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Homework Help: Bernoulli's Equation and plugging water hole

  1. Jun 15, 2011 #1
    1. The problem statement, all variables and given/known data
    Here is the problem, I am able to calculate the velocity, but I don't know where to go from there.

    A legendary Dutch boy saved Holland by plugging a hole in a dike with his finger, which is 1.10 cm in diameter.
    (a) If the hole was 2.40 m below the surface of the North Sea (density 1030 kg/m3), what was the force on his finger?
    (b) If he pulled his finger out of the hole, how long would it take the released water to fill 1 acre of land to a depth of 1 ft assuming the hole remained constant in size? (A typical U.S. family of four uses 1 acre-foot of water, 1234 m3, in 1 year.)

    2. Relevant equations

    P1 + (1/2)[itex]\rho[/itex]v12 + [itex]\rho[/itex]gy1 = P2 + (1/2)[itex]\rho[/itex]v22 + [itex]\rho[/itex]gy2

    3. The attempt at a solution

    I calculated the velocity to be 5.238 m/s, but I have no idea how to get force from this (for part a) or time (part b). Am I missing some other equations?

  2. jcsd
  3. Jun 15, 2011 #2


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    Staff Emeritus
    Science Advisor
    Homework Helper

    Part a) Hint: You have the diameter of the hole, the depth of the water, and the density of the water. What else do you need to calculate the force on the Dutch Boy's finger? Remember, while the finger is in the hole, velocity = 0.

    Part b) Hint: You have the diameter of the hole and the velocity of water flowing through it. You are asked to find out how long it takes a given quantity of water to flow through the hole. What else do you need?
  4. Jun 16, 2011 #3
    I think I got it now, thanks I appreciate it.
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