Why does a hose have a wider flow at the end than at the beginning?

[bruceflea]

Water flows from a garden hose. If the end of the garden hose is turned downward, a steady stream of water is seen to emerge from it. Upon closer observation, it can be seen that the flow of water is wide when it has just emerged from the hose pipe, and becomes more narrow as it descends (see Figure 5).

http://img4.imageshack.us/img4/9007/gardenhose8xh.th.png

Figure 5. Flow from a garden hose.


a) Explain why this happens.

b) If the water emerges from the tap with velocity u1 = 0.1 m/s, and the hosepipe diameter is 12 mm, calculate how many seconds it takes for the diameter of the water flow to halve, and calculate how far the water has fallen from the end of the hosepipe in that time.

c) If I open the tap further, put a nozzle on the end of the hosepipe with a diameter of 6 mm, and point it upwards, then the water reaches a maximum height of 2 metre above the end of the hosepipe. Calculate the water pressure in the hosepipe, assuming that the height difference between the hosepipe itself and the nozzle exit can be ignored.

I just need a little guidance with b and c.

For c, I think I'm supposed to take bernoullis between the exit of the nozzle and the height the water reaches to calculate the pressure at the nozzle exit. Then bernoullis between the exit and the hose pipe to calculate the hose pressure. But what I'm not too sure about is the column of water - is it reasonable to use bernoullis as I would if it was 2 metres of vertical pipe?

I've no idea where to start with b.

 

[FredGarvin]

b)Think of it this way...if you halved the area of the pipe, what velocity would the water have to be flowing? What was your answer to part A? Do you remember your basic mechanics equations with a constant acceleration?

c)You're on the right track. One hint you may want to look up...instead of the term "pressure" think of the term "head".

 

[bruceflea]

For a,

Velocity of the water increases as there is no longer friction with the pipe. For a constant volumetric flow rate the area has to decrease as the velocity increases.