W104hndout2
UNIT CONVERSIONS:
Convert 16” into feet.
16 in. x (1 ft. / 12 in.)
16 in. x (1 ft. / 12 in.) = 16/12 ft. = 1.33 ft.
Convert 16’ into inches.
16 ft. x (12 in. / 1 ft.)
16 ft. x (12 in. / 1 ft.) = (16 x 12) in. = 192 in.
Since 1 foot = 12 inches, the quantity (1’ / 12”) or (12” / 1’) is equal to one, or unity.
Multiplying a quantity by ONE in this way does not change the quantity
This same approach can be used to convert the units of any AREA, VOLUME,
FLOW RATE, or LINEAR quantity.
Convert 8 square feet into square inches.
8 sf x (144 in2 / 1 sf)
8 sf x (144 in2 / 1 sf) = (8 x 144) in2
= 1,152 in2
Convert 8 square inches into square feet.
8 in2 x (1 sf / 144 in2)
8 in2 x (1 sf / 144 in2) = (8 / 144) sf
= 0.0556 sf
Convert 950 gallons into cubic feet.
950 gal x (1 cf / 7.48 gal)
950 gal x (1 cf / 7.48 gal) = (950 / 7.48) cf
= 127.0 cf
Convert 950 cubic feet into gallons.
950 cf x (7.48 gal / 1 cf)
950 cf x (7.48 gal / 1 cf) = (950 x 7.48) gal
= 7,106 gal
ALWAYS CHECK TO BE SURE LIKE UNITS CANCEL EACH OTHER OUT!
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DIMENSIONAL ANALYSIS:
Used to convert quantities from one unit to another. Arrange the necessary conversion
factors to convert the original quantity into the desired units. ALWAYS CHECK TO BE
SURE THAT SIMILAR UNITS CANCEL, LEAVING ONLY THE UNITS YOU WANT.
Convert 1500 gpm into mgd.
1500 gal / min. x (1 mg / 1,000,000 gal) x (60 min / 1 hour) x (24 hours / 1 day)
1500 gal / min. x (1 mg / 1,000,000 gal) x (60 min / 1 hour) x (24 hours / 1 day)
= (1500 x 60 x 24) / (1,000,000) mg / day
= 2.16 mgd
Convert 1500 mgd into gpm.
1500 mg / day x (1,000,000 gal / 1 mg) x (1 day / 24 hours) x (1 hour / 60 min)
1500 mg / day x (1,000,000 gal / 1 mg) x (1 day / 24 hours) x (1 hour / 60 min)
= (1500 x 1,000,000) / (24 x60) gal / min.
= 1,041,666.67 gpm
Convert 8 cfs into gpm.
8 cf / sec x (7.48 gal / 1 cf) x (60 sec / 1 min)
8 cf / sec x (7.48 gal / 1 cf) x (60 sec / 1 min)
= (8 x 7.48 x 60) gal / min
= 3,590.4 gpm
Convert 8 gpm into cfs.
8 gal / min x (1 cf / 7.48 gal) x (1 min / 60 sec)
8 gal / min x (1 cf / 7.48 gal) x (1 min / 60 sec)
= 8 / (7.48 x 60) cf / sec
= 0.0178 cfs
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DIMENSIONAL ANALYSIS (cont’d):
Using conversion factors in Dimensional Analysis:
Apply the conversion factor in the same manner as the examples of the previous page,
considering the relationship on each side of the “equal” sign as UNITY.
EXAMPLE: Convert 12 cfs into gpm
Using the “Formula and Conversion Factors” handout on the following page, identify the
conversion factor involving both “cfs” and “gpm”
Find “1 cubic foot per second = 448.8 gallons per minute”
Apply the conversion factor in the following form:
(
448.8 gpm
Therefore,
1 cfs
)=(
12 cfs x
1 )=
448.8 gpm
1 cfs
448.8 gpm
(
1 cfs
)
UNITY
= 12 x 448.80 = 5,385.60 gpm
EXAMPLE: Convert 28 mgd into cfs
Look for the conversion factor involving “mgd” and “cfs”
Find “1 million gallons per day = 1.55 cubic feet per second”
1.55 cfs
Then,
28 mgd x
= 28 x 1.55 = 43.40 cfs
1 mgd
(
)
EXAMPLE: Convert 7,000 gpm into mgd
Look for the conversion factor involving “gpm” and “mgd”
Find “1 million gallons per day = 694.4 gallons per minute”
1 mgd
Then,
7,000 gpm x
= 7,000 / 694.4 = 10.08 mgd
694.4 gpm
(
)
TRY MEMORIZING THIS STRING OF CONVERSION NUMBERS:
mgd x (1.55) = cfs x (448.8) = gpm
IN REVERSE:
gpm / (448.8) = cfs / (1.55) = mgd
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SOLVING FOR UNKNOWNS:
Some helpful tips:
1.
2.
3.
4.
Solve for x:
16x + 5 = 37
16x = 37 – 5
16x = 32
x = 32 / 16
x=2
15 + 3x = 40 – 2x
15 + 3x + 2x = 40
3x +2x = 40 – 15
5x = 25
x = 25 / 5
x=5
½x – 30 = 45 – 2½x
½x = 45 – 2½x + 30
½x + 2½x = 45 + 30
3x = 75
x = 75 / 3
x = 25
17x – 31 = 5x + 77
17x – 5x = 77 + 31
12x = 108
x = 108 / 12
x=9
Combine like terms.
Separate unknown quantities and known quantities.
Place unknowns to one side of equal sign, known
quantities to the other side.
Be calm, don’t panic, think it through.
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SOLVE THE FOLLOWING PROBLEMS:
1.
Convert 126,000 gallons per hour into cubic feet per minute.
(280.75)
2.
Convert 47.25 mgd into gallons per minute.
(32,812.5)
3.
A 126’ diameter tank rises 4.66’ over 3 hours, what is flow in gpm?
(2,414.6)
4.
Water in a pipe travels 12.55 miles in 5.66 hours, what is the flow
velocity in feet per second?
(3.25)
5.
Convert 280.75 cfm into gallons per second.
(35)
6.
If a pump can put out 4,861.1 gpm, how many mg will it pump
in one day?
(7)