Unit Conversion and Cancellation Reinforcement Questions

1.

1 pound per square inch (PSI) is equivalent to 6,894.76 Pascal. Convert 100 kPa to PSI.

We start by setting up our equation and checking to make sure we have the conversion from PSI to Pascals in the correct orientation such that the units cancel out:

begin mathsize 14px style 1 P S I space equals space fraction numerator 100 comma 000 space P a over denominator 1 end fraction space cross times space fraction numerator 1 space P S I over denominator 6 comma 894.76 space P a end fraction end style

With Pascals in both the numerator and denominator, all we are left with is PSI. This looks correct and yields a pressure of:

begin mathsize 14px style x P S I space equals space fraction numerator 100 comma 000 space P a over denominator 1 end fraction space cross times space fraction numerator 1 space P S I over denominator 6 comma 894.76 space P a end fraction end style

 begin mathsize 14px style equals space 14.5 space P S I end style

2.

What is the temperature of 1,200°C in Fahrenheit? You can use the equation below:

begin mathsize 14px style degree C space equals space fraction numerator 5 degree C over denominator 9 degree F end fraction space space left parenthesis x ℉ space minus space space 32 ℉ right parenthesis end style

Plugging in what we know:

begin mathsize 14px style 1 comma 200 degree C space equals space fraction numerator 5 degree C over denominator 9 degree F end fraction space left parenthesis x ℉ space minus space 32 ℉ right parenthesis end style

Now we need to rearrange our equation to isolate °F. We first need to put the °F variables on the left side of the equation:

begin mathsize 14px style fraction numerator 5 degree C over denominator 9 degree F end fraction space left parenthesis x ℉ space minus space 32 ℉ right parenthesis space equals space 1 comma 200 degree C end style

Next, to just have the F on one side, we address the fraction on the left side by multiplying both sides of the equation by its reciprocal, a technique we have used in the past:

begin mathsize 14px style open parentheses fraction numerator 9 degree F over denominator 5 degree C end fraction close parentheses space open parentheses fraction numerator 5 degree C over denominator 9 degree F end fraction space close parentheses space left parenthesis x ℉ space minus space 32 ℉ right parenthesis space equals space open parentheses fraction numerator 9 degree F over denominator 5 degree C end fraction space close parentheses space 1 comma 200 degree C end style

We are left with:

begin mathsize 14px style x ℉ space minus space 32 ℉ space equals space space open parentheses fraction numerator 9 degree F over denominator 5 degree C end fraction close parentheses space space open parentheses 1 comma 200 degree C close parentheses end style

We then move the -32°F to the right-hand side of the equation by adding it both sides:

begin mathsize 14px style x ℉ space equals space space open parentheses fraction numerator 9 degree F over denominator 5 degree C end fraction close parentheses space open parentheses 1 comma 200 degree C close parentheses space plus space 32 ℉ end style

We then calculate the value of the fraction in the brackets:

begin mathsize 14px style x ℉ space equals space space open parentheses 1.8 space fraction numerator degree F over denominator degree C end fraction close parentheses space open parentheses 1 comma 200 degree C close parentheses space plus space 32 ℉ end style

We can now make the 1,200 a fraction with 1 as the denominator, which allows us to cancel the °C units:

begin mathsize 14px style x ℉ space equals space space open parentheses 1.8 space fraction numerator degree F over denominator horizontal strike degree C end strike end fraction close parentheses space open parentheses fraction numerator 1 comma 200 horizontal strike degree C end strike over denominator 1 end fraction close parentheses space plus space 32 ℉ end style

We then perform the multiplication to simplify the equation:

begin mathsize 14px style x ℉ space equals space open parentheses 1.8 space degree F space close parentheses space open parentheses fraction numerator 1 comma 200 over denominator 1 end fraction close parentheses space plus space 32 ℉ end style

Leaving us the simple addition:

begin mathsize 14px style x ℉ space equals space 2 comma 160 ℉ space plus space 32 ℉ end style

Finally, we can add the two values together:

begin mathsize 14px style x ℉ space equals space 2 comma 192 end style

3.

Viscosity, a measure of a fluid’s resistance to flow, has the SI unit of Poise (P). If we know that 1 P is equal to 0.1 kg/m.s, what is 500 cP (centipoise) in kg/m.s?

The prefix ‘centi-’ which means 10-2 or 0.01. So :

begin mathsize 14px style 1 space c P space equals space 0.01 P end style

Starting with what we were provided:

begin mathsize 14px style 500 space c P space cross times space fraction numerator 0.01 space P over denominator 1 space c P end fraction end style

Now we make 500 cP a fraction with one as the denominator so we can cancel the cP units will cancel leaving just Poise (P):

begin mathsize 14px style fraction numerator 500 space c P over denominator 1 end fraction space cross times space fraction numerator 0.01 space P over denominator 1 space c P end fraction end style

So we have:

begin mathsize 14px style 500 horizontal strike space c P end strike space cross times space fraction numerator 0.01 space P over denominator 1 space horizontal strike c P end strike end fraction space equals space 5 space P end style

We were asked to provide this viscosity in terms of kg/m.s. Time for one more conversion:

begin mathsize 14px style 1 space P space equals space 0.1 space fraction numerator k g over denominator m. s end fraction end style

So, we convert with confidence by once again verifying our units can cancel:

begin mathsize 14px style fraction numerator 5 horizontal strike P over denominator 1 end fraction space cross times space fraction numerator 0.1 space begin display style fraction numerator k g over denominator m. s end fraction end style space over denominator 1 horizontal strike P end fraction end style

This leaves us with:

begin mathsize 14px style 0.5 space fraction numerator k g over denominator m. s end fraction end style

You can perform these conversions consecutively, which would look like:

begin mathsize 14px style fraction numerator 500 space horizontal strike c P end strike over denominator 1 end fraction space cross times space fraction numerator 0.01 space P over denominator 1 space horizontal strike c P end strike end fraction space cross times space fraction numerator 0.1 space begin display style fraction numerator k g over denominator m. s end fraction end style over denominator 1 horizontal strike P end fraction space equals space 0.5 space fraction numerator k g over denominator m. s end fraction end style

As before, be certain to make sure the units of measure can cancel out, and you will be not go wrong.

Next, we find out how to put our equations into action to calculate an answer.

You have completed 0% of the lesson
0%