Acylindrical blood vessel is partially blocked by the buildup of plaque. at one point, the plaque decreases the diameter of the vessel by 59.0%. the blood approaching the blocked portion has speed v0. just as the blood enters the blocked portion of the vessel, what is its speed v, expressed as a multiple of v0?

2.87 V₀

Explanation:

d₀ = diameter of vessel before blood enters blocked portion

d = diameter of vessel in the blocked portion = 0.59 d₀

V₀ = speed of blood before blocked portion

V = speed of blood in blocked portion

Using equation of continuity

(0.25) π d₀² V₀ =  (0.25) π d² V

d₀² V₀ =  (0.59 d₀)² V

d₀² V₀ =  (0.59)² d₀² V

V = 2.87 V₀

The blood enters the blocked portion of the vessel at .

Explanation:

The blood is flowing through the vessel.

Let the radius of the vessel is .

At some point, the radius of the vessel is decreased by 59.0%. So, the radius at the point will be,

The velocity of the blood initially is .

Now, apply the continuity equation to get the velocity of blood at the contracted point. Let and are the area of the vessel at initial point and contracted point, respectively.

Thus, the blood enters the blocked portion of the vessel at .

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