The Physics of Balloons and Submarines…cont’d…

1. The Physics of Balloons and Submarines…cont’d…

2. The Ideal Gas Law Equation We learned that Pressure of an Ideal Gas is proportional to Particle Density. P   Temperature is a measure of the average kinetic energy of atoms, and is related to the pressure. In fact, Pressure is proportional to Temperature. P  T This leads to the ‘ideal gas law equation’ (holds only for non-interacting particles): P = k    T Boltzmann’s constant 1.38 x 10-23 Pa-m3/particle-K Absolute Temperature ( Kelvin) C + 273 =  K(Kelvin scale) e.g. 0 C = 273  K Particle density

3. Do fluids obey Newton’s Laws ? Consider a horizontal pipe with some fluid: P1 P2 • Fluids have inertia (need to apply forces to change their flow. ) • Pressure differences P1-P2 lead to net force, acceleration to the right. • Fluids accelerate to lower pressures. (similar to F=ma) • 3. Apply pressure on fluid; fluid applies same amount of pressure on you • (Newton’s 3rd law) • Pumping water requires work. • Pumped water carries this energy with it. • For Steady State flow, Work done in moving volume V using Pressure P • = P  V (similar to F  d) • = ‘energy required to pump fluid’ for steady state flow

4. ‘Pressure potential energy’ For horizontal flow: Total Energy E of Fluid = PV + Kinetic Energy Energy/unit volume E/V = P + (½)v2 = constant, (for horizontal flow) In general (including vertical flow): P + (½)v2 + gh = constant (along a streamline) i.e. When a stream of water speeds p in a nozzle or flows uphill in a pipe, its pressure drops. (Bernoulli’s Principle/Equation) A: slow velocity, high Pressure B: fast velocity, low Pressure Examples: A A B

5. Airplane Wing The Perfume Atomizer

6. Why does the ball float ?

7. Physics of Moving Fluids: In Garden Hoses, around Baseballs, Planes and Frisbees

8. Fluids in Motion: Using Hoses, Baseballs & Frisbees Real liquids have viscosity – fluid friction when 1 layer of fluid tries sliding across another. e.g. Fluid Viscosity Honey (20C) 1000 Pa-s Water (20C) 0.001 Pa-s Helium (2C) 0 Pa-s Result: Speed of H20 thru a pipe is not constant (fastest at the center, stationary at the walls) Velocity profile due to viscosity Viscosity affects the volume flow rate through a hose or pipe.

9. p1 p2 In fact: Diameter D length L p = p1 - p2 Volume flow rate V/t =   p  D4 128  L   (Poiseuille’s Law) viscosity Or….It’s hard to squeeze honey thru a long, thin tube. Example: When new, a kitchen faucet delivered 0.5 liters/s. Mineral deposit built up, reducing diameter by 20 % over the years. What’s the new volume flow rate ? Since V/ t  D4, and D is now 0.8 of its value before, then V/ t changed by a factor of (0.8)4, or it is currently 0.2 liter/s. ( a reduction of  60 % !).

10. How Frisbees Fly • Above Frisbee: • airflow bends inward • high velocity • lower pressure • Below Frisbee: • airflow bends outward • low velocity • higher pressure Pressure Difference gives ‘lift’

11. A Spinning Baseball Magnus Force Low Pressure Spin High Pressure Direction of throw • Spin forces flow on one side to be faster, • resulting in lower pressure. • Spin forces flow on the other side to be slower, • resulting in higher pressure. • Pressure difference causes a lateral deflection

12. Laminar vs Turbulent Flow • Flow near surface forms a ‘boundary layer’ • If Reynolds number < 100,000 • laminar flow of boundary layer • slowed by viscous drag • If Reynolds number > 100, 000 • Turbulent flow of boundary layer Reynolds number = density  obstacle length  flow speed viscosity