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Fluid Mechanics-Bernoulli and Energy Equations

  1. May 22, 2016 #1
    1. The problem statement, all variables and given/known data
    media-ea1-ea184f27-2552-4f66-9ba1-210cc540694a-phpWLbN6e.png

    A well-fitting piston with 4 small holes in a sealed water-filled cylinder,shown in Fig is pushed to the right at a constant speed of 4 mm /s while the pressure in the right compartment remains constant at 50 kPa gage. Disregarding the frictional effects,determine the force F that needs to be applied to the piston to maintain this motion.


    2. Relevant equations
    Bernoulli Equation: P1/ρ + V1^2/2 + gz1 = P2/ρ + V2^2/2 + gz2

    Flow Rate : Q1 = Q2 V1.A1=V2.A2

    3. The attempt at a solution

    I set two points.The first point (1) is back of the piston and the other point (2) front of the piston.So applied Bernoulli Equation:

    P1/ρ + V1^2/2 +gz1 = P2/ρ + V2^2 / 2 + gz2 No elevation difference z1=z2

    P1/ρ + V1^2/2 = P2/ρ + V2^2/2 V1=4 mm/s =0.004 m/s
    V2= V1.A1/A2 = 0.004 x 0.0113 / 0.0000031 m/s
    V2=3.64 m/s but there are 4 small holes so V2/4= 14.58/ 4 m/s=3.64 m/s

    P1= P2 + ρV2^2/2 (V1 can be neglected)

    P1= 50 kPa + 1000 (3.64)^2 /2 Pa = 56624.8 Pa

    F/πDr^2/4=56624.8 Pa

    F=40 N
     
  2. jcsd
  3. May 22, 2016 #2

    BvU

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    I'm not following this. (1) is back of piston and (2) is front of piston. So why is V1 so small and v2 so big ?
    What does it say here ? Could you explain the symbols and place appropriate brackets ?
     
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