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Garden Hose Problem

  1. Dec 4, 2012 #1
    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. jcsd
  3. Dec 4, 2012 #2

    SteamKing

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    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)
     
  4. Dec 4, 2012 #3
    Check your units and formulas, you got some major mistakes in there. This question is easy and mistake proof if you use dimensional anaylsis.
     
  5. Dec 4, 2012 #4
    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...
     
  6. Dec 5, 2012 #5
    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.
     
  7. Dec 5, 2012 #6

    SteamKing

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    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
     
  8. Dec 5, 2012 #7
    As stated, it's 1:00am :bugeye:
    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
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