The third math formula from our MOST Five is the Density Equation. Today we will discuss the two common applications for this formula, as we prepare for the California Water Distribution Operator certification exam this coming Saturday.
For the D1 and D2 exams, we often see questions asking us to find the Weight of water in a storage tank. That is the first application of this formula. To find the Weight, we need to know both the Volume of the water and its Density. Usually for this problem, we will not get the Volume directly. Instead, we will need to find it, using the first equation from our MOST Five. And we’ll get that from the dimensions of the water in the tank: the diameter (or length and width) and the Height of the water. Remember that Height is the key to recognizing the need to use our first formula.
As to the Density, while the density of water does change — notably with temperature — for the purposes of our Water Math calculations we treat it as a constant. It is always 8.34 pounds per gallon. Or if you prefer to express the volume in cubic feet, it is 62.4 pounds per cubic foot.
In this type of problem, expect to see an incredibly large answer. That’s because the density of water is very high. For example, the weight of 50,000 gallons of water is 417,000 pounds. That’s a lot of weight, and that’s a relatively small amount of water. So don’t be surprised when your calculator screen shows a huge number: it’s probably right!
The second application of this formula is most often found when we deal with sodium hypochlorite — or bleach — problems. The normal result of the Pounds Formula — Number Five of our MOST Five — is the Weight of a chemical to be applied. But when we deal with a liquid chemical like bleach, we normally measure its quantity by Volume instead of Weight. This formula is the way to convert from Weight to Volume.
To find the Volume, we need to know the other two variables, Weight and Density. As we just noted, the Weight in this case will usually come from the Pounds Formula. Unlike the density of water, in our Water Math problems, the density of bleach is really variable. That’s the bad news. However, the good news is that the actual density that you must use in your calculation has to be stated directly in the math problem!
A common twist on this that we’ve seen in recent exams is to give you the Specific Gravity instead of the Density. This is an easy fix, although it is one more step in the always-involved bleach calculations. All you need to do is multiply the Specific Gravity by 8.34. That will give you the Density that you need to make that conversion from Weight of bleach to Volume of bleach — which is usually the final step in a bleach question.
Look for both of these applications of this Density Equation — the third formula in our MOST Five — on the certification exam on Saturday.