3.1: It's All About the Weight
- Page ID
- 7131
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Water is essential for the survival of all life forms. It makes up approximately 60% of our total body weight and as much as 75% of the earth’s surface. So, how much does water actually weigh? There are a few variables, such as temperature, that determine the weight of water, but for all practical purposes in waterworks mathematics, water weighs 8.34 pounds per gallon. The density (mass per unit volume) of water is 1.00. This is also referred to as specific gravity. When discussing specific gravity, many things are compared to water. For example, if something has a specific gravity less than water (<1), then the substance will float on water. Conversely, if a substance has a specific gravity greater than 1, it will sink in water.
The table below lists common specific gravities/densities and weight of substances used in the waterworks industry. Remember, these are only examples and should not be put to memory. On any State exam, you will be given the specific gravity or corresponding weight of the substance in the question.
|
Substance |
Specific Gravity |
Weight |
|
Crude Oil |
0.815 |
6.80 lbs/gal |
|
Water |
1.00 |
8.34 lbs/gal |
|
Chlorine (g) |
2.49 |
20.77 lbs/gal |
|
Calcium hypochlorite |
2.35 |
19.60 lbs/gal |
|
Alum |
1.16 – 1.40 |
9.67 – 11.68 lbs/gal |
|
Ferric chloride |
1.43 |
11.93 lbs/gal |
Examples
Since water is the reference, then a specific gravity (SG) of 1 and a weight of 8.34 lbs/gal are the numbers needed to calculate the SG and weight of other substances.
What is the weight of a substance in lbs/gal if it has a SG of 1.25? Remember, anything that has a SG >1 will weigh more than 8.34 lbs/gal.
- 8.34 lbs/gal1 SG x 1.25 SG1 = 10.43 lbs/gal
What is the SG of a substance that weighs 5.75 lbs/gal? Remember, anything with a weight <8.34 lbs/gal will have a SG <1.
- 1 SG8.34 lbs/gal x 5.75 lbs/gal1 = 0.69 SG
Exercises
Solve the following density related problems.
-
Liquid sodium hypochlorite has a specific gravity of 1.47. What is the corresponding weight in pounds per gallon?
-
Chlorine gas has formed into a liquid state. It weighs 19.75 lbs/gal. What is the specific gravity?
-
What is the weight difference between 75 gallons of water and 42 gallons of sodium hypochlorite with a specific gravity of 1.42?
-
A treatment operator has 50 gallons of 12.5% sodium hypochlorite. How many pounds of the 50 gallons are available chlorine?
-
How much does 45 gallons of 25% Alum weigh if the specific gravity is 1.35?
-
Ferric chloride weighs 14.25 lbs/gal. What is the specific gravity?
-
Chemical A has a specific gravity of 2.31 and chemical B has a specific gravity of 1.95. Chemical A is what percent heavier than chemical B?
-
How many pounds of ferric chloride are in 250 gallons of 22% strength? (Assume the specific gravity is 1.41)
-
What is the weight in lbs/cf of a substance that has a specific gravity of 2.05?
-
A shipment of crude oil has a specific gravity of 0.825. What is the weight in lbs/cf?