Write a Matab script to solve the following: The flow in a volcanic dike is desc

Question

Write a Matab script to solve the following:

The flow in a volcanic dike is described by the equation: (g) / () = (^2 u) / (x^2 ) where u is velocity, is a constant called the viscosity, and is the density difference between magma and country rock. You can assume that the dike is 10 m wide and that the viscosity of magma is 100 Pa*s and that the density difference between magma and country rock is 50 kg/m3. You can use g=10 m/s2. The velocity at the margins of the dike is zero.

Write a MatLab script to solve this equation numerically using a centered difference method. Solve it analytically, and compare your analytic solution with the numerical solution. What is the maximum speed of the lava in the dike, and where in the dike is does this maximum velocity occur?

Explanation / Answer

Here,   (g) / () = (^2 u) / (x^2 )

=>    u =    [(g) /2()] * x2 - 10x

=>    the maximum speed of the lava in the dike =    [(50 * 9.8) /2(100)] * 2.0412 - 10 * 2.041

                                                                            =    10.204 m/sec

=>    In the dike does this maximum velocity occur =     2.041 m

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