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Fluid Mechanics - Linear momentum Analysis

  1. Oct 22, 2013 #1
    1. The problem statement, all variables and given/known data

    Water is flowing into and discharging from a U-shaped pipe section as shown. At flange
    (1), 30 kg/s of water flows into the section with the total absolute pressure of 200 kPa. At flange (2), the absolute pressure is 150 kPa. At location (3), 8 kg/s of water discharges to the atmosphere at 100 kPa. Determine the total x and y forces on the flanges connecting the pipe bend. Do not neglect the viscous losses in the pipe bend. Use a momentum-flux correction factor to be 1.03. In your discussion answer the following question: Is it possible to find the force on each flange individually? Why or why not?

    This is the given question. What I don't understand is when we are summing the forces, why is the force at flange 2 acting in the positive direction(to the right)? If you see in my solution attempt, I made it negative but in my teachers solution she has it positive. If someone could explain this too me that would be great.

    2. Relevant equations

    eqn.1 [itex]\dot{m}[/itex] = [itex]\rho[/itex]VA

    eqn.2 [itex]\Sigma[/itex]F = [itex]\Sigma[/itex]out[itex]\beta[/itex][itex]\dot{m}[/itex]V - [itex]\Sigma[/itex]in[itex]\beta[/itex][itex]\dot{m}[/itex]V

    3. The attempt at a solution

    Used eqn.1 to solve for all 3 velocites

    then eqn.2 to solve for Frx: Frx + P1V1 - P2V2 = [itex]\beta[/itex][itex]\dot{m}[/itex](-V2) - [itex]\beta[/itex][itex]\dot{m}[/itex]V1

    Attached Files:

  2. jcsd
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