Physical Variables at the Junction

• The law for conservation of mass and momentum dictate that the pressure at the junction must be continuous.

• Therefore, for a junction with $N$ ports, the junction pressure $p_J$ is given by
  $$p_J = p_n, \qquad n = 1 \hdots N.$$

• By the same law, the volume flow at the N-port junction sums to zero,
  $$\sum_{n=1}^N U_n = 0.$$