SLIDE 1
Splat?
An example of computational Physics in action!
Reaal Khalil
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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
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Splat? An example of computational Physics in action! Reaal Khalil - - PowerPoint PPT Presentation
Splat? An example of computational Physics in action! Reaal Khalil - - PowerPoint PPT Presentation
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
SLIDE 2
SLIDE 3
The question:
A human leaps out of a plane holding a pressurised tank of helium and a weather balloon. What happens next?
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SLIDE 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
SLIDE 5
The Physics:
Drag Force:
= Aρ FD 1 2 CD v2
Buoyancy:
= ρgV FB
Gravity:
= mg FG
Reynolds Number:
= Re vD ν 5
SLIDE 6
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The Physics
SLIDE 7
= − ∆P Patmospheric Pballoon
∆P = 2µ (( ) − )(1 + ) t0 r0 r0 r ( ) r0 r
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1 − α α ( ) r r0
2
= Pballoon nRT π
4 3
r3
The Mooney-Rivlin model:
The Physics
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MATLAB’s built-in functions make life so much easier!
SLIDE 8
initial non-inflated balloon radius = 0.54m initial balloon thickness = 0.2mm
r0 t0
SN: 400-8242
µ α
= 300,000 Pa = 10/11
m
balloon mass = 0.8kg
rmax maximum radius = 3.4m
The Tank:
= 2900psi = 20,000,000Pa SN: HP Steel 50 = 50L = 0.05m3
(t = 0) Ptank Vtank mtank = 60kg
The Balloon
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SLIDE 9
Use Bernoulli’s equation:
ρ + ρgz + P = constant 1 2 v2 ∝ v ∝ dn dt − Ptank Pballon − − − − − − − − − − − √
The Physics
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SLIDE 10
Falling with MATLAB
The MATLAB
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Set initial values Find update Plot graph update and yes no
∑ F(t)
a(t) → a(t + dt) h(t) v(t) t = tmax
SLIDE 11
Test: Inflating a balloon at ground level
The MATLAB
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Set initial values
= C dn dt − Ptank Pballoon − − − − − − − − − − − − √
; → nballoon ntank Ptank Find
→ & rballoon Vballoon Pballoon
Plot graph yes no
t = tmax
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vs t Rballoon vs t Pballoon
Test: Inflating a balloon at ground level
The Results
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SLIDE 13
The Main Code
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+
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Some neat graphs!
(t) y ˙ y(t) 14
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So what happens?
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SLIDE 16
What if the balloon was already inflated?
y(t) (t) y ˙ (t) rballoon 16
SLIDE 17
What if there were no balloon at all?
17 y(t) (t) y ˙
SLIDE 18
Thank You!
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