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.
Next Generation Science Standards
- NGSS HS-ETS1-3 “Evaluate a solution to a complex real-world problem based on prioritized criteria and trade-offs that account for a range of constraints, including cost, safety, reliability, and aesthetics, as well as possible social, cultural, and environmental impacts”
Common Core State Standards
- CCSS.Math.Practice.MP1 “Make sense of problems and persevere in solving them”
- CCSS.Math.Practice.MP2 “Reason abstractly and quantitatively”
- CCSS.Math.Practice.MP4 “Model with mathematics”
Supplies
- Balloons (3)
- 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)
Part A: Pressure
Fill a balloon with air and estimate its radius. (If you’re having trouble measuring the radius, you can use the relationship between the radius and the circumference of a sphere: circumference=2π radius). Radius in air =_________ cm
Now, put your air-filled balloon under water. What is its radius? Radius in water = _________cm.
Did the radii in air and under water differ? How? Why do you think that is?
Pressure! Pressure (in pascals) is measured in terms of force (newtons) per area (meters squared). 1,000 pascals are in a kilopascal (kPa). The standard atmospheric pressure at sea level is 101.325 kPa of pressure (also referred to as 1 ATM, 1 atmosphere) – there’s a lot of air weighing down on top of you every day! As you rise in elevation, the pressure decreases. On top of Mt. Everest, 8,848 m above sea level, atmospheric pressure is about 30 kPa. What do you think would happen to your balloon if you carried it up to the top of Mt. Everest?
The ideal gas law tells us PV=nRT where P is pressure, V denotes volume, n is equal to the number of gas molecules, R is the ideal gas constant, and T is the temperature of the gas. If we were able to keep the temperature of the air inside the balloon constant (tuck it into your jacket as you climb Everest), and assuming no air escapes the balloon, we can estimate how much the balloon will expand by setting PV for the balloon at sea level equal to PV for the balloon atop Everest. If the pressure atop Everest is about 0.3 (30/101.325) times the pressure at sea level, what would be the volume of the balloon atop Everest?
Balloons are used to study earth and space from high altitudes, heights of 30,000m (30km) are not uncommon! If you were filling a balloon with helium, standing outside your school, to launch for high altitude research, would you want to fill it fully? Why or why not?
Part B: 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 stated in the first aero/hydrodynamics lesson, 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 back in Part A, when we concluded that pressure was the reason our balloon shrank under water, 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 previous aero/hydrodynamics lesson, we talked about Archimedes principle and buoyancy, stating that upward buoyant force on a body in a fluid 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!
Part C: Viscosity
Viscosity is a measure of the stickiness of a fluid. A fluid that flows easily has a lower viscosity. A fluid that flows slowly has higher viscosity. Which do you think has a higher viscosity: water or honey?
Experiment: gather a few kitchen liquids (work with a teacher or parent to verify you are using safe items – e.g. water, honey, ketchup, vegetable oil, molasses) and put a drop of each on a non-porous surface (the water container you used in Part A would work well). Tilt the surface so the liquids flow downhill. Whichever one moves fastest has the lowest viscosity. Rank your liquids in order of lowest to highest viscosity.
Viscosity is relevant for our blimps because it is the cause of a boundary layer of fluid around the blimp. When a body is in a fluid flow, viscosity causes what’s known as a no-slip condition – that the fluid at the body has zero speed relative to the body. As you move further from the body, the fluid speed will equal the speed of the free stream flow. This results in a drag force on the body. If you are interested in diving into this more, a great lesson on this is available through MIT’s Open Courseware: https://ocw.mit.edu/courses/mechanical-engineering/2-016-hydrodynamics-13-012-fall-2005/readings/2005reading5.pdf .
Bonus: Non-Newtonian Fluids
A particularly interesting, and fun, type of fluid is known as a non-Newtonian fluid. In Newtonian fluids, the viscosity does not change based on how you push on it. A non-Newtonian fluid’s viscosity does change with how you push on it. Quicksand is an example of a non-Newtonian fluid, because the harder something stuck in quicksand struggles, the faster they sink. A common experiment demonstrating a non-Newtonian fluid is to make a mixture of corn starch and water. If you press slowly on the corn starch and water mixture, your hand will sink in like it is a liquid. But if you press quickly on it, then it can feel almost like a solid surface. Check out this video: https://www.youtube.com/watch?v=v581Y50-bow, or do the experiment yourself!
Last updated June 1, 2022.
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