Resistance in Series and Parallel
In the cardiovascular system, the vascular beds are arranged in series or in parallel. The arrangement of blood vessels within a given organ supplied by a large artery, smaller arteries, arterioles, capillaries, and veins are arranged in series. Individual members of a given category of vessels (i.e., arterioles or venules) are usually arranged in parallel. The main large arteries (branches of the aorta) supplying the different organs in the systemic circulation are also examples of parallel resistance. Formulas have been derived for the series and parallel arrangements.
i. Series resistance: In the schematic below, three hydraulic resistances are arranged in series, and the inflow and outflow for the system remain constant. The pressure drop across the entire system, Pi and Po, consists of the sum of the pressure drops across each of the individual resistances. The flow through any cross-section should remain constant, so dividing each component in (a) by flow it is evident that the total resistance of the entire system of tubes in series equals the sum of individual resistances.
Example in the circulation: Rtotal = Rartery + Rarterioles + Rcapillaries
Each blood vessel (e.g., the largest artery) or set of blood vessels (e.g., all of the capillaries) in series receives the same total blood flow.
As blood flows through the series of blood vessels, the pressure decreases.