## Answer #84

The answer is: 3 > 2 = 4 > 1 = 5, as seen in the photograph below and
in an mpeg video by clicking your mouse on the photograph.

The kinetic energy of an exiting water stream is proportional to the
potential energy of the water and therefore to the pressure of the water
at that level. Therefore the horizontal velocity of the water in each
stream, being proportional to the square root of the kinetic energy, is
proportional to the square root of the distance below
the surface of the water. (We can arbitrarily set the zero point of
potential energy at the top of the container.) The time taken for water
in the water stream to fall from the hole to the level of the bottom of
the container is proportional to the square root of the height above the
bottom of the container.

With the heights of the respective holes above the bottom of the
container equal to:

1*d*, 2*d*, 3*d*, 4*d*, and 5*d*,

the time of fall for each jet respectively is proportional to the
square root of:

1*d*, 2*d*, 3*d*, 4*d*, and 5*d*,

and the horizontal velocities of the respective jets proportional to
the square root of:

5*d*, 4*d*, 3*d*, 2*d*, and 1*d*,

the ranges of the jets are equal to the velocity of efflux
multiplied by the time of fall, so they are proportional to
the square root of:

5*d*, 8*d*, 9*d*, 8*d*, and 5*d*,

as seen in the photograph. QED.

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