A simple model of accumulation and flow.

waterbucketNoDrain.gif (6015 bytes) click to enlarge A tank filling up (video 0:45)

Imagine a 10 gallon bucket that is filled by a faucet.  We refer to the faucet as the source of water flowing into the bucket, S.  If S=2.0 gallon per minute (2.0 gal/min) then the bucket will become completely filled in 5 minutes.   The amount of water in the bucket at any given time will be referred to as the bucket content, C.  

If we start with an empty bucket and turn on the faucet at a constant flow (S in gallons per minute), then the water content C at any time t is easy to calculate from

  C = S t

Complete the table below for S=2.0 gal/min (gallons per minute)


Check your understanding.  If the bucket starts out empty (C0=0) and is filled at a rate of S=3.0 gal/min, how much water will be in the bucket in 3.0 minutes?  The symbol C0 stands for the initial bucket content at time t=0.

   Bucket content in 3 minutes will be gallons