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Fluid - Piston Question

  1. Dec 7, 2014 #1
    1. The problem statement, all variables and given/known data

    A block of mass m is connected to a massless rod and plunger of area A1 on a cylindric container of water. At

    the bottom of the container there is a pipe that leads to an opening of area A2 where the water pours out at a

    velocity v. The block starts at rest with the plunger a distance h from the bottom of the container.

    A] What pressure does the block apply to the water? Only use A1 , m, and g in your answer.

    B] What kinetic energy does the block have as water pours from the opening? Express your answer in terms of m, g, A1 , A2 , P0 , h, and ρ .

    HINT* - solving for 1⁄2 v2 will get you very close to an expression for K.

    [ATTACHED PICTURE OF PROBLEM]

    2. Relevant equations

    F = PA
    Bernoulli's equation
    KE = 1/2mv^2

    3. The attempt at a solution
    A] F = PA
    mg = PA1

    answer:
    mg/A1 = P

    B] Using Bernoulli's equation
    P + pgh = P0 + 1/2pv^2
    mg/A1 + pgh = P0 + 1/2pv^2

    REARRANGE

    (1/p)(mg/A1 + pgh + P0) = 1/2v^2

    answer:
    KE = 1/2mv^2 = (m/p)(mg/A1 + pgh + P0)



    AM I CORRECT OR WRONG? I don't know how to get that A2 to the answer of part B
     

    Attached Files:

  2. jcsd
  3. Dec 7, 2014 #2

    haruspex

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    There are two velocities here, which you need separate variables for: the velocity of the water from the outlet (the given v), and the velocity of the mass (for which you need another symbol) . There is a relationship between them.
     
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