Question

If the diameter of an artery was found to be reduced to one-third. By what value does the resistance of the artery increase?

• A. 9 times
• B. 81 times
• C. 27 times
• D. 18 times

Hint:

The resistance in a vessel is inversely proportional to the fourth power of the radius. A small change in the radius of an artery can cause a large change in its resistance.

Answer 1

The Correct Option is B

The Poiseuille's law describes the relationship between the flow rate of a fluid through a tube (or vessel) and the radius of the tube. The resistance \( R \) in a tube is given by the formula: \[ R \propto \frac{1}{{r^4}} \] where \( r \) is the radius of the artery. According to this law, if the diameter (and thus the radius) of the artery is reduced to one-third, the radius \( r \) becomes \( \frac{1}{3} \) of its original value. The change in resistance can be calculated as: \[ \text{New resistance} = \left(\frac{1}{\frac{1}{3}}\right)^4 = 3^4 = 81 \] Thus, the resistance increases by a factor of 81 times. Thus, the correct answer is 81 times (2), as the resistance increases by a factor of \( 3^4 \) when the diameter is reduced to one-third.