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Finding centerline speed of a flow through a nozzle

  1. Apr 24, 2016 #1
    1. The problem statement, all variables and given/known data
    finding an equation for centerline speed.png


    2. Relevant equations

    u=a+ b(x-c)^2

    We have two boundary conditions at x=0, u=u(entrance) and x=L, u=u(exit)

    Source: Fluid Mechanics by Çengel/Cimbala








    3. The attempt at a solution

    I cannot understand the parabolic equation in the x-direction.
     
  2. jcsd
  3. Apr 24, 2016 #2
    relevant equation.png

    This is the original solution but it is still hard to understand for me. First I cannot understand general parabolic equation as 1 and why is cet set to 0, a=uentrance and b=(uexit-uentrance)/L^2.

    Would you like to explain them?

    Thank you.
     
  4. Apr 24, 2016 #3

    SteamKing

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    Did you set x = 0? What speed did you obtain?

    Did you set x = L? What speed did you obtain there?

    What about some intermediate location, say x = L/2? What is the speed there?
     
  5. Apr 24, 2016 #4
    for x=0, u=a+b*(0-c)^2, u=a+b*(c^2)

    for x=L, u=a+b*(L-c)^2, u=a+b*(L^2 -2Lc + c^2)

    for x=L/2, u=a+b*(L/2 - c)^2, u=a+ b*(L^2 /4 - Lc +c^2)
     
  6. Apr 24, 2016 #5

    SteamKing

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    No, you use Eq. (2) and make the substitutions there. Eq. (1) is just a generic parabola.
     
  7. Apr 24, 2016 #6
    Meanwhile, would you like to guide me how I can use Latext more effecitively? For example, a link.

    Thank you.
     
    Last edited: Apr 24, 2016
  8. Apr 24, 2016 #7

    SteamKing

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    You can use the PF Guide here:
    https://www.physicsforums.com/help/latexhelp/

    Or you can Google "Latex" for more help on the net.
     
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