Tuesday, August 28, 2012
Barrel of Holes - Springer's Leaks
If all of the holes were the same size and at the same level, the solution is simple. With 10 holes initially, plugging one hole would increase the rate of flow through the other holes by 10 percent. If you increase 90 percent by 10 percent the result would be 99 percent. There would be less total flow but all the open holes would have greater flow than initially. If there were a constant flow in the top of the barrel with ten holes, closing one would increase the level in the barrel. If the barrel were full initially, then closing one hole would cause the barrel to over flow. If the barrel were not full initially, then the rising water level would increase the pressure on each open hole increase in the flow. If the barrel is large enough, the flow of all the open hole would increase to the original rate of total flow with the barrel having a new higher level.
If you don't know how many holes there were, or how full the barrel was, or what the the rate of flow into the barrel initially was,or how much the barrel can hold, then the problem is more complicated. Now put the barrel in the back of a pickup traveling down a bumpy dirt road. Welcome to climate change.