# Garden Hose Problem

1. Dec 4, 2012

### Alex Wiseman

1. The problem statement, all variables and given/known data
A garden hose is used to fill a large metal container which can hold 24.0 L of liquid. If the radius of the garden hose's nozzle is 1.2 cm, and the speed of the water at this point is 272.0 cm/s, how long (in seconds) would it take to fill the container with water, assuming that none of it splashes out?
Hint: Use the fact that 1 L = 1000 cm3

Placing all relevant data in SI;
24L = 24,000cm3
= 0.024m3

V = 272cm/s
= 2.72 m/s

2. Relevant equations

ΔV/Δt = Av
Δt = ΔV/Av

3. The attempt at a solution

ΔV(metal container) = 0.024m 3
Δt = ?
A(nozzle) = ∏(0.012)2 = 0.00045m2
v(water) = 2.72m/s

Δt = ΔV/Av
Δt = 0.024/(0.00045)*(2.72)
Δt = 19.6s

Now that I've figured it out, I suppose this doesn't really belong in advanced physics - even though it is part of my undergraduate.

Last edited: Dec 5, 2012
2. Dec 4, 2012

### SteamKing

Staff Emeritus
How many centimeters in 1 meter?

24L = 24000 cm^3 (OK)
24L = 24 M^3 (???)

272 cm/s = .272m/s (???!!!)

What is the formula for the area of a circle given the radius?

(Hint: it's not 2 pi r)

3. Dec 4, 2012

Check your units and formulas, you got some major mistakes in there. This question is easy and mistake proof if you use dimensional anaylsis.

4. Dec 4, 2012

### Alex Wiseman

I am aware I have some major mistakes, which is why I posted it. I need help getting started, I only posted what I had to show I made an attempt.

Edit: Oh I see what you are talking about, yes. This is rather embarrassing. Never trust a friend with conversions...

5. Dec 5, 2012

### Alex Wiseman

I fixed up the silly mistakes, it is 1:00am and I've been reviewing for nearly 14 hours now. I just need help finding the correct formulas for solving this problem.

6. Dec 5, 2012

### SteamKing

Staff Emeritus
You still have a major problem:

24L = 24000 cm^3 OK

24L = 240 m^3 (????!!!!)

I trust you know that if I have a cube which measures 10 cm on each side, the volume of the cube is 10 cm * 10 cm * 10 cm = 1000 cm^3 = 1.0 L

7. Dec 5, 2012

### Alex Wiseman

As stated, it's 1:00am
Thanks for pointing that out, any idea where I can start to look for the correct equation? I looked at continuity (as suggested), but I am getting a massive amount of time for that.

Edit: I think I figured it out, it was entirely conversions that threw me off. Wow, how embarrassing.I posted my final answer.

Last edited: Dec 5, 2012