SOLUTION: simplify use unit multipliers to convert 27 cubic feet per minute to liters per hour

Question 66035This question is from textbook An Incremental Development
: simplify
use unit multipliers to convert 27 cubic feet per minute to liters per hour This question is from textbook An Incremental Development

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
simplify
use unit multipliers to convert 27 cubic feet per minute to liters per hour

SEE THE FOLLOWING EXAMPLE TO UNDERSTAND THE METHODOLOGY.THE ANSWER TO YOUR QUESTION IS GIVEN AT THE END AFTER THE EXAMPLE.
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I am needing a step-by-step process on how to convert
kilometers to miles.
The problem is 4690 km to miles?
A FOOL PROOF UNIT CONVERSION METHOD IS GIVEN BELOW.
1.LIST OUT THE CONVERSION FACTORS.HERE,WE KNOW
A.1KM=1000 M
B.1M=100 CM
C.2.54 CM =1INCH
D.12 INCHES=1 FEET
E. 3 FT=1 YARD
F.1760 YARDS =1 MILE.
2.START WITH WHAT IS GIVEN.....4690 KM.
3.KEEP THE OBJECTIVE IN MIND.WE HAVE TO CONVERT THIS
INTO MILES
4.NOW GO ON MULTIPLYING THE 4690 KM WITH UNIT RATIOS
FROM ABOVE CONVERSION FACTORS,PUTTING THE UNITS EVERY
TIME AND SEEING THAT AT THE END YOU GET ONLY MILES AND
ALL REST OF THE UNITS GET CANCELLED.SEE THE WORKING
BELOW.
5.UNIT RATIOS FROM ABOVE CONVERSIONS...
A.UNITY =1KM/1000M=1000 M/1 KM
B.UNITY = 1 M/100 CM = 100 CM/1 M.
C.UNITY = 2.54 CM/1 INCH = 1 INCH / 2.54 CM
D.UNITY = 12 INCHES/1 FT = 1 FT/12 INCHES
E.UNITY = 3 FT/1 YARD = 1 YARD /3 FT
F.UNITY = 1760 YARDS/1 MILE = 1 MILE/1760 YARDS.
6.WHICH UNITY RATIO YOU SHOULD USE BECOMES OBVIOUS
WHEN YOU PUT THE UNITS.
SEE THE EXAMPLE
STARTING WITH
4690 KM *1 KM/1000M...OR...WE SHOULD USE 4690
KM*1000M/1 KM IS THE QUESTION.THE GUIDING PRINCIPLE IS
THAT WE SHOULD END UP WITH METERS ON CONVERSION WHICH
HAPPENS IN THE SECOND CASE AS KM IN NUMERATOR CANCELS
WITH KM IN DENOMINATOR LEAVING ONLY METRES.IN THE
FIRST CASE WE GET KM*KM/METRE WHICH IS NOT WHAT WE
WANT..SO FOLLOWING THIS PRINCIPLE WE GET
4690KM*(1000M/1KM)*(100CM/1M)*(1INCH/2.54CM)*(1FT/12INCHES)*(1YARD/3FT)*(1MILE/1760
YARDS)
NOTE THAT KM,M,CM.INCH,FEET,YARD ALL CANCEL OUT IN
NUMERATOR AND DENOMINATOR LEVING ONLY MILES IN THE
NUMERATOR WHICH IS WHAT WE WANT.IF WE MAKE A MISTAKE
IN PUTTING THE UNIT RATIO APPROPRIATELY IT WILL
IMMEDIATELY SHOW UP.
SO REST IS SIMPLE ARITHMATIC WHICH YOU CAN DO I
SUPPOSE THE ANSWER IS
4690 KM = 2914.3 MILES
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27 cubic feet per minute to liters per hour....................
=27[[FT*(12INCHES/FT)(2.54CM/INCH)]^3][(LITRE/1000CM^3)]/[MT*(HR/6O MT)
=27[(12*2.54)^3]*60/1000 LITRES/HOUR
=45873.29 LITRES/HR

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