Final answer:
The velocity of blood entering a blocked portion of a blood vessel, which has experienced a 30.0% decrease in diameter, increases to slightly more than twice the initial velocity, as dictated by the continuity equation.
Step-by-step explanation:
Understanding Blood Flow and Physics
A cylindrical blood vessel with a build-up of plaque results in a decrease in the diameter by 30.0%. This raises the question of how blood speed changes as it enters this narrower section. In fluid dynamics, the continuity equation states that for an incompressible fluid, the product of cross-sectional area (A) and velocity (v) is constant along a streamline. This can be written as A1v1 = A2v2, where subscript 1 refers to initial conditions and subscript 2 refers to conditions at the constriction. The area of a circle (cross-section of our vessel) is given by πr2, where r is the radius. If the diameter, and thus the radius, is decreased by 30%, then the new radius r2 is 0.7r1. Therefore, the new area A2 is (0.72)A1. Using the continuity equation, we can solve for v2:
v2 = (A1/A2)v0 = (1/0.72)v0 = (1/0.49)v0 ≈ 2.04v0. This indicates the velocity of blood increases by slightly more than twice the initial velocity v0 when entering the blocked segment.
In the context of blood flow in arteries affected by plaque deposits, similar principles apply. If a blood vessel's radius is reduced, the blood flow rate decreases. The body may respond by increasing blood pressure to maintain the flow rate. If the radius is decreased to 90% of its original size, the flow rate would depend on the fourth power of the radius change, based on Poiseuille's Law. Hence, the pressure difference would need to increase by a factor greater than 1.5 to keep the flow rate constant. Introducing turbulence due to the obstruction could further affect the flow rate by increasing resistance and potentially decreasing flow, opposing the body's compensatory measures.