Question
What will be the increase in resistance of an artery if its diameter is reduced to one-third?
| A. |
9 times
|
| B. |
81 times
|
| C. |
27 times
|
| D. |
18 times
|
Show Answer
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Correct Answer � B
Explanation
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To find the increase in resistance of an artery when its diameter is reduced to one-third, we can use the formula for resistance in a cylindrical conductor like an artery, which is also analogous to Poiseuille’s law for fluid flow.
Poiseuille’s law states that the resistance to laminar flow through a long cylindrical tube (like an artery) varies inversely with the fourth power of the radius (or diameter) of the tube. The law is given by:
R∝ 1/r4
Where R is the resistance & r is the radius of the tube
d= 2r ; reducing the diameter to one-third means the radius also reduces to one-third.
Therefore, if the new diameter is d/3 and new radius is r/3
Rnew ∝ 1/(r/3)4
Thus, the resistance increases by a factor of 81 when the diameter (and thus the radius) is reduced to one-third. Therefore, the correct answer is 81 times
