Final answer:
Blood flow is proportional to the difference in blood pressure across the vessel. The vessel's diameter is a critical factor in determining blood flow, with small changes in diameter causing significant changes in resistance and, therefore, flow.
Step-by-step explanation:
Blood flow is proportional to the difference in blood pressure at either end of the tube (vessel). The circulation of blood throughout the body is governed by complex relationships between the heart's pumping action, the structure and diameter of blood vessels, and the physical properties of the blood itself. When blood passes through the circulatory system, it travels from areas of higher pressure to areas of lower pressure. As stated in the principles of hemodynamics, the flow rate (Q) is directly proportional to the pressure difference (∆P) between two points in a vessel and inversely proportional to the resistance (R) the blood encounters in the vessels.
Several variables can affect this resistance, including the length of the vessel, as a longer vessel provides more surface area to impede flow, and the viscosity of the blood. However, the most significant contributor to resistance is the vessel's diameter. Because resistance is inversely proportional to the fourth power of the radius of the vessel (according to Poiseuille's law), even a small decrease in the diameter of a blood vessel can cause a significant increase in resistance, thereby slowing blood flow. Conversely, vasodilation, or the widening of a vessel, can significantly reduce resistance and increase blood flow.