Question

A cylindrical blood vessel is partially blocked by the buildup of plaque. At one point, the...

A cylindrical blood vessel is partially blocked by the buildup of plaque. At one point, the plaque decreases the diameter of the vessel by 64.0%. 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?

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Answer #1

Diameter of the cylindrical blood vessel = d0

Cross-sectional area of the cylindrical blood vessel = A0 = d02/4

Speed of flow of blood in the blood vessel = V0

Plaque decreases the diameter of the vessel by 64% that is the diameter in the blocked portion is 36% of the diameter in the unblocked portion.

Diameter of the vessel in the blocked portion of the vessel = d1 = 0.36d0

Cross-sectional area of the vessel in the blocked portion = A1 = d12/4

Speed of flow of blood in the blocked portion of the vessel = V1

By Continuity equation,

A0V0 = A1V1

(d02/4)V0 = (d12/4)V1

d02V0 = d12V1

d02V0 = (0.36d0)2V1

V1 = 7.72V0

Speed of flow of blood in the blocked portion of the vessel = 7.72V0

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