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The Physics of Balloons and Submarines…cont’d…

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

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The Physics of Balloons and Submarines…cont’d…

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  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

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