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Static Pressure along bounded channel

  1. Feb 4, 2015 #1
    1. The problem statement, all variables and given/known data

    20iux3t.png

    Note: There is NO z variation, everything is horizontal (imagine looking down at streamlines)


    2. Relevant equations

    Bernoulli's Equation along streamline:

    P + 1/2*ρ*V2 + ρ*g*h = Constant ... (1)

    Bernoulli's Equation normal to streamline:

    P + ρ*V2*(1/R) + ρ*g*h = Constant ... (2)

    R: Radius of Curvature

    Continuity Equation from Conservation of mass:

    Needed to find out what is happening with velocity from inlet to outlet

    ρ1*A1*V1 = ρ2*A2*V2 ... (3)


    3. The attempt at a solution


    For the plots of AF:
    I think that the static pressure should be constant along the top wall as it is straight and there is no dynamic pressure. Also, I think that it should equal the total pressure.

    GL:

    Same as the plot of AF?

    Plot of average static pressure in the streamwise direction:

    Using ρ1*A1*V1 = ρ2*A2*V2, where 1 is the inlet and 2 is the outlet:

    V2 = A1*V1/A2
    A1 > A2
    -->V2 > V1
    --> P2 < P1

    Given this, my assumption is that the pressure drops from the inlet to the outlet, however my main issue is understanding how the static pressure is affected during the concave up and down walls. From (2), I believe that the static pressure should increase as the radius of curvature increases. At the maximum radius of curvature (bottom wall) I think that the static pressure is therefore at its maximum and there will be no dynamic pressure along the bottom wall during the curved regions. My question is how will the average static pressure in the streamwise direction decrease as the fluid passes through the curved regions?

     
  2. jcsd
  3. Feb 10, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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