The following material has been taken from a sheet entitled Several Faulty Assumptions Are Used in all Radiometric Dating Methods.
The barrel represents the earth's atmosphere in which the carbon-14 accumulates.
The water leaking out the sides of the barrel represents the loss (mainly by radioactive decay) of the atmosphere's supply of carbon-14.
Now, the fuller that barrel gets the more water is going to leak out the thoroughly perforated sides, just as more carbon-14 will decay if you have more of it around.
Finally, when the water reaches a certain level in the barrel, the amount of water going into the barrel is equal to the amount leaking out the perforated sides.
We say that the input and output of water is in equilibrium.
The water level just sits there even though the hose is going full blast.
(The barrel is made deep enough so that we don't have to worry about water overflowing the rim.) Henry Morris argued that if we started filling up our empty barrel it would take 30,000 years to reach the equilibrium point.
This argument was popularized by Henry Morris (1974, p.164), who used some calculations done in 1968 by Melvin Cook to get the 10,000-year figure. Whitelaw, using a greater ratio of carbon-14 production to decay, concluded that only 5000 years passed since carbon-14 started forming in the atmosphere!
The argument may be compared to filling a barrel which has numerous small holes in its sides.