Density

When a boat goes from the saltwater ocean to a freshwater river, what changes about how it floats?

Learning Objectives

After completing this lesson, the student will be able to describe similarities and differences in loads on a body based on fluid properties.

Standards

  • NGSS HS-ETS1-3
  • CCSS.Math.Practice.MP1 
  • CCSS.Math.Practice.MP2
  • CCSS.Math.Practice.MP4

Supplies

  • Balloons (2)
  • Tub of water
  • Tape measure

Units Used

  • Mass: kilogram (kg)
  • Length: centimeter (cm)
  • Length: meter (m)
  • Temperature: Celsius (C)
  • Time: second (s)
  • Force: Newton (N) (1 N=1 kg m/s2)
  • Pressure: kilopascal (kPa=1000 N/m2)

Density

Fill two balloons, one with air and one with water.  Which one is heavier?  Why?

Water is denser than air, meaning that for the same size container (the balloon), water weighs more!  As we learned previously, density varies by temperature, pressure, and humidity.  At 101.325 kPa of pressure and at 15 degrees Celsius, the density of air of is approximately ρair=1.225 kg/m3.  The density of freshwater is ρfreshwater=1,000 kg/m3 at 4 degrees Celsius. So when we concluded that pressure was the reason our balloon shrank under water in the lesson on pressure, the reason there was more pressure under water is because water is denser than air.  We can calculate what is known as hydrostatic pressure, the pressure due to being submerged under water at some depth, h, using the equation Phydrostatic=ρgh, where g is the acceleration due to gravity, 9.81 m/s2.  What is the hydrostatic pressure if you go 5 meters under water?  10 meters under water?  20 meters under water?  30 meters under water?  Use care with units.  You are multiplying ρ in kg/m3 with g in m/s2 with h in m.  This means your pressures are in units of Pascals (kg/m3)(m/s2)(m)=(kg)(m/s2)(1/m2)=N/m2=Pa.  There are 1,000 Pascals in a kilopascal.

Graph your findings.

While you’d have to hike to the top of Mount Everest to have the pressure drop to 0.3 of standard atmospheric pressure, by descending just 10 m under water, you’ve added 100 kPa of pressure, e.g. another standard atmosphere of pressure!

Saltwater, because it has salt in it, is a little bit denser than freshwater, with typical saltwater densities between 1,020 to 1,030 kg/m3.  Recall in the lesson on Force Balance, we talked about Archimedes principle and buoyancy, stating that the upward buoyant force on a body in a fluid is equal to the weight of the fluid that is displaced by the body.  If saltwater is denser than freshwater, is it heavier or lighter than freshwater? 

So, if a boat needs to displace an amount of water equal to the boat’s weight in order to float, which will it float higher in, freshwater or saltwater?  

You might have felt this difference before, floating in a pool versus the ocean.  This has real implications for boats transiting from oceans to rivers or canals – they have to be mindful of the density difference or they could end up running aground!

Next Steps

Interested in numerical simulation? This video will show you how to do the graph of hydrostatic pressure versus depth using Matlab.

Next, let’s understand why the stickiness of a fluid matters with the lesson on viscosity.

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The Literate Engineer

Last updated: November 23, 2022.