Why do water streams get thinner as they fall?

[goleynik]

Homework Statement

Develop an equation that will allow you to determine the radius of the stream (r) at any distance (y) below the rim of the faucet.

It would seem that the initial velocity of the water coming out of the faucet and the acceleration due to gravity have something to do with the radius of the stream at any point.

Homework Equations

The only equations needed are :
Area of a circle,
Volume of a cylinder,
v=v_o + at
y=y_o + v_y0t+ 1/2 at²

The Attempt at a Solution

I solved for a faucet opening of .96 cm and determined that the water exits at 7.67cm³/sI don't even know if what I found is relevant but I am really stuck and any help would be greatly appreciated.

 

[Simon Bridge]

What are the forces on a small cylindrical section of a stream of falling water?

 

[Chestermiller]

In terms of the cross sectional area of the stream and the downward velocity of the water, what is the volume flow rate of the water? Is the volume flow rate out of the faucet constant? Does the volume flow rate change with distance below the faucet? If the downward velocity of the water is increasing with distance from the faucet, what is happening to the cross sectional area?

Chet