Great question- I hadnít even realized this was true.
The original question asked something a little different. If you have the hole at a fixed place, the higher the water goes above the hole, the more pressure there will be and the farther the water will squirt.
Your question assumes that the water has a fixed height (the tower height) and asks where to put the hole to get the maximum stream distance. This involves a tradeoff. If you put the hole too high, there wonít be much pressure on it. If you put the hole too low, the stream will hit the ground before it travels far.
If you assume:
1. The stream goes out straight sideways initially.
2. You can ignore the viscosity and calculate the water speed from Bernoulliís principle.
3. You can ignore air friction.
then itís a straightforward calculation to show that putting the hole halfway up gives the farthest distance sideways, and that that distance is also just the height of the water column.
Amazing but true.
Just like Mike, Iíve never done the calculation.
íYou learn something every dayí
(published on 01/29/08)