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Help me solving this differential equation please

by ahm_11
Tags: differential, equation, solving
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ahm_11
#1
Nov3-11, 09:29 AM
P: 6
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 ...
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Mark44
#2
Nov3-11, 01:13 PM
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P: 21,249
Quote Quote by ahm_11 View Post
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 ...
Is there any other information? In particular, is there anything known about p?
ahm_11
#3
Nov3-11, 02:10 PM
P: 6
∂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

Ray Vickson
#4
Nov3-11, 03:10 PM
Sci Advisor
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P: 5,013
Help me solving this differential equation please

Quote Quote by ahm_11 View Post
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 ...
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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