This nullifies the carbon-14 method as well as demonstrating that the earth is less than 10,000 years old. One suspects that the scientific world would not be using the carbon-14 method if it were so obviously flawed.
The water coming out of the hose is analogous to the continuous production of carbon-14 atoms in the upper atmosphere.
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.
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.