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**Introduction**

AP Physics 1 has added Unit 8: Fluids. This video and article will give you some timely tips on how to deliver this content.

The thing about teaching fluids in introductory physics is that there are three main principles: Pascal, Archimedes, and Bernoulli. Below we will outline six Fluid Physics Experiments – two for each – that will help you instruct on these important ideas.

**Figure 1. Pascal’s Vases show us that pressure depends on depth and not area. **

**#1 The Definition of Pressure**

Pascal gives us the definition of pressure, that P = F/A it is a force over an Area. Pressure is something that exists in a fluid, it is everywhere equal, at a given height. And, pressure, being a force causes acceleration. Fluids will flow from a place of high pressure to a place of low pressure, by Newton’s 2nd Law, it’s a net force. And because of area difference, it is possible to establish a mechanical advantage. Either using hydraulic pressure (liquids) or pneumatic pressure (gases).

**Figure 2. A small syringe can have a mechanical advantage over a large one syringe because the pressure in the fluid, be it air or water, is constant throughout. P = F/A = ^{F}/_{A}**

But, pressure can also be measured by depth, Pascal explains this too. P = ρgh means that pressure doesn’t depend on area, only depth h and density ρ (usually constant), so we can use depth to predict pressure. Torricelli found the atmospheric pressure to be strong enough to lift Mercury to a height of 760 mm, and less so on the mountains. But if you use water, you can lift it to a height of 10 meters.

**Figure 3. Torricelli’s experiment, the atmosphere can lift liquid mercury 760 mm, but no further. The space above is vacuum.**

**Figure 4. Depth increases the pressure in a fluid, this is explained by the formula P = ρgh. Where ρ is density. The manometer at right shows the pressure is higher than the atmosphere: the right end of the U-shaped tube is open for direct comparison.**

Thus, if you were to dive 10 meters deep, you would experience an additional atmosphere of pressure (by ρgh) and you would definitely feel it. Because the ratio of 760mm to 10 meters is about 13 to 1, we conclude that mercury has a density that is 13 about times greater than water.

**#2 The Concept of Fluid Density**

If we are going to understand fluid physics - we need to use the MKS units of kilograms per meter cubed. I suggest a lab on these density cubes – which all have different masses - despite being the same size.

**Figure 5. The density blocks can be a fun window into teaching the MKS units of kg/m3 that are used extensively in physics.**

As a lab, try to measure their densities in the new units of kg/m3 which turns out to be 1000 times bigger than g/cm^{3} . For example the density of water is 1000 kg / m^{3} . In the lab, you can try to guess which block is which based on the density you measure and comparing to a chart.

**Figure 6. The float test is one way to distinguish the blocks nylon (sinks) and polypropylene (floats) which otherwise look almost identical.**

For a liquids example, comparing the density of salt water to regular water can be done easily with a density manometer. It helps to keep the waters cold so that they don’t mix quickly. The ratio is about 6 to 5 for fully saturated salt water (be sure to dye them different colors, and use salt without iodine). Thus, saturated salt water is 20% denser, or 1200 kg/m^{3}. The equilibrium statement of P = P becomes ρ_{1}gh_{1} = ρ_{2}gh_{2}.

**Figure 7. Salt water (green) vs. Pure Acetone (pink) the density ratio is 3 to 2. The zero line is established at the height at which the substances meet. The green is just food dye but the pink is from a little nail polish. The salt must be pure and not iodized to get this high density of 1.2 g/mL.**

My favorite demo with the density manometer is to compare saturated salt water to pure acetone… These two liquids will not mix and are -- easy to clean. I have added a little nail polish as a dye for the pure acetone. The ratio is a - quite large - 3 to 2, thus acetone has a density of only about .8 g/cm3 or 800 kg/m^{3}.

**#3 Floating and Bouyancy**

Archimedes Principle is that the weight of the displaced fluid is the same as the buoyant force. F = pVg But, this too is a consequence of pressure increasing with depth.

**Figure 8. The pressure increase with depth is canceled out left and right, but not up and down. Thus, the net force from the water is Fnet = Fup – Fdown = P2*A – P1*A = ρgh2*A - ρgh1*A = ρgΔh*A = ρgV = Mg where M is the mass of the displaced fluid. which is the formula for buoyancy. (Recall that in fluids h means depth.) So, we see that buoyancy is really caused by depth pressure.**

As we get deeper underwater the pressure increases, therefore the force is greater on the bottom than the top. These left and right side arrows cancel out. The result is that the pressure difference between the top and bottom, equal to ρgh, becomes a force equal to the volume of the object times the fluid density. Since density times volume is mass and with g weight, we easily see the weight of the fluid is equal to the net fluid force on the object, this is the buoyant force.

**Figure 9. Pine floats about 50% below the surface of water and from that we immediately know its density is near .50 g/mL = 500 kg/m3 half that of water.**

Floating objects of course are completely lifted by the fluid, so their buoyant force is the same as their weight. But not all objects float the same. Here, we see pine floats about halfway, while Styrofoam floats about 90% above the surface. Ice, famously is about 90% below, it depends if the water is fresh or salty.

