(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve the Laplace equation in one dimension (x, i.e. (∂^2h)/(∂x^2)= 0)

Boundary conditions are as follows:

h= 1m @ x=0m

h= 13m @ x=10m

For 0≤x≤5 K1= 6ms^-1

For 5≤x≤10 K2 = 3ms^-1

What is the head at x = 3, x = 5, and x = 8?

What is the Darcy velocity (specific discharge)?

NOTE: There are multiple steps that will need to be done. Realize that system is heterogeneous. In a multiple layer system with steady-state conditions, Darcy velocity in one layer must equal the Darcy velocity in the other layers

2. Relevant equations

h(x) = h_{o}- [(h_{0}- h_{D})/D]*x

3. The attempt at a solution

I tried to use the equation above subbing in 3, 5, and 8 for the x and using 10m as D, 1m as h_{0}, and 13m for h_{D}

Then I used the specific specific discharge for the Darcy's velocity (q=K(dh/dL))

That was apparently all wrong. Apparently this needs to be broken into 2 systems, coupled. Each individual system can be treated as homogenous. So it need two separate LaPlace equations? I really don't know what to do with this problem, please help!

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# Homework Help: LaPlace equation in 1D

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