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Engineering LibreTexts

3.1: Mass and Weight

  • Page ID
    11932
  • Before we calculate pressure, let’s calculate the mass of our storage. As stated before, weight is critically important as systems can fail if the storage becomes too heavy for the platform, or worse, too heavy for the roof or hill on which the storage sits. In addition, knowing how to calculate the weight of storage leads well into calculating pressure, which is force over area where the force is the weight of the water.

    To calculate mass, we use the following formula:

    \[m=ρ*V\]

    Where:

    m = mass

    ρ = fluid density (i.e. mass/volume for water is approximately 1,000 \(\frac{kg}{m^3}\), 62.4 \(\frac{lb}{ft^3}\), or 8.34 \(\frac{lb}{gal}\)) 

    V= volume of storage

    Example \(\PageIndex{1}\)

    For the 500-gallon tank in Figure 2-24, calculate the mass in pounds:

    Solution

    \[ m=ρ*V = 8.34 \frac{lb}{gal} * 500\;gal = 4,170\;lb\]

    Knowing that 1 ton = 2,000 lb, we can see that that 500-gallon tank is:

    \[4,170\;lb*\frac{1\;ton}{2,000\;lb}=2.085\;tons\]

    So, our 500-gallon tank weighs just over 2 tons, which is around the same weight as a small car, three dairy cows, or over 20 adult humans!

    Example \(\PageIndex{2}\)

    For the 19,000-liter ferrocement tank in Figure 2-26, calculate the mass in kg, remembering that in SI units (the International System of Units, e.g. meter, kilogram, second, etc.) 1,000 liters equals \(1 m^3\)

    Solution

    \[19,000\;liters*\frac{1\;m^3}{1,000\;liters} = 19\;m^3\]

    And:

    \[ m=ρ*V = 1,000\frac{kg}{m^3} * 19\;m^3 = 19,000\;kg\]

    At this point you might notice how awesome SI units really are, but they are even more awesome than that; remember that 1 kilogram is defined to equal 1 liter of water, so:

    \[ m=ρ*V = 1\frac{kg}{liter} * 19,000\;liters = 19,000\;kg\]

    Note that this is quite heavy and is approximately the weight of 10 Tesla Model S60 cars or approximately 300 adults.