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Re: Animation: sphere filling with water

• To: mathgroup at smc.vnet.net
• Subject: [mg38840] Re: Animation: sphere filling with water
• From: Tom Burton <tburton at brahea.com>
• Date: Wed, 15 Jan 2003 02:21:11 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hello,

After I posted a hasty reply showing the level rising at a constant rate, it
occurred to me that the sphere is more likely to fill at a constant
volume-flow rate. Here is a simulation of the filling of a unit sphere by a
unit volume-flow rate.

Tom Burton

Needs["Graphics`Colors`"]

tf = 4 \[Pi]/3

answers = DSolve[{L'[t]==With[{A = \[Pi](1-L[t]^2)},1/A], L[0]==-1}, L, t]

L2 = L/.answers[[2]]

Plot[Evaluate[ Re[L2[t]] ],{t,0,tf}]

Table[ 
  Show[Graphics[{
Blue,Disk[{0,0},1],
White,Rectangle[{-1,Re[L2[t]]},{1,1}],
Black,Circle[{0,0},1]
  },AspectRatio->Automatic]],
{t,0,tf,tf/50}];

• Follow-Ups:
  • Re: Re: Animation: sphere filling with water
    • From: Dr Bob <majort@cox-internet.com>