km = 1 mi5280 ft = 1 mi


incr

easi

ng

Common Units – Kitchen

Relative VolumesmL(ml)

tTozcpLqtgal

Equivalents4.9 ml = 1 t

3 t = 1 T2 T = 1 oz8 oz = 1 c

355 ml = 12 oz2 c = 1 p2 p = qt

128 oz = 4 qt = 1 gal3.8 L =1 gal


Common Units – Weight

Relative Weightsmgglbkgkgton

metric ton

Equivalents1000 µg = 1 mg1000 mg = 1 g

454 g ~ 1 lb1000 g = 1 kg2.2 lb = 1 kg

2000 lb = 1 ton1000 kg = 1 metric ton


For water: ρw=1 g/cm3 = 1 g/ml = 1 kg/L = 1000 kg/m3

Common Units – Field

Relative VolumesmL(ml)

Lgalft3

m3

ccfaf

Equivalents1000 ml = 1 L3.8 L = 1 gal

7.48 gal = 1 ft3

264 gal = m3

748 gal = ccf1,234 m3 = 1 af

43,560 ft3 = 1 af325,851 gal = 1 af1 Mgal = 3.07 af810 af = 1 Mm3



Units of Interest

Time:seconds[s], minutes[min], hours[hr], days[d], years[yr]

Length:English units: inch[in], foot[ft], mile[mi]metric units: centimeter[cm], meter[m], kilometer[km]

Area:English units: [in2], [ft2], [mi2], acre[ac]Metric units: [cm2], [m2], [km2], hectare[ha]

Volume:English units: [gal], [ft3], [acre-feet] or [af]Metric units: [L], [m3], [Mm3]



New Units? - VolumeAcre-footThe volume of water necessary to cover one acre to a depth of one foot. Equal to 43,560 cubic feet or 325,851 gallons or 1,234 cubic meters.This is about the amount needed to cover a football field with a foot of water.

another fun fact

It takes ~1000 m3 waterto produce ~ 1 ton of grain

= 264,000 gal = 0.81 af ~ 1100 ton water


this is why it makes more sense to import

grain rather than water.


160 ac

40 ac

10 ac

USGS maps divided bytownship & range

Each T/R is subdividedinto a 6x6 grid

Each map section is1 square mile = 640 ac

Metric: A hectare (ha = 2.47ac) is 100 m x 100 m

Acres & Hectares

Tucson street grid is:Primary streets – every mileex. Speedway – BroadwayCampbell – Country Club

Secondary streets – every ½ miEx. 5th St, Tucson

So Sam Hughes is 160 ac


Useful Equivalents NotationAttention: common error!


1 ha = (100 m)2 = 100 m * 100 m =10,000 m2

(1 km)2 = (1000 m)2 = (103 m)2 = 106 m2

1 ac = (208.7 ft)2 = 43560 ft2

(1 m)3 = (100 cm)3 = (102 m)3 = 106 cm3


Orders of Magnitude


Lake Mead 32 [M-af] 40 [B-m3]

Annual Flow in Colorado 15 [M-af] 19 [B-m3]

Roosevelt Lake 3.8 [M-af] 4.7 [B-m3]

TAMA annual use 365 [k-af] 450 [M-m3]

TW CAP recharge 30 [k-af] 37 [M-m3]

TAMA daily use 1 [k-af] 1.2 [M-m3]

Volume of Chem-Bio 50 [af] 62 [k-m3]

Annual family use 0.5 [af] 620 [m3]


What units do I use?

Think about the idea of scale:What units are appropriate for the volume of water in a:

(1) bucket?

(2) pond?

(3) reservoir?16© 2012 - The University or Arizona - HWR203


Performing unit conversions

(Step 1)What units are you given? What units do you want to end up with? Write these down on the left and right sides of the paper, respectively.

Example: How many inches in 10 feet?

What you know What you don’t know“Given” “Answer”

10 [ft] ?[inch]




(Step 2)How do you convert between these two measures? Look at your

table of Useful Equivalents under the particular measure of interest (Length) and find the appropriate equivalents.

In this case, the likely equivalents looks like this:1 ft = 12 in = 0.3048 m

Convert this into a fraction: either 1 ft/12 in or 12 in/ 1 ft

Which?




(Step 3): Multiply this by the Given value

“Given” “Conversion” = “Answer”10 [ft] * 12 [in/ft] = 120 [in]



Multiple conversions

Most conversions are relatively straightforward, though they may require a few steps to complete

Example: How many seconds are in one day?



AreaRemember your basic area formulas:

Area =

Length

width

Length * width

Area = 1/2* base *height base

height

r

Area = pi * r2; pi=3.1416



Area

Conversions for area can be a little tricky: In converting areas, it is critical to either use area to area conversions or to multiply by the length conversion factor twice

Example: How many square feet are in one square meter?

Equivalents: 1 m2 = 10.76 ft2 1 ft = 0.3048 m

Correct:1[m2] * 10.76 [ft2/m2] = 10.76 [ft2](1 m)2 * (1 [ft]/0.3048[m])2 = 10.76 [ft2]

Incorrect:1[m2] * 1 [ft]/0.3048[m] = 3.28 [ft-m]



VolumeIn performing unit conversions on volumes, a similar problem occurs

Remember how to calculate the volume of a cube

V = L * W * HSo volume is

a L3 term


Example: How many cubic centimeters are in 1 cubic meter?

Equivalents: 1 m = 100 cm

Correct:1 [m3] * (100 [cm]/[m])3 = 1,000,000 [cm3] = 106

Incorrect:1 [m3] * 100 ([cm]/[m])3 = 100 [cm3]


Sample problems

Get together in groups of two to answer these questions:2. How many square miles (mi2) in 160 acres?

3. How many square feet in a hectare?

3. How many gallons are in one million cubic meters?

4. How many gallons in a metric ton (1000 kg)



Estimation

Goals:(1) Get a feel for how big these units are.

(2) Understand how to estimate volumes.

*Sometimes we do not have access to exact measurements. How can we estimate the size of a volume or area?



Estimating the volume of this room

Team 1: Estimate the volume of this room.

What techniques can we use to estimate the dimensions of this room? H

WL



Estimate the volume of the ILC



Estimating the volume of the ILC(1)Get into groups of 4; half work inside; half outside

(2)Estimate the volume of the ILC (order of magnitude)

(3)Write this estimate down below your names.

(4)Estimate your pace – length of courtyard is 69 m

(5)Team 2: Find the area of the ILC by pacing, est. height

(6)Come back to class to pick up part two.28© 2012 - The University or Arizona - HWR203

Documents

Units and Conversions - Sahraweb.sahra.arizona.edu/.../lesson2b/Hwr203Units.pdf · Arizona Water Issues New Units? - Volume Acre-foot The volume of water necessary to cover one acre