# Water reach (Hose without and with a nozzle)

## Homework Statement

A hose of inside diameter $1.5cm$ can reach a distance of $1.5m$. A nozzle is inserted in the hose and water can now reach $24m$. What is the inside diameter of the nozzle? The height is the same in both cases.

## Homework Equations

Use continuity equation $v_{hose}A_{hose}=v_{nozzle}A_{nozzle}$

## The Attempt at a Solution

Continuity equation gives $1.5/t\pi r_{hose}^{2}=24\pi r_{nozzle}^{2}$ which is the same as $1.5(0.015/2)^{2}=24r_{nozzle}^{2}$. So $r_{nozzle}=0.1875cm$ and the inside diameter will be twice that or $d=0.375cm$.

The solution however is $d=0.75cm$ (twice what I got). Where am I wrong?

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haruspex
Homework Helper
Gold Member
What is the relationship between launch speed and range?

What is the relationship between launch speed and range?
$x=v_{horizontal}t=v_{horizonta}\sqrt{\frac{2h}{g}}$. $h$ is the same in both cases

haruspex
Homework Helper
Gold Member
h is the same in both cases
I see no reason why either t or h should be the same in both. What should we assume is the same?

I see no reason why either t or h should be the same in both. What should we assume is the same?
The problem states the height is the same in both cases (with and without the nozzle)

haruspex
Homework Helper
Gold Member
The problem states the height is the same in both cases (with and without the nozzle)
I think they mean the heights of the end of the hose and of the point reached by the jet are the same.

I think they mean the heights of the end of the hose and of the point reached by the jet are the same.
Yes exactly

haruspex
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Yes exactly
But you have used it in post #3 as though the height the water reaches at the top of its trajectory is the same in both scenarios. That is not the case.

But you have used it in post #3 as though the height the water reaches at the top of its trajectory is the same in both scenarios. That is not the case.
I see. Still if the water exits with only horizontal velocity it can only fall down not go up. That means the point the water reaches has to be at a lower height.

haruspex
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Gold Member
if the water exits with only horizontal velocity
It says "can reach". What does that imply about the angle of the hose?

It says "can reach". What does that imply about the angle of the hose?
If the angle is 90 with the horizontal obviously cant reach. So some angle between 0 and 90 degrees. I am imagining it must be 45 for some reason but I dont see what reason

gneill
Mentor
If the angle is 90 with the horizontal obviously cant reach. So some angle between 0 and 90 degrees. I am imagining it must be 45 for some reason but I dont see what reason
Look up the "range equation" for projectile motion.

haruspex