**Figure 10. Ice floats 92% below the surface, thus it has a density of .92 g/mL or 920 kg/ m^{3}. **

Generally, we can tell the density based on how well the object is floating. The % amount an object will sink is the same as its density, compared to water or the fluid it is in. As an example, ice sinks 92% in water, so its density is 92%. A styrofoam boat will sink more and more as I add passengers (washers) until it has the same density as water at which point it completely sinks.

**Figure 11. As a lab, we will fill a Styrofoam boat with passengers until it completely sinks. Predicting this number is a good challenge and it usually works perfectly. The sinking moment occurs when the density of the boat matches the density of water. **

**#4 Boyle's Law:**

Now the compressibility of gases is NOT tested in AP Physics 1 – only AP 2, so why is Boyle’s Law still an appropriate lab for AP Physics students?

Well , students probably already know gases are compressible from 8th grade physical science, and they are also important examples of fluids. But the compression of a gas under pressure is one of the surest metrics by which to gauge the pressure of a fluid.

**Figure 12. The Elasticity of Gases Demo is a great way to get to know the formula for pressure and to make a measurement of the ambient atmospheric pressure.**

When we add books to an Elasticity of Gases Demo we are demonstrating a familiarity with the formula for pressure: P = F/A. Each book provides a unit force of about 20 N and the syringe plunger's the area is constant at .0004 m2, thus, the pressure is increasing in 50,000 pascals (n/m2) with each book. A pascal is the unit of pressure and the atmosphere itself is measured by this experiment to be about 100,000 N/m2 of pressure. And that value is on the AP Physics test. Therefore, we conclude that yes, this is a great experiment on the physics of fluids.

**#5 The Spouting Cylinder:**

The spouting cylinder is a classic physics demonstration and a staple problem in AP Physics. Holes at different heights are permitted to emit water when subjected to fluid pressure. The question is, which spout will shoot the furthest? The lower spout has more pressure due to depth and so goes faster, but the upper spout has the height advantage.

The answer is to apply Torricelli’s theorem: ρgh = ½ ρv^{2} which is a simpler version of Bernoulli’s Theorem. In short, the conservation of energy can be applied to fluids. Now that’s not how Torricelli said it, but this, combined with the laws of projectile motion, results in the maximum distance occurring always when the depth is equal to the height of the spout, or exactly right in the middle.

**Figure 13. The Spouting Cylinder is a classic demonstration in AP Physics and demonstrates that the principles of projectile motion and conservation of energy can be applied to fluids.**

**#5 Bernoulli's Principal:**

A fast-moving fluid is at a lower pressure, that is Bernoulli’s Principle, and it is somewhere here in the Bernoulli Equation:

P + ρgy + ½ ρv^{2 } = P + ρgy + ½ ρv^{2}

This principle explains the airplane lift force, because if there is a faster moving fluid over the curved wing it will generate a pressure difference between the top and bottom. Now, while you might not have an airplane at the ready, you do have a frisbee.

**Figure 14. Airplane lift is explained by Bernoulli’s formula. When there is a greater velocity v, there is lower pressure P. This pressure reduction occurs on the top because the larger curve over the top compared to the bottom. **

The frisbee displays a similar curving and obeys the same principle. So, explain that frisbees, when thrown through the air, are seen to float easily because they receive lift from the Bernoulli’s principle of fast-moving fluids.

The purpose of the spin, on the other hand, is that the frisbee will maintain a flat orientation so that the air is always lifting it up, always a lower pressure on top.

**Figure 15. The frisbee is actually a great example of the Bernoulli Principle in effect. With a fluid streamline almost identical to that of the airplane wing.**

So, play frisbee with your students. But, let us now ask, what if I were to glue two frisbees together in a macaroon shape and give that a throw. How would the range compare to two frisbees nested together.

**Figure 16. The washers are taped to the yellow frisbee to match the mass of the double frisbee on the right. But this is optional not essential. The double frisbee loses either way.**

The result, we can prove by experiment, is that a double frisbee will not have a lift advantage over a single frisbee, even when accounting for the weight increase. The added washers, which are taped in place, are optional and the experiments works well in either case and is quite convincing: a double frisbee will never go as far because it lacks the lift force to keep it aloft.

**James Lincoln**

Physics Instructor

James Lincoln is an experienced physics teacher with graduate degrees in education and applied physics. He has become known nationally as a physics education expert specializing in original demonstrations, the history of physics, and innovative hands-on instruction. The American Association of Physics Teachers and the Brown Foundation have funded his prior physics film series and SCAAPT's New Physics Teacher Workshops. Lincoln currently serves as the Chair of AAPT's Committee on Apparatus and has served as President of the Southern California Chapter of the AAPT, as a member of the California State Advisory for the Next Generation Science Standards, and as an AP Physics Exam Reader. He has also produced Videos Series for UCLA's Physics Demos Project, Arbor Scientific, eHow.com, About.com, and edX.org.