Maths for Diploma Studies

We have, through our mathematical brilliance, produced the exact equation we need to find the answer that will guarantee exam success. Now it’s time to calculate the answer. As with all things mathematical, there are rules we need to follow to avoid getting it wrong.

Inputting the numbers for the terms and checking units

In all CIBD lessons, we see an equation and a list of numbers that correspond to the terms in the equation. While working through the calculation, it is important to check that the units agree. Let’s go through an example to help with this important point.

We are given the mass flow rate, represented by the symbol G, of a product being transferred from one vessel to another. We are asked to convert that mass flow rate into volumetric flow rate with units of cubic metres per second:

The equation to convert mass flow rate to volumetric flow rate is:

To isolate volumetric flow rate (Q), we rearrange the equation:

You will notice another term in this equation. The symbol ρ, pronounced ‘row’, represents fluid density and has units of mass per unit volume. For this example, the product being transferred has a density of 1,010 kg/m³. With this process information, we can proceed by adding these values to our equation:

Let’s look at the units for a moment:

Remembering the unit cancellation techniques we used earlier, we can rearrange this to:

Then cancel the kg to get:

As this is volume per unit time, it confirms that we properly performed this calculation. Given this, we then can complete the calculation:

Terrific. We have a volumetric flow rate! One thing remains – converting the rate from hours to seconds. As there are 60 seconds in a minute and 60 minutes in an hour, then 60 × 60 = 3,600 seconds in an hour:

As before, the hrs cancel, and we are left with the volumetric flow rate in m³/s.

And to consolidate what we know, we can tackle a problem from a topic we will master in Module 3. The equation below can be rearranged and used to calculate the area (A) of a heat transfer surface:

For this question, here are the values you will need:

We don’t need to know what the other terms relate to here because we are only interested in the techniques.

The first thing we will need to do is rearrange the equation to isolate A. This is nice and easy as A is being multiplied so, we just divide both sides by everything that is multiplying it:

Insert the provided values and units for each term. Notice that we need to convert the  into the fraction form of this unit:

Let’s check our units by using the cancellation techniques we have already learned:

First, we make K a fraction with 1 as the denominator:

Next, start cancelling out units:

This leaves:

And becomes:

To cancel the Watts, we can rearrange to change this from one fraction divided by another to one fraction multiplied by the reciprocal of the other. Like so:

 Leaving:

With a sensible final unit of measurement confirmed, we calculate the answer following the PEMDAS order of operation:

First parenthesis:

Then multiplication and division:

Then we verify that our units of measurement are correct. After all of the cancellations are complete, we are left with m², which is an appropriate unit for the area. This provides a sense of validation that we understood the question, used the proper equation, and input the right values. Because of this, it is quite likely that our answer is correct.

To help reinforce what we have just learned, on the next page there are some practice questions. Answers and explanations can be revealed by clicking on show answer.