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What is the Three Reservoir Problem?

Updated: 10/14/2022
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12y ago

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This is a classic problem in hydraulic engineering. Three reservoirs are connected by pipes. All the reservoirs have surfaces at different elevations.

Given the height each reservoir and pressure loss in each leg of the pipe network, liquid will either flow into or out of each reservoir.

If you apply the Bernoulli equation from the surface of each reservoir to the pipe junction, you end up with three nonlinear equations in four unknowns (the flowrates in each leg of the piping network and the total pressure head at the junction). An additional equation is supplied by applying the Continuity Law at the pipe junction (i.e. the sum of all flowrates at the junction is zero if there is no outflow).

This now gives four equations in four unknowns; no analytical solution is possible. You can solve the equations iteratively, however, using a tool like Excel. See the spreadsheet in the related link for an example

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