Help me solving this differential equation please

  1. μ[uyy + uzz] - ∂p/∂x = 0 ... (1)

    ∂u/∂x = 0 ;

    i tried assuming u(y,z) = Y(y)Z(z)

    so (1) becomes ... μ[ZYyy + YZzz] - ∂p/∂x = 0

    hence (1/Y)*Yyy + (1/Z)*Zzz = (R/YZ) = -λ2
    where, R = (1/μ)*∂p/∂x

    now Yyy + λ2Y = 0 ... can be solved easily but what about the remaining part .... i couldn't solve it due to the constant ...
     
  2. jcsd
  3. Mark44

    Staff: Mentor

    Is there any other information? In particular, is there anything known about p?
     
  4. ∂p/∂x = constant

    Some boundary conditions:
    x=0 , x=L ..... ∂u/∂x = 0 , v=0 , w=0 , ∂p/∂x = constant
    y=-a,y=a ..... u=0,v=0,w=0, ∂p/∂y=0
    z=-b,z=b ..... u=0,v=0,w=0, ∂p/∂z = 0
     
  5. Ray Vickson

    Ray Vickson 5,861
    Science Advisor
    Homework Helper

    Since [itex] \partial{p}/\partial{x} = c[/itex] (a constant) your DE is just
    [tex] u_{yy} + u_{zz} = k, [/tex]
    where [itex] k = c/ \mu [/itex] is a constant. Your condition [itex] u_x = 0[/itex] means that 'x' does not appear anywhere in the problem.

    RGV
     
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