I'm trying to educate myself on modelling solute flows through pipe networks.
This is a follow up of my previous post here
$$\frac{\partial C}{\partial t} = - v\frac{\partial C}{\partial x}$$
While modelling flow through pipe junctions, I understand that the junction is assumed to have complete mixing, negligible volume, and algebraic equations are written for mass conservation.
However, I recently found an illustration in a notes posted here(the same figure is provided below), the junctions are displayed to have spherical volume. Is it appropriate to consider that the pipe junctions have spherical volumes? I've been asked to do so for discretizing and solving the solute transport equation.
This really confuses me. On one hand, the velocity of fluid flowing in each branch of the pipe is computed with the assumption that there is no accumulation at the pipe junctions using the continuity equation (Inflow rate is equal to outflow rate). Wouldn't the velocities obtained by solving the continuity equation be wrong if the nodes are assumed to have spherical volume?