Final Answer:
The total flow in the vertebrate circulatory system is determined by the total pressure change (AP) divided by the combined resistance of the blood vessels, expressed as (8ηL) / (πr^4).
Step-by-step explanation:
The concepts of fluid dynamics can be used to express the overall flow in the circulatory system of vertebrates.
Blood flow (Q) is inversely related to the viscosity (n) and length (L) of the blood vessels, but directly proportional to the pressure differential (AP) and the fourth power of the vessel's radius (r), according to Poiseuille's Law. In terms of math, the relationship is provided by:
Q = (пAP r^4)/(8L)
So, the total flow is determined by the total pressure change (AP) divided by the combined resistance of the blood vessels (8ηL) / (πr^4).
The intricate interactions between pressure, vessel radius, viscosity, and length that control blood flow in the circulatory system are explained by this equation.