Three reservoirs at different elevations are connected through a piping network at a single point, with an outflow from the common junction.  This application will calculate the flowrates, flow directions and head at the common junction.  This is a classic problem in hydraulic engineering. Through an understanding of the concepts associated therein, many hydraulic challenges can be solved.

The Bernoulli equation (ignoring the losses associated with pipe fittings) for Reservoir 1 is

 ,  

where z₁ is the resevoir elevation, f₁ is the friction factor, L₁ and D₁ are the pipe length and diameter, V₁ is the liquid velocity and H is the head at the common junction.  However, since flow can be either into or out of a reservoir (i.e. a positive or negative velocity), we rewrite the Bernoulli equation thus

.

Similar equations can be defined for the other reservoirs.  These equations, along with the continuity equation,

,

 and a correlation for the friction factor, can be used to find the flowrates, flow directions and the head at the junction.