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Splat? An example of computational Physics in action! Reaal Khalil - PowerPoint PPT Presentation

Nov 29, 2023 •316 likes •509 views

Splat? An example of computational Physics in action! Reaal Khalil 1 Why not just use pen and paper? A lot of the equations arent "solvable" (no analytic solutions) There are too many variables in play Saves time

  1. Splat? An example of computational Physics in action! Reaal Khalil 1

  2. Why not just use pen and paper? • A lot of the equations aren’t "solvable" 
 (no analytic solutions) • There are too many variables in play • Saves time • Neat graphs 2

  3. 
 The question: A human leaps out of a plane holding a pressurised tank of helium and a weather balloon. What happens next? 3

  4. The details: • Air resistance and buoyancy • Pressure, temperature and density vary with altitude • Radius of the balloon depends on the pressure inside the balloon and atmosphere • Speed of inflation of the balloon depends on pressure in the tank and in the balloon 4

  5. The Physics: Gravity: Drag Force: 1 v 2 F G = mg F D 2 C D A ρ = Reynolds Number: Buoyancy: vD F B = ρ gV R e = ν 5

  6. The Physics 6

  7. The Physics The Mooney-Rivlin model: ( ( )( 1 + ) 7 2 ) − ( ) ( ) t 0 r 0 r 0 1 − α r ∆ P = 2 µ r 0 r 0 r r α − ∆ P P atmospheric P balloon = nRT P balloon = 4 r 3 π 3 MATLAB’s built-in functions make life so much easier! 7

  8. The Balloon SN: 400-8242 = 300,000 Pa = 10/11 µ α initial non-inflated balloon radius = 0.54m r 0 balloon mass = 0.8kg m r max maximum radius = 3.4m initial balloon thickness = 0.2mm t 0 The Tank: SN: HP Steel 50 = 2900psi = 20,000,000Pa ( t = 0) P tank = 50L = 0.05m 3 V tank m tank = 60kg 8

  9. The Physics Use Bernoulli’s equation: 1 v 2 + ρ gz + P = constant ρ 2 dn − − − − − − − − − − − √ P tank P ballon ∝ v ∝ − dt 9

  10. The MATLAB Set initial values ∑ F ( t ) Find update a ( t ) → a ( t + dt ) update and v ( t ) h ( t ) Falling with MATLAB yes no t = t max Plot graph 10

  11. The MATLAB Set initial values dn − − − − − − − − − − − − √ P tank P balloon = C − dt Find n balloon n tank P tank ; → Test: Inflating a balloon 
 & r balloon V balloon P balloon → at ground level no yes t = t max Plot graph 11

  12. The Results Test: Inflating a balloon at ground level R balloon vs t P balloon vs t 12

  13. The Main Code + 13

  14. Some neat graphs! y ( t ) ( t ) ˙ y 14

  15. So what happens? 15

  16. What if the balloon was already inflated? y ( t ) ( t ) ˙ y ( t ) r balloon 16

  17. What if there were no balloon at all? y ( t ) ( t ) ˙ y 17

  18. Thank You! 18

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