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?

Bernoulli's equation applies here; without friction, the sum of the hydrostatic potential (weight of the column of liquid) + flow pressure (essentilly kinetic flow energy) + relative height of the liquid surface (inlets, outlets etc.) is a constant between any two points in the system.  In this equation, all terms have the units of length (i.e. height).  As others have stated, the flows are equal.

One key assumption not previously stated is that the original vessel needs to be large enough that the "bulk velocity" of the fluid in the vessel is zero - that just means the vessel has a "large" volume of fluid compared to the voume flow going in/out of the system, such that it can be said to be at "steady state".  This can be the cause of errors in real world problems and demonstrations.

 

Of course, the level of the fluid surface must remain above the inlet of "T" also.

 

Edited on September 29, 2006, 3:40 pm

Edited on September 29, 2006, 3:41 pm

Posted by Kenny M on 2006-09-29 15:36:28