1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differential Equations Project

  1. Jan 30, 2008 #1
    1. The problem statement, all variables and given/known data

    Torricelli's Law of Fluid Flows

    How long does it take for water to drain through a 1cm diameter hole in the bottom of a conic tank (like a large funnel: 50cm tall, base radius is 30cm)?

    This problem has a few steps, some of them i'm not worried about at all.


    a.)Show that if h''=-g, and an object is dropped from a height h(0), h'=[itex]-\sqrt{2gh(0)}[/itex] at h=0.

    b.)Discuss and derive the given differential equation.

    c.)Determine A(h) and [itex]a[/itex], and solve the differential equation deriving a formula relating time and height of the water in the tank.

    d.)Predict how long it will take to drain the tank.

    e.)flip the tank upside down and have it drain through a 1cm hole. the rest of the tank has the same dimensions.

    f.)find a tank with two open ends and time how long it takes to drain. then set up the differential equation based on the geometry of the tank and make a prediction.

    2. Relevant equations


    [tex]A(h)=\pi [r(h)]^2[/tex]

    [tex]A_{drain}=a=\pi (r_f)^2[/tex]

    3. The attempt at a solution
    I want an opinion on my project, i.e. am i missing anything, does anything look wrong, etc... My work and everything is attached in a word document. I'm mostly concerned with parts c.) through f.). Any help is greatly appreciated.

    Attached Files:

  2. jcsd
  3. Feb 4, 2008 #2
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Differential Equations Project
  1. Differential equation (Replies: 4)

  2. Differential Equation (Replies: 12)

  3. Differential Equations (Replies: 1)