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Problem $2$

There is an underground pipe moving wet raw sludge down a hill at a $25$ angle with an elevation difference of $200ft.$ Pressure readings are $P_1$ and $P_2$ in psi. The inlet diameter is $D_{1}ft$ and the outlet diameter is $D_{2}ft$ and the flowrate through the pipe network is approximately $Q$ cfs$.$ The combined weight of the water and pipe is approximately $50lbf.$ After a slope stability analysis, you determine the maximum vertical force that can applied onto the surrounding soil is $500lbf.$ Is the slope stable or will it collapse $($i$.$e$.,$ is the vertical force required to keep the system in balance greater than $500lbf?$ State your assumptions.

FYI, most wet raw sludges have a specific gravity ranging from about $1\mathrm{.}01$ to $1\mathrm{.}03.$