Question

A cylindrical blood vessel is partially blocked by the build up of plaque. At one point, the plaque decreases the diameter of the vessel by 30.0%. The blood approaching the blocked portion has speed v0. Just as the blood enters the blocked portion of the vessel, what will be its speed in terms of v0?

V1= v0

Answer 1

The speed of the blood as it enters the blocked portion of the vessel is 49.0% of the initial speed v0.

Step-by-step explanation:

When a cylindrical blood vessel is partially blocked by plaque, the diameter of the vessel decreases. In this case, the diameter of the vessel is reduced by 30.0%. To find the speed of the blood as it enters the blocked portion of the vessel, we can use the principle of conservation of mass.

The cross-sectional area of the blood vessel remains constant, so the product of the speed and the cross-sectional area must remain constant as well. Let's call the speed of the blood as it enters the blocked portion of the vessel V1.

V1 * (0.7 * r)^2 = v0 * r^2

Here, r is the original radius of the vessel, and v0 is the initial speed of the blood. We can solve this equation to find V1 in terms of v0:

V1 = v0 * (0.7 * r / r)^2 = v0 * 0.7^2 = v0 * 0.49

Therefore, the speed of the blood as it enters the blocked portion of the vessel is 49.0% of the initial speed v0.