simple model of accumulation and flow.
click to enlarge A tank filling up (video 0:45)
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.
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
C = S t
QuesA1: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.