This article proposes a theoretical overview of the distribution of fluid flow through manifolds composed of parallel channels connected through T-junctions to a distributor and to a collector channel, thus composing a ladder-like network. Such networks are used in solar heaters, fuel cells, heat exchanger plates, and other engineering devices, one issue being to achieve a nearly uniform distribution. This first part focuses on the discrete mesoscopic momentum and energy balances governing the T-junctions, with particular attention to the empirical, flow-rate and geometry dependent, pressure change coefficients. By ``mesoscopic'', it is meant that the control volume for the balance equations includes the junction zone and that the local flow-field in that zone is not described. The existing results and correlations for these coefficients are reviewed, compared, and synthesized. In keeping with the discrete character of the channel network, the overall network relations are compacted as a single non-linear finite-difference equation relating the flow-rates in the different segments of the distributor. This formulation is suitable for convenient numerical resolution even when all the coefficients are allowed to vary with local conditions. The conditions for simplifications, such as assuming constancy of certain coefficients, are carefully investigated. A number of approximate analytical, semi-explicit or explicit solutions are constructed. In particular, an original view of the structure of these solutions is proposed, relying on an invariance property which is demonstrated, and on the analogy with the classical McCabe-Thiele construction in chemical engineering. These approximations are compared to exact numerical solutions.