## Principles of Heat and Fluids: First class Notes on conversion

In the first class, we went through the details regarding the course “Principle of Heat and Fluids” and had a short lecture on conversion.

- 1 mile = 5280 ft

- 14 miles = 14 * 5280 ft = 73920 ft or
- 14 miles * (5280 ft/1 mile) = 73920 ft

When converting to and from different units, it is very important to always mark all of units.

For example, note that the unit “mile” is present in the first equation but not in the second equal since in the second one, the same two units cancelled each other out.

14 miles * 1 = 14 miles

1 mile / 1 mile = 1

Note here too that the answer for both equations are just numbers with units. There is no need to put a unit since 1 mile equals 5280 ft if put in another way, it would be the same thing as 5180 ft / 5280 ft which is just one with the ft unit cancelled out. The reverse can apply for the second case as 5280 ft equals 1 mile, the equation can be rewritten as 1 mile / 1 mile = 1.

- 1 mile / 5280 ft = 1
- 5280 ft / 1 mile = 1

## Two way conversion

So far, the conversion above are straightforward since it is a one way conversion. However, if you have to convert more than twice to get the converted number. For example,

but you are only given the two facts thatyou want to convert 11 km to feet

- 1 mile equals 1.608 km
- and that 1 mile equals 5280 ft.

## Two way conversion question 1.

It is not possible to convert

directly, however, we know that from the given fact from the question that we can convert miles to feet, and we can convert 11 km to miles since it is given that 1 mile equals to 1.608 km. So to put it in a equation,km to ft

- 11 km * (1 mile / 1.608 km) = 6.840 miles, (To convert km to miles)
- 6.840 miles * (5280 ft / 1 mile) = 36,119 ft (To convert miles to ft)
- 11 km * (1 mile / 1.608 km) * (5280 ft / 1 mile) = 36,119 ft (Full equation)

## Three way conversion Question 2.

In question 2, we want to

and you are given three following pieces of information,convert 4,000,000 inches to km

- 12 inches = 1ft
- 1 mile = 5280 ft
- 1.608 km = 1 mile
This is a three way conversion because in order to convert the 4 millions to km, it has to be first converted from inches to feet, then from feet to miles, and finally from miles to km.

4,000,000 inches have to be converted to feet first, and we know that 12 inches equals 1 ft. So 4,000,000 inches * (1 ft / 12 inches) equals 333,333 ft. Now that we have the 4 million inches in feet which is 333,333 ft, we can now convert the feet to miles. Since, 333,333 ft * (1 mile / 5280 ft) equals 63,1312 miles. Finally let’s convert 63,1312 miles to km. Since 63,1312 miles * (1.608 km / 1 mile) comes out to 101.515 km.

- 4,000,000 inches * (1 ft / 12 inches) * (1 mile / 5280 ft) * (1.608 km / 1 mile) = 101.515 km

Three way conversion Question 3.In question 3, we want to

using the following three pieces of information.convert 11,000 cfm to m^3 / s

- 1 mile = 5280 ft
- 1 mile = 1.608 km
- 1 km = 1000 m
Since cfm (cubic feet meter) equals f^3 / minute, the equation can be re-written as “11,000 f^3 / minute”. We can also convert the minute to seconds since, the question requires it to be in seconds. so we can write the equation to be 11,000 f^3 / minute * (1 minute / 60 seconds). We want the feet converted to meter but there is not direct way of converting it so we must go through each conversion with the given information. Therefore, the equation would be in full:

11,000 f^3 / minute * (1 minute / 60 seconds) * (1 mile / 5280 ft)^3 * (1.608 km / 1 mile)^3 * (1000 m / 1 km)^3.