Consider a bucket of water with two holes of equal area through which water is discharged. The water can flow out through hole ( B ), at the bottom, or through the down-spout, which begins at the top ( T ) and has its opening the same distance below the water level as the center of hole ( B).

  \-------------------------/
   \                       /
    \                     /__
     \                  T/--+|
      \                 /   ||
       \               /    ||
    ____\             /     ||
    -----\B          /      ||
          \---------/

Ignoring any friction effects, out of which opening will the water flow faster, and why?

(In reply to well well... by Art M)

If the pipe for hole T was extended down by 100ft, then there would be a column of water 100ft tall forcing the water out of the pipe at relatively high speed.

The water is not in free fall.  Take any point along the vertical pipe. The force on the water in the down direction is based on the weight of the water above that point, and the "suction" of the water below that point as it pulls down.

This can be demonstrated in the real world by a siphon that takes water from a tank.

      _________

      | ______ |

      | |    | |

|     | | |  | |

|     | | |  | |

|^^^^^| |^|  | |

|     | | |  | |

|     | | |  | |

|     | | |  | |

|_________|  | |

             | |

 According to your theory, the water wouldn't flow through the part of the pipe above the water line.  However, after filling the pipe with water, the weight of the water in the discharge side of the pipe will pull more water into the pipe. This will continue as long as the water level in the tank is higher than the exit of the pipe. This could only happen if the weight of the water in the pipe acted on the water above it.

Edited on September 29, 2006, 12:30 pm

Posted by Leming on 2006-09-29 12:29:20